It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gra...It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.展开更多
In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws fo...In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed.展开更多
We discuss the stationarity of generator G for gauge symmetries in two directions.One is to the motion equations defined by total Hamiltonian H T,and gives that the number of the independent coefficients in the genera...We discuss the stationarity of generator G for gauge symmetries in two directions.One is to the motion equations defined by total Hamiltonian H T,and gives that the number of the independent coefficients in the generator G is not greater than the number of the primary first-class constraints,and the number of Noether conserved charges is not greater than that of the primary first-class constraints,too.The other is to the variances of canonical variables deduced from the generator G,and gives the variances of Lagrangian multipliers contained in extended Hamiltonian H E.And a second-class constraint generated by a first-class constraint may imply a new first-class constraint which can be combined by introducing other second-class constraints.Finally,we supply two examples.One with three first-class constraints(two is primary and one is secondary)has two Noether conserved charges,and the secondary first-class constraint is combined by three second-class constraints which are a secondary and two primary second-class constraints.The other with two first-class constraints(one is primary and one is secondary)has one Noehter conserved charge.展开更多
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.展开更多
Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face...Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.展开更多
The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in futu...The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.展开更多
In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the op...In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.展开更多
To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control inpu...To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.展开更多
For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for s...For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.展开更多
A constrained system associated with a 3 × 3 matrix spectral problem of the nonlinear Schroedinger（NLS） hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body...A constrained system associated with a 3 × 3 matrix spectral problem of the nonlinear Schroedinger（NLS） hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R^3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C^2N.展开更多
A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of i...A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.展开更多
Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained u...Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained under deterministic conditions may not be stable and economical. This paper studies the optimization of circulating cooling water systems under uncertain circumstance. To improve the reliability of the system and reduce the water and energy consumption, the influence of different uncertain parameters is taken into consideration. The chance constrained programming method is used to build a model under uncertain conditions, where the confidence level indicates the degree of constraint violation. Probability distribution functions are used to describe the form of uncertain parameters. The objective is to minimize the total cost and obtain the optimal cooling network configuration simultaneously.An algorithm based on Monte Carlo method is proposed, and GAMS software is used to solve the mixed integer nonlinear programming model. A case is optimized to verify the validity of the model. Compared with the deterministic optimization method, the results show that when considering the different types of uncertain parameters, a system with better economy and reliability can be obtained(total cost can be reduced at least 2%).展开更多
This paper aims to fuse two well-established and,at the same time,opposed control techniques,namely,model predictive control(MPC)and active disturbance rejection control(ADRC),to develop a dynamic motion controller fo...This paper aims to fuse two well-established and,at the same time,opposed control techniques,namely,model predictive control(MPC)and active disturbance rejection control(ADRC),to develop a dynamic motion controller for a laser beam steering system.The proposed technique uses the ADRC philosophy to lump disturbances and model uncertainties into a total disturbance.Then,the total disturbance is estimated via a discrete extended state disturbance observer(ESO),and it is used to(1)handle the system constraints in a quadratic optimization problem and(2)injected as a feedforward term to the plant to reject the total disturbance,together with the feedback term obtained by the MPC.The main advantage of the proposed approach is that the MPC is designed based on a straightforward integrator-chain model such that a simple convex optimization problem is performed.Several experiments show the real-time closed-loop performance regarding trajectory tracking and disturbance rejection.Owing to simplicity,the self-contained approach MPC+ESO becomes a Frugal MPC,which is computationally economical,adaptable,efficient,resilient,and suitable for applications where on-board computational resources are limited.展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of ...In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.展开更多
The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Ham...The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.展开更多
The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information,and the limited tolerance relation is developed to overcome the problem that o...The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information,and the limited tolerance relation is developed to overcome the problem that objects leniently satisfy the tolerance relation.However,the classification based on the limited tolerance relationship cannot reflect the matching degree of uncertain information of objects.In this article,we explore the influence of null values in an incomplete system,and propose the constrained tolerance relation based on the matching degree of uncertain information of objects.The proposed rough set based on the constrained tolerance relation can provide a more detailed structure of an object class through threshold.Proofs and example analyses further show the rationality and superiority of the proposed model.展开更多
Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the sys...Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.展开更多
Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular syst...Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.展开更多
The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations. The definition and criteria of the form invariance of constra...The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations. The definition and criteria of the form invariance of constrained Birkhoffian system are given, and the relation of the form invariance and the Noether symmetry is studied.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11272050,11202090,11472124,11572034,and 11572145)the Science and Technology Research Project of Liaoning Province,China(Grant No.L2013005)+1 种基金China Postdoctoral Science Foundation(Grant No.2014M560203)the Doctor Start-up Fund in Liaoning Province of China(Grant No.20141050)
文摘It is a difficult problem to study the stability of the rheonomic and nonholonomic mechanical systems. Especially it is difficult to construct the Lyapunov function directly from the differential equation. But the gradient system is exactly suitable to study the stability of a dynamical system with the aid of the Lyapunov function. The stability of the solution for a simple rheonomic nonholonomic constrained system is studied in this paper. Firstly, the differential equations of motion of the system are established. Secondly, a problem in which the generalized forces are exerted on the system such that the solution is stable is proposed. Finally, the stable solutions of the rheonomic nonholonomic system can be constructed by using the gradient systems.
