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Optimal stabilization of adaptive dynamical systems with distributed parameters. I. (English. Russian original) Zbl 0995.93066

Differ. Equ. 37, No. 8, 1148-1159 (2001); translation from Differ. Uravn. 37, No. 8, 1096-1107 (2001).
The author solves some problems of adaptive optimal and stabilizing controls for systems described by vector PDE’s of parabolic type using a unique approach based on the dynamic programming method. Performance functionals are assumed to be quadratic ones. As an example the author considers a problem of adaptive control modelling of the process of heat conduction in \(\mathbb{R}^1\) with the Dirichlet boundary condition.

MSC:

93D21 Adaptive or robust stabilization
93C20 Control/observation systems governed by partial differential equations
35K05 Heat equation
49L20 Dynamic programming in optimal control and differential games
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