Feedback Design in Linear Control Problems as an Optimization Problem

Abstract

We provide and discuss a new approach to the design of linear control systems based on the optimization viewpoint. Three basic classes of control problems are analyzed: a) static state and output feedback for linear quadratic regulator problem; b) rejection of nonrandom bounded exogenous disturbances via static linear feedback; c) the same rejection via dynamic output feedback using an observer. These three problems are considered as optimization ones with feedback gains as matrix variables. The iterative algorithms for its solution are formulated in a uniform way, and the explicit expressions for gradients of the cost functions are provided. The gradient method exhibits its efficiency for test examples, including double pendulum.