Mathematical Sciences: Studies in Stochastic Adaptive Control

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9623439 Duncan A variety of problems of stochastic adaptive control will be investigated in this project. Stochastic adaptive control is the control of an incompletely known stochastic system. Typically to solve an adaptive control problem it is necessary to identify the unknown parameters of the system and simultaneously to construct a control based on an ergodic cost functional. The stochastic systems to be considered include finite dimensional, linear and nonlinear systems and infinite dimensional systems that include both linear and semilinear partial differential equations. The control for the partial differential equations can occur only on the boundary or at discrete points. Some specific systems include stochastic models in the mathematics of finance and in stochastic manufacturing processes. Since self-optimal adaptive controls often cannot be determined or may not exist, the construction of almost optimal adaptive controls will be continued. An important component of this study is the computational investigations in adaptive control which includes the performance of estimation algorithms and adaptive controls. Many important physical systems are controlled. Typically a system is not completely known and often there are perturbations or errors that can be naturally modeled by noise. The control of an unknown system with noise is called stochastic adaptive control. This project will investigate some stochastic adaptive control problems that have applications to some important physical systems. The investigation includes both theoretical and computational aspects.