The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model struc...The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.展开更多
This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consen...This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consensus under average dwell time switching.Then sufficient conditions are derived to guarantee the positive consensus.The gain matrices of the control protocol are described using a matrix decomposition approach and the corresponding computational complexity is reduced by resorting to linear programming and co-positive Lyapunov functions.Finally,two numerical examples are provided to illustrate the results obtained.展开更多
Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was poin...Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.展开更多
Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy syst...Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system.The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models.The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily.After the linearization of T-S fuzzy model,a robust H∞ controller with the robustness of sliding model control(SMC) is designed.As a result,controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.展开更多
In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed b...In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed based on continuously differentiable reshaping of the probability density function(PDF) of signal amplitudes. The original PDF is cut off for PAPR reduction, and lower and medium segments of original PDF are scaled and linearized respectively, for maintaining power and cumulative distribution constraints. The linearized segment is set to be the tangent of the scaled version at the inflexion point, so as to reduce the out-ofband(OOB) radiation as much as possible. Parameters of the proposed scheme are solved under joint constraints of constant power and unity cumulative distribution. A new receiving method is also proposed to improve the bit error rate(BER) performance of OFDM systems. Simulation results indicate the proposed scheme can achieve better OOB radiation and BER performance at same PAPR levels, compared with existing similar companding algorithms.展开更多
The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actua...The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actuator with a four-way sliding valve and a hydraulic cylinder.A 4-order nonlinear mathematical model is introduced accordingly.Through the linearization of the feedback law of the high order EHB model,a sliding mode control method is proposed for the hydraulic pressure.The hydraulic pressure tracking controls are simulated and analyzed by MATLAB/Simulink soft considering separately different conditions,i.e.,a sine wave,a square wave and a square wave with superimposed sine disturbance.The results show that the proposed strategy can track the target within 0.25 s,and the mean observed error is less than 1.2 bar.Moreover,with such a strategy,faster response and less overshoot are possible,which should be regarded as significant advantages.展开更多
A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertai...A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.展开更多
This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feed...This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.展开更多
A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of erro...A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is simulated on a one-link robot system to show its efficacy.展开更多
This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and ...This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.展开更多
To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structura...To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.展开更多
Partial linearization method is proposed for controlling Lü-system.Through partially cancelling the nonlinear cross-coupling terms the stabilization of the resulting system was realized.This method can be easily ...Partial linearization method is proposed for controlling Lü-system.Through partially cancelling the nonlinear cross-coupling terms the stabilization of the resulting system was realized.This method can be easily realized.The robust behavior was proved with respect to an uncertain system.Numerical simulation are provided to show the effectiveness and feasibility of the method.展开更多
A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to conve...A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was de- signed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track vari- able desired output, which could be a time variant function or an equilibrium points. Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.展开更多
This paper treats the problem of designing an optimal size for a lookup table used for sensor linearization. In small embedded systems the lookup table must be reduced to a minimum in order to reduce the memory footpr...This paper treats the problem of designing an optimal size for a lookup table used for sensor linearization. In small embedded systems the lookup table must be reduced to a minimum in order to reduce the memory footprint and intermediate table values are estimated by linear interpolation. Since interpolation introduces an estimation uncertainty that increases with the sparseness of the lookup table there is a trade-off between lookup table size and estimation precision. This work will present a theory for finding the minimum allowed size of a lookup table that does not affect the overall precision, i.e. the overall precision is determined by the lookup table entries’ precision, not by the interpolation error.展开更多
This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a ...This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.展开更多
The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on rea...The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.展开更多
This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat...This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.展开更多
New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polyn...New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences. Subsequently, the systems of depth-one polynomial recurrence relations are discussed. The corresponding transition matrix is constructed and upper triangularized. Furthermore, the powers of the transition matrix are calculated using the back substitution procedure. The explicit expression for a solution to a broad family of recurrence relations is obtained. We investigate to which recurrences the framework can be applied and construct sufficient conditions for the method to work. It is shown how introduction of auxiliary variables can be used to reduce arbitrary depth systems to the depth-one system of recurrences dealt with earlier. Finally, the limitations of the method are discussed, outlining possible directions for future research.展开更多