基金This work was supported by Beijing Science Foundation of the People's Republie of China.
文摘In this paper the generalized Bianchi's identities for the variant constrained system (GBIVOS)w ith non-invariant action integral and constraint conditions was derived, and the strong and weak conservation laws for such system was deduced. The preliminary applications of the GBIVCS to the case for some models of field theories was given. The Dirac constraint of such system was discussed.
基金Supported by National Natural Science Foundation of China under Grant Nos.11047020 and 11047173Natural Science Foundation of Shandong Province,China under Grant Nos.ZR2011AM019,ZR2010AQ025,BS2010DS006,and Y200814Scientific and Technological Development Projection of Shandong Province,China under Grant No.J08LI56
文摘We discuss the stationarity of generator G for gauge symmetries in two directions.One is to the motion equations defined by total Hamiltonian H T,and gives that the number of the independent coefficients in the generator G is not greater than the number of the primary first-class constraints,and the number of Noether conserved charges is not greater than that of the primary first-class constraints,too.The other is to the variances of canonical variables deduced from the generator G,and gives the variances of Lagrangian multipliers contained in extended Hamiltonian H E.And a second-class constraint generated by a first-class constraint may imply a new first-class constraint which can be combined by introducing other second-class constraints.Finally,we supply two examples.One with three first-class constraints(two is primary and one is secondary)has two Noether conserved charges,and the secondary first-class constraint is combined by three second-class constraints which are a secondary and two primary second-class constraints.The other with two first-class constraints(one is primary and one is secondary)has one Noehter conserved charge.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.
基金supported in part by the Natural Sciences and Engineering Research Council of Canada(NSERC)supported by the National Natural Science Foundation of China under Grant 62303403Zhejiang Provincial Natural Science Foundation of China under Grants LR25F030004 and LQ24F030022。
文摘Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.
基金Project(2022YFC2904502)supported by the National Key Research and Development Program of ChinaProject(62273357)supported by the National Natural Science Foundation of China。
文摘The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.
基金Supported by the National Natural Science Foundation of China(12071133)Natural Science Foundation of Henan Province(252300421993)Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
文摘In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
文摘To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.
基金The National Natural Science Foundation of China(No.10972151,11272227)
文摘For an in-depth study on the integration problem of the constrained mechanical systems the method of integration for the Birkhoffian system with constraints is discussed and the method of variation of parameters for solving the dynamical equations of the constrained Birkhoffian system is provided.First the differential equations of motion for the constrained Birkhoffian system as well as for the corresponding free Birkhoffian system are established.Secondly a system of auxiliary equations is constructed and the general solution of the equations is found.Finally by varying the parameters and utilizing the properties of the generalized canonical transformation of the Birkhoffian system the solution of the problem can be obtained.The proposed method reveals the inherent relationship between the solution of a free Birkhoffian system and that of a constrained Birkhoffian system. The research results are of universal significance which can be further used in a variety of constrained mechanical systems such as non-conservative systems and nonholonomic systems etc.
基金Foundation item: Supported by the National Natural Science Foundation of China(10471132)Supported by the Youth Teacher Foundation and Natural Science Foundation of Henan Education Department(2004110006)
文摘A constrained system associated with a 3 × 3 matrix spectral problem of the nonlinear Schroedinger（NLS） hierarchy is proposed. It is shown that the constrained system is a Hamiltonian system with the rigid body type Poisson structure on the Poisson manifold R^3N. Further, the reduction of the constrained system extended to the common level set of the complex cones is proved to be the constrained AKNS system on C^2N.
