In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building...In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.展开更多
This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum L...This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.展开更多
This paper studies the infinite time horizon mixed H-two/H-infinity control problem for descriptor systems using Nash game approach. A necessary/sufficient condition for the existence of infinite horizon H-two/H-infin...This paper studies the infinite time horizon mixed H-two/H-infinity control problem for descriptor systems using Nash game approach. A necessary/sufficient condition for the existence of infinite horizon H-two/H-infinity control is presented in the form of two coupled algebraic Riccati equations, respectively. Finally, a suboptimal H-two/H-infinity controller design is given based on an iterative linear matrix inequality algorithm.展开更多
In this paper, we present a linear matrix inequality （LMI）-based solution to implement H-two and H- infinity decentralized robust control strategies. Appropriate parametrization of optimal H-two and H-infinity contr...In this paper, we present a linear matrix inequality （LMI）-based solution to implement H-two and H- infinity decentralized robust control strategies. Appropriate parametrization of optimal H-two and H-infinity controllers is used. The general formulation of the decentralized control design leads to the optimal determination of both the state feedback gains and the observer gains of the decentralized controllers. This formulation is two folds： first, a centralized controller is obtained, and then, a simplified decentralized solution is derived by optimizing only the observer gains. The mathematical determination of these gains is formulated as an LMI optimization problem that can be easily solved using LMI solvers. As an experimental evaluation of these controllers, a real time application to an aerothermic process is carried out. A continuous-time model of the process obtained with a suitable direct continuous-time identification approach is elaborated. Results illustrating the real performance obtained from the H-two and H-infinity decentralized controllers are di^cu^ge.d and comnare, d with th~ ce^ntraliTed nn^g展开更多
This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis togeth...This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis together with placing the spectrum into a strip region is considered, which is achieved via solving a convex optimization problem.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 61203309, 61104088, 60835004)the Scientific Research Fund of Hunan Provincial Education Department (No. 12B043)+2 种基金the Natural Science Foundation of Hunan Province (No. 10JJ9007)the Industry-University-Research Combination Innovation Platform of Hunan Province (No. 2010XK6066)the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective opti-mization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.
基金supported by the National Natural Science Foundation of China(No.71171061)the Natural Science Foundation of Guangdong Province(No.S2011010004970)
文摘This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.
基金supported by the National Natural Science Foundation of China (Nos. 60674019, 61074088)
文摘This paper studies the infinite time horizon mixed H-two/H-infinity control problem for descriptor systems using Nash game approach. A necessary/sufficient condition for the existence of infinite horizon H-two/H-infinity control is presented in the form of two coupled algebraic Riccati equations, respectively. Finally, a suboptimal H-two/H-infinity controller design is given based on an iterative linear matrix inequality algorithm.
文摘In this paper, we present a linear matrix inequality （LMI）-based solution to implement H-two and H- infinity decentralized robust control strategies. Appropriate parametrization of optimal H-two and H-infinity controllers is used. The general formulation of the decentralized control design leads to the optimal determination of both the state feedback gains and the observer gains of the decentralized controllers. This formulation is two folds： first, a centralized controller is obtained, and then, a simplified decentralized solution is derived by optimizing only the observer gains. The mathematical determination of these gains is formulated as an LMI optimization problem that can be easily solved using LMI solvers. As an experimental evaluation of these controllers, a real time application to an aerothermic process is carried out. A continuous-time model of the process obtained with a suitable direct continuous-time identification approach is elaborated. Results illustrating the real performance obtained from the H-two and H-infinity decentralized controllers are di^cu^ge.d and comnare, d with th~ ce^ntraliTed nn^g
基金the National Natural Science Foundation of China (No.60174001)Beijing Education Community (No.290122)Specialized Research Fund for the Doctoral Program of Higher Education (No.20050424002)
文摘This paper studies the problem of suboptimal state-feedback H-two/H-infinity control of stochastic systems with spectrum constraint. Concretely speaking, a mixed suboptimal H-two/H-infinity controller synthesis together with placing the spectrum into a strip region is considered, which is achieved via solving a convex optimization problem.
