Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to ma...Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.展开更多
A compound neural network is utilized to identify the dynamic nonlinear system. This network is composed of two parts： one is a linear neural network, and the other is a recurrent neural network. Based on the inverse...A compound neural network is utilized to identify the dynamic nonlinear system. This network is composed of two parts： one is a linear neural network, and the other is a recurrent neural network. Based on the inverse theory a compound inverse control method is proposed. The controller has also two parts： a linear controller and a nonlinear neural network controller. The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated .based on the Lyapunov theory. Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.展开更多
A novel control method for a general class of nonlinear systems using fuzzy logic systems （FLSs） is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a ...A novel control method for a general class of nonlinear systems using fuzzy logic systems （FLSs） is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.展开更多
In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two i...In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.展开更多
In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torq...In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torques matching is conducted.Meanwhile,a Nonlinear Model Predictive Control(NMPC)method is proposed,which combines the control index of the power turbine speed with torques matching of double engines creatively.In addition to the control index,the difference of output torques between each engine is also incorporated in the objective function as a penalty term to ensure constant speed control and short torques matching time.Simulation results demonstrate that relative to unilateral torques matching,the settling time of the bidirectional matching method can be reduced by nearly 30.8%.Nevertheless,compared with the bidirectional torques matching method under the cascade PID controller,the NMPC method can decrease the overshoot of the power turbine speed by 65%and reduce the matching time by 15.5%synchronously.Besides fast response control of turboshaft engines,fast torques matching control of double engines is accomplished as well.展开更多
This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under e...This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under external sea wave disturbance. In addition to having such typical nonlinear underactuated property, as it is well known, an offshore ship-mounted crane also suffers from much unexpected persistent disturbances induced by sea waves or currents, which, essentially different from an overhead crane fixed on land, cause much difficulty in modeling and controller design. Inspired by the desire to achieve appropriate control performance against those challenging factors, in this paper, through carefully analyzing the inherent mechanism of the nonlinear dynamics, we first construct a new composite signal to enhance the coupling behavior of the trolley motion as well as the payload swing in the presence of ship′s roll motion disturbance. Based on which, an energy-based coupling control law is presented to achieve asymptotic stability of the crane control system′s equilibrium point. Without any linearization of the complex nonlinear dynamics, unlike traditional feedback controllers, the proposed control law takes a much simpler structure independent of the system parameters. To support the theoretical derivations and to further verify the actual control performance, Lyapunov-based mathematical analysis as well as numerical simulation/experimental results are carried out, which clarify the feasibility and superior performance of the proposed method over complicated disturbances.展开更多
This paper focuses on the stability analysis of nonlinear networked control system with integral quadratic constraints(IQC) performance, dynamic quantization, variable sampling intervals, and communication delays. By ...This paper focuses on the stability analysis of nonlinear networked control system with integral quadratic constraints(IQC) performance, dynamic quantization, variable sampling intervals, and communication delays. By using input-delay and parallel distributed compensation(PDC) techniques, we establish the Takagi-Sugeno(T-S) fuzzy model for the system, in which the sampling period of the sampler and signal transmission delay are transformed to the refreshing interval of a zero-order holder(ZOH). By the appropriate Lyapunov-Krasovskii-based methods, a delay-dependent criterion is derived to ensure the asymptotic stability for the system with IQC performance via the H∞ state feedback control. The efficiency of the method is illustrated on a simulation exampler.展开更多
In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matri...In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.展开更多
A robust controller method for flexible joint robot considering the effect caused by nonlinear friction was presented.The nonlinear friction was denoted as inverse additive output uncertainty relative to the nominal m...A robust controller method for flexible joint robot considering the effect caused by nonlinear friction was presented.The nonlinear friction was denoted as inverse additive output uncertainty relative to the nominal model in our work,based on which the describing function was analyzed in frequency domain,and the weighting function of nonlinear friction was further calculated as well. By combining the friction uncertainty,the mixed sensitivity H∞optimization was proposed as the benchmark for controller design, which also leaded to good performance of robustness. Furthermore,unstructured perturbation to the system was analyzed so that the stability was guaranteed. Simulation results show that the proposed controller can provide excellent tracking and regulation performance.展开更多
