Krener, A. J. Necessary and sufficient conditions for nonlinear worst case \((H_ \infty)\) control and estimation. (English) Zbl 0814.93028 J. Math. Syst. Estim. Control 4, No. 4, 485-488 (1994). 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. Cited in 1 ReviewCited in 6 Documents 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 Keywords:nonlinear \(H_ \infty\) control and estimation; worst case controllers and estimators; nonlinear systems; measurement feedback; Hamilton-Jacobi equation PDFBibTeX XMLCite \textit{A. J. Krener}, J. Math. Syst. Estim. Control 4, No. 4, 485--488 (1994; Zbl 0814.93028) Full Text: File