This work demonstrates experimentally the close relation between return currents from relativistic laser-driven target polarization and the quality of the relativistic laser–plasma interaction for laser-driven second...This work demonstrates experimentally the close relation between return currents from relativistic laser-driven target polarization and the quality of the relativistic laser–plasma interaction for laser-driven secondary sources,taking as an example ion acceleration by target normal sheath acceleration.The Pearson linear correlation of maximum return current amplitude and proton spectrum cutoff energy is found to be in the range from~0.70 to 0.94.kA-scale return currents rise in all interaction schemes where targets of any kind are charged by escaping laser-accelerated relativistic electrons.Their precise measurement is demonstrated using an inductive scheme that allows operation at high repetition rates.Thus,return currents can be used as a metrological online tool for the optimization of many laser-driven secondary sources and for diagnosing their stability.In particular,in two parametric studies of laser-driven ion acceleration,we carry out a noninvasive online measurement of return currents in a tape target system irradiated by the 1 PW VEGA-3 laser at Centro de Láseres Pulsados:first the size of the irradiated area is varied at best compression of the laser pulse;second,the pulse duration is varied by means of induced group delay dispersion at best focus.This work paves the way to the development of feedback systems that operate at the high repetition rates of PW-class lasers.展开更多
Resilience studies for water distribution systems(WDS)coupled with other interdependent infrastructure systems attract increasing attention from stakeholders and researchers.However,most existing large-scale WDS model...Resilience studies for water distribution systems(WDS)coupled with other interdependent infrastructure systems attract increasing attention from stakeholders and researchers.However,most existing large-scale WDS models are single infrastructure-based without consideration of other infrastructure systems.This is due to a lack of needed information on systems coupling,the structure of the simulator used,and the computation load involved.To address these gaps,this paper presents a synthetic modeling framework for a real-world WDS as coordinating with other infrastructure systems via a building-mediated clustering approach through consideration of physical distance and node capacity.First,the WDS network topology and operation parameters are inferred via bulk open-source information.A building-mediated clustering approach is designed to systematically derive the interdependence between the WDS and the power system similarly created as a case study.Second,a novel linearization method is developed in formulating the WDS model that can relieve computation load while maintaining accuracy.Finally,a disruption-recovery framework is developed to demonstrate the proposed methodology in modelling WDS resilience.The framework is applied to a neighborhood in Queenstown,Singapore,an area of 20.43 km^(2) and 96,000 population.The near-real-time simulations on the coupled system involving 308 nodes and 384 links showcase the effectiveness and application of the proposed synthetic modeling and formulation.展开更多
基金funded by the project new smart and adaptive robotics solutions for personalized minimally invasive surgery in cancer treatment−ATHENA,European Union-NextGenerationEU and Romanian Government,under National Recovery and Resilience Plan for Romania(CF116/15.11.2022)through the Romanian Ministry of Research,Innovation and Digitalization(within Component 9,investment I8)。
文摘The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.
基金supported by the National Natural Science Foundation of China(62463007,62463005)the Natural Science Foundation of Hainan Province(625RC710,625MS047)+1 种基金the System Control and Information Processing Education Ministry Key Laboratory Open Funding,China(Scip20240119)the Science Research Funding of Hainan University,China(KYQD(ZR)22180,KYQD(ZR)23180).
文摘This paper focuses on the leader-following positive consensus problems of heterogeneous switched multi-agent systems.First,a state-feedback controller with dynamic compensation is introduced to achieve positive consensus under average dwell time switching.Then sufficient conditions are derived to guarantee the positive consensus.The gain matrices of the control protocol are described using a matrix decomposition approach and the corresponding computational complexity is reduced by resorting to linear programming and co-positive Lyapunov functions.Finally,two numerical examples are provided to illustrate the results obtained.
文摘Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.
基金Research financially supported by Changwon National University in 2009
文摘Takagi-Sugeno(T-S) fuzzy model is difficult to be linearized because of membership functions included.So,novel T-S fuzzy state transformation and T-S fuzzy feedback are proposed for the linearization of T-S fuzzy system.The novel T-S fuzzy state transformation is the fuzzy combination of local linear transformation which transforms local linear models in the T-S fuzzy model into the local linear controllable canonical models.The fuzzy combination of local linear controllable canonical model gives controllable canonical T-S fuzzy model and then nonlinear feedback is obtained easily.After the linearization of T-S fuzzy model,a robust H∞ controller with the robustness of sliding model control(SMC) is designed.As a result,controlled T-S fuzzy system shows the performance of H∞ control and the robustness of SMC.
基金supported by National Natural Science Foundation of China(No.61821001)Science and Technology Key Project of Guangdong Province,China(2019B010157001)。
文摘In this paper, a novel nonlinear companding transform(NCT) is proposed to reduce the Peak-to-Average Power Ratio(PAPR) of orthogonal frequency division multiplexing(OFDM) signals. The companding function is designed based on continuously differentiable reshaping of the probability density function(PDF) of signal amplitudes. The original PDF is cut off for PAPR reduction, and lower and medium segments of original PDF are scaled and linearized respectively, for maintaining power and cumulative distribution constraints. The linearized segment is set to be the tangent of the scaled version at the inflexion point, so as to reduce the out-ofband(OOB) radiation as much as possible. Parameters of the proposed scheme are solved under joint constraints of constant power and unity cumulative distribution. A new receiving method is also proposed to improve the bit error rate(BER) performance of OFDM systems. Simulation results indicate the proposed scheme can achieve better OOB radiation and BER performance at same PAPR levels, compared with existing similar companding algorithms.
