| THE RELATIONSHIP BETWEEN THE STABILITY AND THE OPTIMALITY OF LINEAR SYSTEMS——Another kind of the inverse problem of linear optimal control |
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| 引用本文： | 陈小林,黄琳.THE RELATIONSHIP BETWEEN THE STABILITY AND THE OPTIMALITY OF LINEAR SYSTEMS——Another kind of the inverse problem of linear optimal control[J].应用数学和力学(英文版),1985(2). |
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| 作者姓名： | 陈小林 黄琳 |
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| 作者单位： | Department of Mechanics，Peking University，Beijing，Department of Mechanics，Peking University，Beijing |
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| 摘 要： | Different from the inverse problem put forward by R. E. Kalman, another kind ofinverse problem of linear optimal control is proposed and dicussed in this paper.which is asfollows: If an asymptotically stable system x=Ax and a performance indexJ=integral from n=0 to ∞(x(?)Qx u(?)u)at are given, when can A be decomposedinto (?)A BK(?)so thatthe control lawu=K(?)x is optimal for the systeem x=Ax Bu and the index J? This papergives the solution for the problem and presents certain correspondence between theasymptotically stable system and the optimal system.
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