In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for nonstandard singularly perturbed discrete time systems. The methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem cannot be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast reduced-order continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast reduced-order Kalman filters. In order to show the effectiveness of the proposed method, we present the numerical result for a one-link flexible robot arm.

Keywords:
linear quadratic Gaussian control, singularly perturbed systems, singular optimal control, continuous time systems, Kalman filters, reduced order systems, Riccati equations, discrete time systems, flexible manipulators
Topics:
Algebra, Discrete time systems, Filters, Kalman filters, Optimal control, Robots
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