基金supported by the National Natural Science Foundation of China[grant number 51565011]the Foundation of Educational Department of Jiangxi Province[grant number GJJ180302].
文摘The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actuator with a four-way sliding valve and a hydraulic cylinder.A 4-order nonlinear mathematical model is introduced accordingly.Through the linearization of the feedback law of the high order EHB model,a sliding mode control method is proposed for the hydraulic pressure.The hydraulic pressure tracking controls are simulated and analyzed by MATLAB/Simulink soft considering separately different conditions,i.e.,a sine wave,a square wave and a square wave with superimposed sine disturbance.The results show that the proposed strategy can track the target within 0.25 s,and the mean observed error is less than 1.2 bar.Moreover,with such a strategy,faster response and less overshoot are possible,which should be regarded as significant advantages.
基金the National Natural Science Foundation of China (90716028 and 90405011).
文摘A robust adaptive trajectory linearization control （RATLC） algorithm for a class of nonlinear systems with uncertainty and disturbance based on the T-S fuzzy system is presented. The unknown disturbance and uncertainty are estimated by the T-S fuzzy system, and a robust adaptive control law is designed by the Lyapunov theory. Irrespective of whether the dimensions of the system and the rules of the fuzzy system are large or small, there is only one parameter adjusting on line. Uniformly ultimately boundedness of all signals of the composite closed-loop system are proved by theory analysis. Finally, a numerical example is studied based on the proposed method. The simulation results demonstrate the effectiveness and robustness of the control scheme.
基金supported by Russian Foundation for Basic Research(No.15-08-06859a)and by the Ministry of Education and Science of the Russian Federation in the framework of the basic part of the state order(No.2.8629.2017).
文摘This article is devoted to the problem of composite control design for continuous nonlinear singularly perturbed(SP)system using approximate feedback linearization(AFL)method.The essence of AFL method lies in the feedback linearization only of a certain part of the original nonlinear system.According to AFL approach,we suggest to solve feedback linearization problems for continuous nonlinear SP system by reducing it to two feedback linearization problems for slow and fast subsystems separately.The resulting AFL control is constructed in the form of asymptotic composition(composite control).Standard procedure for the composite control design consists of the following steps:1)system decomposition,2)solution of control problem for fast subsystem,3)solution of control problem for slow subsystem,4)construction of the resulting control in the form of the composition of slow and fast controls.The main difficulty during system decomposition is associated with dynamics separation condition for nonlinear SP system.To overcome this,we propose to change the sequence of the design procedure:1)solving the control problem for fast state variables part,2)system decomposition,3)solving the control problem for slow state variables part,4)construction of the resulting composite control.By this way,fast feedback linearizing control is chosen so that the dynamics separation condition would be met and the fast subsystem would be stabilizable.The application of the proposed approach is illustrated through several examples.
文摘A fuzzy logic compensator is designed for feedback linearizable nonlinear systems with deadzone nonlinearity. The classification property of fuzzy logic systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the fuzzy logic parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The fuzzy logic deadzone compensator is simulated on a one-link robot system to show its efficacy.
基金supported partly by China Postdoctoral Foundation(20070410725)the National Natural ScienceFoundation of China(60805036).
文摘This paper presents a new trajectory linearization control scheme for a class of nonlinear systems subject to harmonic disturbance. It is supposed that the frequency of the disturbance is known, but the amplitude and the phase are unknown. A disturbance observer dynamics is constructed to estimate the harmonic disturbance, and then the estimation is used to implement a compensation control law to cancel the disturbance. By Lyapunov＇s direct method, a rigorous poof shows that the composite error of the closed-loop system can approach zero exponentially. Finally, the proposed method is illustrated by the application to control of an inverted pendulum. Compared with two existing methods, the proposed method demonstrates better performance in tracking error and response time.
基金Project supported by the Aviation Science Foundation of China (No.2000CB080601) the National Defence Key Pre-research Project of the 'Tenth Five-Year-Plan' of China (No.2002BK080602)
文摘To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
文摘Partial linearization method is proposed for controlling Lü-system.Through partially cancelling the nonlinear cross-coupling terms the stabilization of the resulting system was realized.This method can be easily realized.The robust behavior was proved with respect to an uncertain system.Numerical simulation are provided to show the effectiveness and feasibility of the method.
基金Supported by National Natural Science Foundation of China (60374013) and Natural Science Foundation of Zhejiang Province (Y104414, M603217)
文摘A new method was proposed for tracking the desired output of chaotic dy- namical system using the feedback linearization and nonlinear extended statement ob- server method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was de- signed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track vari- able desired output, which could be a time variant function or an equilibrium points. Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.
