Hybrid Estimation of State and Input for Linear Discrete Time-varying Systems: A Game Theory Approach
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摘要: 本文研究了线性离散时变系统的混合估计问题, 估计信号是状态和输入的线性组合. 设计目标要求满足一个最坏性能指标, 即从扰动到估计误差的能量增益小于一个给定值. 混合估计问题的最优解是二人零和微分对策的鞍点解. 基于微分对策方法, 混合估计问题有解的充要条件表达为 Riccati 微分方程的可解性. 在问题有解时, 给出了符合要求的估计器. 估计器的结构表达为一个增益矩阵和一个输出映射矩阵, 后者反映了未知输入与输出估计误差之间的内在联系. 最后, 通过数值例子证明了本文方法的有效性.Abstract: The H∞ hybrid estimation problem for linear discrete time-varying systems is investigated in this paper, where estimated signals are linear combination of state and input. Design objective requires the worst-case energy gain from disturbance to estimation error to be less than a prescribed level. Optimal solution of the hybrid estimation problem is the saddle point of a two-player zero sum differential game. On the basis of the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in terms of solutions to a Riccati differential equation. Moreover, one possible estimator is proposed if the solvable conditions are satisfied. The estimator is characterized by a gain matrix and an output mapping matrix, where the latter reflects the internal relations between unknown input and output estimation error. At last, a numerical example is provided to illustrate the proposed approach.
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Key words:
- Time-varying system /
- input estimation /
- game theory /
- Riccati equation
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