A ship, as an object of course control, is characterized by a nonlinear function describing the static maneuvering characteristics. The backstepping method is one of the methods that can be used during the designing p...A ship, as an object of course control, is characterized by a nonlinear function describing the static maneuvering characteristics. The backstepping method is one of the methods that can be used during the designing process of a nonlinear course controller for ships. The method has been used for the purpose of designing two configurations of nonlinear controllers, which were then used to control the ship course. One of the configurations took dynamic characteristic of a steering gear into account during the designing stage. The parameters of the obtained nonlinear control structures have been tuned to optimise the operation of the control system. The optimisation process has been performed by means of genetic algorithms. The quality of operation of the designed control algorithms has been checked in simulation tests performed on the mathematical model of a tanker. The results of simulation experiments have been compared with the performance of the system containing a conventional proportional-derivative （PD） controller.展开更多
The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculati...The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculation model. In order to analyze the material nonlinear seismic response of the cable-stayed bridge, the nonlinear behaviors of the ductile plastic hinges of the bridge towers are taken into account by employing the nonlinear rotational spring element COMBIN40. To simulate a major earthquake, three earthquake records were chosen using a wave-choosing program and input into the bridge structure along longitudinal and transversal directions. Comparisons of the linear and nonlinear seismic responses of the cable-stayed bridge are performed. In addition, a study of TMD primary control is carried out using element MASS21 and element COMBIN14, and it is indicated that the effects of mitigation monitoring are evident.展开更多
This article presents an efficient parallel processing approach for solving the opti- mal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary ...This article presents an efficient parallel processing approach for solving the opti- mal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem （TPBVP） derived from the Pontrya- gin＇s maximum principle is first transformed into a sequence of lower-order deeoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a ma- trix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedbaek suboptimal control, we apply a fast iterative algorithm with low com- putational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.展开更多
In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2...In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2（t） for t〉0 （S）is considered. It is shown that by choosing appropriate control inputs （hi）, （j = 1, 2） one can always guide the system （S） from a given initial state φ∈H^S（α,β）, （s ∈ R） to a terminal state φ∈ H^s（α,β）, in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of SchrSdinger equation posed on the whole line R. The discovered smoothing properties of Schrodinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of （semi-linear） nonlinear Schrodinger equation.展开更多
A new nonlinear integral resonant controller（NIRC） is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides ad...A new nonlinear integral resonant controller（NIRC） is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce highamplitude nonlinear vibration around the fundamental resonance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system.Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results.The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode,unlike conventional second-order compensation methods.This makes the NIRC controlled system robust to excitation frequency variations.展开更多
This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic ...This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.展开更多
To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations a...To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.展开更多
The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed, and a solution is presented based on variable structure control theory and H∞ control theory. A kind of boun...The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed, and a solution is presented based on variable structure control theory and H∞ control theory. A kind of boundary layer is built near the ideal switch surface which can eliminate chattering in the switch surface. The proposed control method with L2 gain can guarantee exponential stability of a system state with no parameter uncertainty and exter- nal disturbance, while it can guarantee state ultimate boundness if parameter uncertainty and external disturbance exist. In the proposed design method, stability of the closed-loop system is analyzed by adopting the Lyapurtov func- tion approach. Finally the numerical simulation results show that the proposed smooth variable structure controller has good pelformance without chattering in the switch surface.展开更多
基金the National Natural Science Foundation of China (No. 50979058)the Special Research Fund for the Doctoral Program of Higher Education (No. 20090073110012)
文摘Autonomous underwater gliders are highly effcient,buoyancy-driven,winged autonomous underwater vehicles. Their dynamics are multivariable nonlinear systems. In addition,the gliders are underactuated and diffcult to maneuver,and also dependent on their operational environment. To confront these problems and to design an effective controller,the inverse system method was used to decouple the original system into two independent single variable linear subsystems. The stability of the zero dynamics was analyzed,and an additional closed-loop controller for each linear subsystem was designed by sliding mode control method to form a type of composite controller. Simulation results demonstrate that the derived nonlinear controller is able to cope with the aforementioned problems simultaneously and satisfactorily.