文摘This paper treats the problem of designing an optimal size for a lookup table used for sensor linearization. In small embedded systems the lookup table must be reduced to a minimum in order to reduce the memory footprint and intermediate table values are estimated by linear interpolation. Since interpolation introduces an estimation uncertainty that increases with the sparseness of the lookup table there is a trade-off between lookup table size and estimation precision. This work will present a theory for finding the minimum allowed size of a lookup table that does not affect the overall precision, i.e. the overall precision is determined by the lookup table entries’ precision, not by the interpolation error.
文摘This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.
文摘The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.
基金supported in part by the National Natural Science Foundation of China(62473221)the Natural Science Foundation of Shandong Province,China(ZR2024MF006)Qingdao Natural Science Foundation(24-4-4-zrjj-165-jch)。
文摘This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.
文摘New approach to systems of polynomial recursions is developed based on the Carleman linearization procedure. The article is divided into two main sections: firstly, we focus on the case of uni-variable depth-one polynomial recurrences. Subsequently, the systems of depth-one polynomial recurrence relations are discussed. The corresponding transition matrix is constructed and upper triangularized. Furthermore, the powers of the transition matrix are calculated using the back substitution procedure. The explicit expression for a solution to a broad family of recurrence relations is obtained. We investigate to which recurrences the framework can be applied and construct sufficient conditions for the method to work. It is shown how introduction of auxiliary variables can be used to reduce arbitrary depth systems to the depth-one system of recurrences dealt with earlier. Finally, the limitations of the method are discussed, outlining possible directions for future research.
基金funding from the European Union’s Horizon 2020 research and innovation program through the European IMPULSE project under Grant Agreement No.871161from LASERLAB-EUROPE V under Grant Agreement No.871124+6 种基金from the Grant Agency of the Czech Republic(Grant No.GM23-05027M)Grant No.PDC2021120933-I00 funded by MCIN/AEI/10.13039/501100011033by the European Union Next Generation EU/PRTRsupported by funding from the Ministerio de Ciencia,Innovación y Universidades in Spain through ICTS Equipment Grant No.EQC2018-005230-Pfrom Grant No.PID2021-125389O A-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER,UEby“ERDF A Way of Making Europe”by the European Unionfrom grants of the Junta de Castilla y León with Grant Nos.CLP263P20 and CLP087U16。
文摘This work demonstrates experimentally the close relation between return currents from relativistic laser-driven target polarization and the quality of the relativistic laser–plasma interaction for laser-driven secondary sources,taking as an example ion acceleration by target normal sheath acceleration.The Pearson linear correlation of maximum return current amplitude and proton spectrum cutoff energy is found to be in the range from~0.70 to 0.94.kA-scale return currents rise in all interaction schemes where targets of any kind are charged by escaping laser-accelerated relativistic electrons.Their precise measurement is demonstrated using an inductive scheme that allows operation at high repetition rates.Thus,return currents can be used as a metrological online tool for the optimization of many laser-driven secondary sources and for diagnosing their stability.In particular,in two parametric studies of laser-driven ion acceleration,we carry out a noninvasive online measurement of return currents in a tape target system irradiated by the 1 PW VEGA-3 laser at Centro de Láseres Pulsados:first the size of the irradiated area is varied at best compression of the laser pulse;second,the pulse duration is varied by means of induced group delay dispersion at best focus.This work paves the way to the development of feedback systems that operate at the high repetition rates of PW-class lasers.
文摘Resilience studies for water distribution systems(WDS)coupled with other interdependent infrastructure systems attract increasing attention from stakeholders and researchers.However,most existing large-scale WDS models are single infrastructure-based without consideration of other infrastructure systems.This is due to a lack of needed information on systems coupling,the structure of the simulator used,and the computation load involved.To address these gaps,this paper presents a synthetic modeling framework for a real-world WDS as coordinating with other infrastructure systems via a building-mediated clustering approach through consideration of physical distance and node capacity.First,the WDS network topology and operation parameters are inferred via bulk open-source information.A building-mediated clustering approach is designed to systematically derive the interdependence between the WDS and the power system similarly created as a case study.Second,a novel linearization method is developed in formulating the WDS model that can relieve computation load while maintaining accuracy.Finally,a disruption-recovery framework is developed to demonstrate the proposed methodology in modelling WDS resilience.The framework is applied to a neighborhood in Queenstown,Singapore,an area of 20.43 km^(2) and 96,000 population.The near-real-time simulations on the coupled system involving 308 nodes and 384 links showcase the effectiveness and application of the proposed synthetic modeling and formulation.
