This paper proposes an efficient method for designing accurate structure-specified mixed H2/H∞ optimal controllers for systems with uncertainties and disturbance using particle swarm (PSO) algorithm. It is designed t...This paper proposes an efficient method for designing accurate structure-specified mixed H2/H∞ optimal controllers for systems with uncertainties and disturbance using particle swarm (PSO) algorithm. It is designed to find a suitable controller that minimizes the performance index of error signal subject to an unequal constraint on the norm of the closed-loop system. Although the mixed H2/H∞ for the output feedback approach control is considered as a robust and optimal control technique, the design process normally comes up with a complex and non-convex optimization problem, which is difficult to solve by the conventional optimization methods. The PSO can efficiently solve design problems of multi-input-multi-output (MIMO) optimal control systems, which is very suitable for practical engineering designs. It is used to search for parameters of a structure-specified controller, which satisfies mixed performance index. The simulation and experimental results show high feasibility, robustness and practical value compared with the conventional proportional-integral-derivative (PID) and proportional-Integral (PI) controller, and the proposed algorithm is also more efficient compared with the genetic algorithm (GA).展开更多
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaini...The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.展开更多
The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinit...The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.展开更多
This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncerta...This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.展开更多
The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant ...The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.展开更多
文摘This paper proposes an efficient method for designing accurate structure-specified mixed H2/H∞ optimal controllers for systems with uncertainties and disturbance using particle swarm (PSO) algorithm. It is designed to find a suitable controller that minimizes the performance index of error signal subject to an unequal constraint on the norm of the closed-loop system. Although the mixed H2/H∞ for the output feedback approach control is considered as a robust and optimal control technique, the design process normally comes up with a complex and non-convex optimization problem, which is difficult to solve by the conventional optimization methods. The PSO can efficiently solve design problems of multi-input-multi-output (MIMO) optimal control systems, which is very suitable for practical engineering designs. It is used to search for parameters of a structure-specified controller, which satisfies mixed performance index. The simulation and experimental results show high feasibility, robustness and practical value compared with the conventional proportional-integral-derivative (PID) and proportional-Integral (PI) controller, and the proposed algorithm is also more efficient compared with the genetic algorithm (GA).
基金This project was supported by the National Nature Science Foundation of China (60374009)Nature Science Foundation of Guangdong Province of China (990795).
文摘The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
基金This work is supported by the National Natural Science Foundation of China (No.60374002 and No.60421002) the 973 program of China (No.2002CB312200) and the program for New Century Excellent Talents in University (No.NCET-04-0547).
文摘The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.
文摘This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.
基金supported by the National Natural Science Foundation of China (No.60774044)the Professional Research Foundation for Advanced Talents of Jiangsu University (No.07JDG037)+2 种基金the Natural Science Fund for Colleges and Universities in Jiangsu Province (No.08KJ510010)the Open Project of National Key Laboratory of Industrial Control Technology of Zhejiang University (No.ICT0910)Qing Lan Project of Jiangsu Province
文摘The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.
