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Necessary and sufficient conditions for nonlinear worst case \((H_ \infty)\) control and estimation. (English) Zbl 0814.93028

Summary: [Full electronic manuscript (published October 1, 1994) = 25 pp, 226,004 bytes. Retrieval Code: 39957.]
We present necessary and sufficient conditions for the existence of worst case controllers and estimators for nonlinear systems. These are also called \(H_ \infty\) suboptimal controllers and estimators. We consider affine and more general nonlinear systems, both time varying and autonomous over finite, semi-infinite and infinite intervals. In particular, we give necessary and sufficient conditions for the solvability of a standard \(H_ \infty\) suboptimal control problem by measurement feedback that involve the solvability of a pair of partial differential equations of the Hamilton-Jacobi type. The first is the one associated with the problem of \(H_ \infty\) suboptimal control by state feedback that has appeared previously in the work of several authors. The second is a new Hamilton-Jacobi equation associated with \(H_ \infty\) suboptimal estimation.

MSC:

93B36 \(H^\infty\)-control
49K15 Optimality conditions for problems involving ordinary differential equations
49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
93E10 Estimation and detection in stochastic control theory
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