基金This work was supported by National Natural Science Foundation of China (No .60374037) Natural Science and Technology Research Project of HebeiProvince (No .E2004000055) .
文摘A compound neural network is utilized to identify the dynamic nonlinear system. This network is composed of two parts： one is a linear neural network, and the other is a recurrent neural network. Based on the inverse theory a compound inverse control method is proposed. The controller has also two parts： a linear controller and a nonlinear neural network controller. The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated .based on the Lyapunov theory. Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
基金This project was supported by the National Natural Science Foundation of China (90405011).
文摘A novel control method for a general class of nonlinear systems using fuzzy logic systems （FLSs） is presertted. Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.
文摘In this paper, a nonlinear control scheme of two identical hyperchaotic Chert systems is developed to realize their modified projective synchronization. We achieve modified projective synchronization between the two identical hyperchaotic systems by directing the scaling factor onto the desired value. With symbolic computation system Maple and Lyapunov stability theory, numerical simulations are given to perform the process of the synchronization.
基金co-supported by the National Natural Science Foundation of China(No.51576096)Qing Lan and 333 Project and Research Funds for Central Universities(No.NF2018003).
文摘In order to reach a compromise between fast response control and torques matching control in double turboshaft engines,research on nonlinear model predictive control for turboshaft engines based on double engines torques matching is conducted.Meanwhile,a Nonlinear Model Predictive Control(NMPC)method is proposed,which combines the control index of the power turbine speed with torques matching of double engines creatively.In addition to the control index,the difference of output torques between each engine is also incorporated in the objective function as a penalty term to ensure constant speed control and short torques matching time.Simulation results demonstrate that relative to unilateral torques matching,the settling time of the bidirectional matching method can be reduced by nearly 30.8%.Nevertheless,compared with the bidirectional torques matching method under the cascade PID controller,the NMPC method can decrease the overshoot of the power turbine speed by 65%and reduce the matching time by 15.5%synchronously.Besides fast response control of turboshaft engines,fast torques matching control of double engines is accomplished as well.
基金supported by National Natural Science Foundation of China (No. 11372144)National Science Fund for Distinguished Young Scholars of China (No. 61325017)National Science Foundation of Tianjin
文摘This paper proposes a novel nonlinear energy-based coupling control for an underactuated offshore ship-mounted crane,which guarantees both precise trolley positioning and payload swing suppressing performances under external sea wave disturbance. In addition to having such typical nonlinear underactuated property, as it is well known, an offshore ship-mounted crane also suffers from much unexpected persistent disturbances induced by sea waves or currents, which, essentially different from an overhead crane fixed on land, cause much difficulty in modeling and controller design. Inspired by the desire to achieve appropriate control performance against those challenging factors, in this paper, through carefully analyzing the inherent mechanism of the nonlinear dynamics, we first construct a new composite signal to enhance the coupling behavior of the trolley motion as well as the payload swing in the presence of ship′s roll motion disturbance. Based on which, an energy-based coupling control law is presented to achieve asymptotic stability of the crane control system′s equilibrium point. Without any linearization of the complex nonlinear dynamics, unlike traditional feedback controllers, the proposed control law takes a much simpler structure independent of the system parameters. To support the theoretical derivations and to further verify the actual control performance, Lyapunov-based mathematical analysis as well as numerical simulation/experimental results are carried out, which clarify the feasibility and superior performance of the proposed method over complicated disturbances.
基金Supported by the National Natural Science Foundation of China(61472136)the Best Youth of the Education Department of Hunan Province(16B023)
文摘This paper focuses on the stability analysis of nonlinear networked control system with integral quadratic constraints(IQC) performance, dynamic quantization, variable sampling intervals, and communication delays. By using input-delay and parallel distributed compensation(PDC) techniques, we establish the Takagi-Sugeno(T-S) fuzzy model for the system, in which the sampling period of the sampler and signal transmission delay are transformed to the refreshing interval of a zero-order holder(ZOH). By the appropriate Lyapunov-Krasovskii-based methods, a delay-dependent criterion is derived to ensure the asymptotic stability for the system with IQC performance via the H∞ state feedback control. The efficiency of the method is illustrated on a simulation exampler.
