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Di erential Equations, Vol. 37, No. 8, 2001, pp. 1148{1159. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 8, 2001, pp. 1096{1107. Original Russian Text Copyright c 2001 by Tertychnyi-Dauri. PARTIAL DIFFERENTIAL EQUATIONS Optimal Stabilization of Adaptive Dynamical Systems with Distributed Parameters: I V. Yu. Tertychnyi-Dauri St. Petersburg Institute for Precision Mechanics and Optics, St. Petersburg, Russia Received January 20, 1998 We develop a uni ed scheme of adaptive synthesis for a distributed multidimensional vector system of the general parabolic type with unknown parameters experiencing a slow space-time drift. Adaptive optimization problems are solved for various classes of quadratic performance functionals. Next, we study the problem on the adaptive control of the heat conduction process in a nite physical volume and nd optimal stabilizational laws for internal and external (surface) controls in a medium with a variable temperature eld. 1. INTRODUCTION Optimal control problems for systems with distributed parameters were considered by numerous authors. Of the publications on the topic, we indicate some well-known fundamental papers [1{11], which made the control theory for such systems an independent, wide direction in the theory of controlled dynamical systems. The state of a system with distributed parameters is described by a function
Differential Equations – Springer Journals
Published: Oct 12, 2004
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