Determination of Compromise Solutions for Linear Steady State Regulator with Vector Valued Performance Index

The use of vector valued performance index as a performance measure in the design of optimal control systems has invited much attention from researchers in the field of control engineering. The problem is of practical significance as the system presents an optimal solution for multiple criteria optimal control problems. A general performance index is defined in the form of a norm which can be expressed as the sum of p th power of deviations of the different performance index elements from their optimal values considering individual performance measures separately. The norm is minimized in k dimensional performance index space to obtain a set of non inferior systems corresponding to a class of compromise solutions. The paper presents a solution method for determining a class of compromise solutions for the standard linear quadratic steady state regulator problem optimizing k performance indices simultaneously. Selection of a single system out of the class of systems obtained is made by an appropriate choice of the parameter p based on the specified application.