This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing t...This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.展开更多
This paper provides preliminary results on performance limitations for a class of discrete time Kleinman control systems whose open loop poles lie strictly outside the unit circle. By exploiting the properties of the ...This paper provides preliminary results on performance limitations for a class of discrete time Kleinman control systems whose open loop poles lie strictly outside the unit circle. By exploiting the properties of the Kleinman controllers and using of Mgebraic Riccati equation （ARE）, the relationship between total control energy of Kleinman control systems and the minimum energy needed to stabilize the open-loop systems is revealed. The result reflects how the horizon length of Kleinman controllers affects the performance of the closed-loop systems and quantifies how close the performance of Kleinman control systems is to the minimum energy.展开更多
文摘This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.
基金supported by the National Nature Science Foundation of China under Grant Nos.61233004,61221003,61074061,61374109,61104091the National Basic Research Program of China (973 Program) under Grant No.2013CB035500+1 种基金partly sponsored by the International Cooperation Program of Shanghai Science and Technology Commission under Grant No.12230709600the Higher Education Research Fund for the Doctoral Program of China under Grant No.20120073130006
文摘This paper provides preliminary results on performance limitations for a class of discrete time Kleinman control systems whose open loop poles lie strictly outside the unit circle. By exploiting the properties of the Kleinman controllers and using of Mgebraic Riccati equation （ARE）, the relationship between total control energy of Kleinman control systems and the minimum energy needed to stabilize the open-loop systems is revealed. The result reflects how the horizon length of Kleinman controllers affects the performance of the closed-loop systems and quantifies how close the performance of Kleinman control systems is to the minimum energy.