基金supported by the National Natural Science Foundation of China(Nos.61473307 and 61304120)the Aeronautical Science Foundation of China(No. 20155896026)
文摘A constrained adaptive neural network control scheme is proposed for a multi-input and multi-output（MIMO） aeroelastic system in the presence of wind gust,system uncertainties,and input nonlinearities consisting of input saturation and dead-zone.In regard to the input nonlinearities,the right inverse function block of the dead-zone is added before the input nonlinearities,which simplifies the input nonlinearities into an equivalent input saturation.To deal with the equivalent input saturation,an auxiliary error system is designed to compensate for the impact of the input saturation.Meanwhile,uncertainties in pitch stiffness,plunge stiffness,and pitch damping are all considered,and radial basis function neural networks（RBFNNs） are applied to approximate the system uncertainties.In combination with the designed auxiliary error system and the backstepping control technique,a constrained adaptive neural network controller is designed,and it is proven that all the signals in the closed-loop system are semi-globally uniformly bounded via the Lyapunov stability analysis method.Finally,extensive digital simulation results demonstrate the effectiveness of the proposed control scheme towards flutter suppression in spite of the integrated effects of wind gust,system uncertainties,and input nonlinearities.
基金Financial support from the National Natural Science Foundation of China (22022816, 22078358)。
文摘Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained under deterministic conditions may not be stable and economical. This paper studies the optimization of circulating cooling water systems under uncertain circumstance. To improve the reliability of the system and reduce the water and energy consumption, the influence of different uncertain parameters is taken into consideration. The chance constrained programming method is used to build a model under uncertain conditions, where the confidence level indicates the degree of constraint violation. Probability distribution functions are used to describe the form of uncertain parameters. The objective is to minimize the total cost and obtain the optimal cooling network configuration simultaneously.An algorithm based on Monte Carlo method is proposed, and GAMS software is used to solve the mixed integer nonlinear programming model. A case is optimized to verify the validity of the model. Compared with the deterministic optimization method, the results show that when considering the different types of uncertain parameters, a system with better economy and reliability can be obtained(total cost can be reduced at least 2%).
基金support through his Master scholarshipThe Vicerrectoría de Investigación y Estudios de Posgrado(VIEP-BUAP)partially funded this work under grant number 00593-PV/2025.
文摘This paper aims to fuse two well-established and,at the same time,opposed control techniques,namely,model predictive control(MPC)and active disturbance rejection control(ADRC),to develop a dynamic motion controller for a laser beam steering system.The proposed technique uses the ADRC philosophy to lump disturbances and model uncertainties into a total disturbance.Then,the total disturbance is estimated via a discrete extended state disturbance observer(ESO),and it is used to(1)handle the system constraints in a quadratic optimization problem and(2)injected as a feedforward term to the plant to reject the total disturbance,together with the feedback term obtained by the MPC.The main advantage of the proposed approach is that the MPC is designed based on a straightforward integrator-chain model such that a simple convex optimization problem is performed.Several experiments show the real-time closed-loop performance regarding trajectory tracking and disturbance rejection.Owing to simplicity,the self-contained approach MPC+ESO becomes a Frugal MPC,which is computationally economical,adaptable,efficient,resilient,and suitable for applications where on-board computational resources are limited.
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
基金Project supported by the Heilongjiang Natural Science Foundation of China （Grant No 9507）
文摘In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(Nos.10932002 and 11272050)
文摘The characteristics of stationary and non-stationary skew-gradient systems are studied. The skew-gradient representations of holonomic systems, Birkhoffian systems, generalized Birkhoffian systems, and generalized Hamiltonian systems are given. The characteristics of skew-gradient systems are used to study integration and stability of the solution of constrained mechanical systems. Examples are given to illustrate applications of the result.
基金National Natural Science Foundation of China,Grant/Award Numbers:61,662,001,61,762,002Young and Middle-aged Talents Training Program of National Ethnic Affair Commission,Grant/AwardNurnber:2016GQR06Ningxia First-class Construction Discipline Program,Grant/AwardNumber:NXYLXK2017B09,Open Foundation ofNingxia Kcy Laboratory of Intelligcnt Informationand Big Data Processing,Grant/Award Number:2019KLBD006。
文摘The tolerance rough set is developed as one of the outstanding extensions of the Pawlak's rough set model under incomplete information,and the limited tolerance relation is developed to overcome the problem that objects leniently satisfy the tolerance relation.However,the classification based on the limited tolerance relationship cannot reflect the matching degree of uncertain information of objects.In this article,we explore the influence of null values in an incomplete system,and propose the constrained tolerance relation based on the matching degree of uncertain information of objects.The proposed rough set based on the constrained tolerance relation can provide a more detailed structure of an object class through threshold.Proofs and example analyses further show the rationality and superiority of the proposed model.
文摘Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.
基金the National Natural Science Foundation of China(12172241,11802193,11972241)the Natural Science Foundation of Jiangsu Province(BK20191454)the"Qinglan Project"of Jiangsu Province。
文摘Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.
文摘The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations. The definition and criteria of the form invariance of constrained Birkhoffian system are given, and the relation of the form invariance and the Noether symmetry is studied.
