A Parameter Optimization Approach to Multiple-Objective Controller Design

A parameter optimization method is presented for controller design. Rather than dealing with the multiple specifications directly, which are difficult to optimize over, a series of cost functions are defined such that an improvement in a cost function results in an improvement in the related specifications. The cost functions are defined in such a way that they and all the gradients have analytical expressions. A unified framework is presented so that controllers of any order and structure may be considered. Because the analytical expressions for the cost functions are only valid for stabilizing controllers, the use of linear quadratic cost functions as barrier functions to enforce stability is introduced. By use of multiplier methods it is shown how to obtain initial stabilizing controllers that can stabilize p specified plants simultaneously as well as how to impose H_infin constraints.