A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state fee...A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality （LMI） approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.展开更多
This paper focuses on the problem of non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems. The controller gain to be designed is assumed to have additive gain variations. Based o...This paper focuses on the problem of non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems. The controller gain to be designed is assumed to have additive gain variations. Based on multiple-Lyapunov function technique, the design of non-fragile hybrid guaranteed cost controllers is derived to make the corresponding closed-loop system asymptotically stable for all admissible uncertainties. Furthermore, a convex optimization approach with LMIs constraints is introduced to select the optimal non-fragile guaranteed cost controllers. Finally, a simulation example illustrates the effectiveness of the proposed approach.展开更多
This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity sol...This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.展开更多
In this paper,the problem of guaranteed cost control and anti-windup design is studied for a class of switched systems with actuator saturation.The switching strategy and anti-windup compensator are designed to ensure...In this paper,the problem of guaranteed cost control and anti-windup design is studied for a class of switched systems with actuator saturation.The switching strategy and anti-windup compensator are designed to ensure the asymptotic stability of the closed-loop system and to obtain the minimum upper bound of the cost function.Some sufficient conditions for the existence of an anti-windup compensator of guaranteed cost are given by using the multiple Lyapunov functions method.On this basis,the minimum upper bound of the cost function is determined by solving the optimisation problem under the constraint of linear matrix inequality(LMI).Finally,a numerical example is given to verify the effectiveness of the proposed method.展开更多
This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with ...This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.展开更多
The electromagnetic force generated by the interaction of electromagnetic coils can be used to replace the conventional propellant consumption mode in close relative motion control,thereby promoting the application of...The electromagnetic force generated by the interaction of electromagnetic coils can be used to replace the conventional propellant consumption mode in close relative motion control,thereby promoting the application of formation flight technology for long-term and continuous space missions.Herein,a hysteresis-switching logic-based switching linear parameter varying(LPV)controller synthesis technique with guaranteed performance for electromagnetic formation flying on a highly elliptical orbit is proposed.First,considering that the relative dynamics model of an elliptical orbit is characterized by time-varying uncertainty,the LPV model is described.By introducing switching LPV controllers among different scheduled parameter subsets,conservativeness can be reduced.Second,the system modeling error,the uncertainty caused by a simplified electromagnetic coil model,and external disturbance are considered to derive switching LPV controller synthesis conditions based on the guaranteed H_(∞)performance.Derivation analysis shows that the proposed switching LPV controller not only ensures the robustness of the system against uncertainties,but also realizes the control input constraints.Finally,numerical simulations and comparative analyses are performed to demonstrate the effectiveness and advantages of the proposed control method.展开更多
基金This project was supported by a Program for Changjiang Scholars and an Innovative Research Team in the University and the National Natural Science Foundation of P. R. China (60474015).
文摘A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality （LMI） approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.
基金This work was supported by the National Natural Science Foundation of China (No.60274009, 60574013), and the Natural Science Foundation ofLiaoning Province(No.20032020).
文摘This paper focuses on the problem of non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems. The controller gain to be designed is assumed to have additive gain variations. Based on multiple-Lyapunov function technique, the design of non-fragile hybrid guaranteed cost controllers is derived to make the corresponding closed-loop system asymptotically stable for all admissible uncertainties. Furthermore, a convex optimization approach with LMIs constraints is introduced to select the optimal non-fragile guaranteed cost controllers. Finally, a simulation example illustrates the effectiveness of the proposed approach.
基金Supported by the SRFEB of Henan Province(2003110002)
文摘This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.
基金This work was supported by the National Natural Science Foundation of China （61273107, 61573077, 61503003）, the Dalian Leading, Dalian, China, the Doctoral Foundation of Tianjin Normal University （135202XB1613）, the Postdoctoral Science Foundation of China （2015M581332）, and the Natural Science Foundation of Anhui Province （150808. 5QF126）
基金the Natural Science Foundation of Liaoning Province of China[grant numbers 2020-MS-283 and 20180551014]the Scientific Research Fund of Education Department of Liaoning Province of China[grant number L2019016].
文摘In this paper,the problem of guaranteed cost control and anti-windup design is studied for a class of switched systems with actuator saturation.The switching strategy and anti-windup compensator are designed to ensure the asymptotic stability of the closed-loop system and to obtain the minimum upper bound of the cost function.Some sufficient conditions for the existence of an anti-windup compensator of guaranteed cost are given by using the multiple Lyapunov functions method.On this basis,the minimum upper bound of the cost function is determined by solving the optimisation problem under the constraint of linear matrix inequality(LMI).Finally,a numerical example is given to verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China under Grant Nos.U1404610,61473115 and 61374077Fundamental Research Project under Grant Nos.142300410293,142102210564 in the Science and Technology Department of Henan Province+1 种基金the Science and Technology Research Key Project under Grant No.14A413001 in the Education Department of Henan ProvinceYoung Key Teachers Plan of Henan Province under Grant No.2016GGJS-056
文摘This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.
基金This study was supported by the National Natural Science Foundation of China(No.11572019)the Natural Science General Fund of Shanghai(No.19ZR1453300).
文摘The electromagnetic force generated by the interaction of electromagnetic coils can be used to replace the conventional propellant consumption mode in close relative motion control,thereby promoting the application of formation flight technology for long-term and continuous space missions.Herein,a hysteresis-switching logic-based switching linear parameter varying(LPV)controller synthesis technique with guaranteed performance for electromagnetic formation flying on a highly elliptical orbit is proposed.First,considering that the relative dynamics model of an elliptical orbit is characterized by time-varying uncertainty,the LPV model is described.By introducing switching LPV controllers among different scheduled parameter subsets,conservativeness can be reduced.Second,the system modeling error,the uncertainty caused by a simplified electromagnetic coil model,and external disturbance are considered to derive switching LPV controller synthesis conditions based on the guaranteed H_(∞)performance.Derivation analysis shows that the proposed switching LPV controller not only ensures the robustness of the system against uncertainties,but also realizes the control input constraints.Finally,numerical simulations and comparative analyses are performed to demonstrate the effectiveness and advantages of the proposed control method.