基金This project was supported by the National Natural Science Foundation of China (No. 69934030)the Foundation for University
文摘In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
基金National Natural Science Foundation of China(No.61273339)
文摘A robust controller method for flexible joint robot considering the effect caused by nonlinear friction was presented.The nonlinear friction was denoted as inverse additive output uncertainty relative to the nominal model in our work,based on which the describing function was analyzed in frequency domain,and the weighting function of nonlinear friction was further calculated as well. By combining the friction uncertainty,the mixed sensitivity H∞optimization was proposed as the benchmark for controller design, which also leaded to good performance of robustness. Furthermore,unstructured perturbation to the system was analyzed so that the stability was guaranteed. Simulation results show that the proposed controller can provide excellent tracking and regulation performance.
基金supported by Polish Ministry of Science and Higher Education (No. N514 015 32/1712)
文摘A ship, as an object of course control, is characterized by a nonlinear function describing the static maneuvering characteristics. The backstepping method is one of the methods that can be used during the designing process of a nonlinear course controller for ships. The method has been used for the purpose of designing two configurations of nonlinear controllers, which were then used to control the ship course. One of the configurations took dynamic characteristic of a steering gear into account during the designing stage. The parameters of the obtained nonlinear control structures have been tuned to optimise the operation of the control system. The optimisation process has been performed by means of genetic algorithms. The quality of operation of the designed control algorithms has been checked in simulation tests performed on the mathematical model of a tanker. The results of simulation experiments have been compared with the performance of the system containing a conventional proportional-derivative （PD） controller.
文摘The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculation model. In order to analyze the material nonlinear seismic response of the cable-stayed bridge, the nonlinear behaviors of the ductile plastic hinges of the bridge towers are taken into account by employing the nonlinear rotational spring element COMBIN40. To simulate a major earthquake, three earthquake records were chosen using a wave-choosing program and input into the bridge structure along longitudinal and transversal directions. Comparisons of the linear and nonlinear seismic responses of the cable-stayed bridge are performed. In addition, a study of TMD primary control is carried out using element MASS21 and element COMBIN14, and it is indicated that the effects of mitigation monitoring are evident.
文摘This article presents an efficient parallel processing approach for solving the opti- mal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem （TPBVP） derived from the Pontrya- gin＇s maximum principle is first transformed into a sequence of lower-order deeoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a ma- trix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedbaek suboptimal control, we apply a fast iterative algorithm with low com- putational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.
文摘In this paper, the boundary control problem of a distributed parameter system described by the Schrodinger equation posed on finite interval α≤x≤β：{ iyt ＋yzz＋｜y｜^2y = 0, y（α, t） = h1 （t）, y（β, t）=h2（t） for t〉0 （S）is considered. It is shown that by choosing appropriate control inputs （hi）, （j = 1, 2） one can always guide the system （S） from a given initial state φ∈H^S（α,β）, （s ∈ R） to a terminal state φ∈ H^s（α,β）, in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of SchrSdinger equation posed on the whole line R. The discovered smoothing properties of Schrodinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of （semi-linear） nonlinear Schrodinger equation.
文摘A new nonlinear integral resonant controller（NIRC） is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce highamplitude nonlinear vibration around the fundamental resonance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system.Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results.The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode,unlike conventional second-order compensation methods.This makes the NIRC controlled system robust to excitation frequency variations.
文摘This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.
基金supported by the National Natural Science Foundation of China(Nos.61174221 and 61402039)
文摘To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.
文摘The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed, and a solution is presented based on variable structure control theory and H∞ control theory. A kind of boundary layer is built near the ideal switch surface which can eliminate chattering in the switch surface. The proposed control method with L2 gain can guarantee exponential stability of a system state with no parameter uncertainty and exter- nal disturbance, while it can guarantee state ultimate boundness if parameter uncertainty and external disturbance exist. In the proposed design method, stability of the closed-loop system is analyzed by adopting the Lyapurtov func- tion approach. Finally the numerical simulation results show that the proposed smooth variable structure controller has good pelformance without chattering in the switch surface.
