Minimal Complexity Control Law Synthesis, Part 1: Problem Formulation and Reduction to Optimal Static Output Feedback

The overall goal in this series of three papers is to make progress towards the development of a control law design methodology which supports the following paradigm: Minimize control law complexity subject to the achievement of a specified accuracy in the face of a specified level of uncertainty. We achieve this goal by developing a general theory of optimal constrained-structure dynamic output feedback compensation. By applying this theory in an iterative fashion, where here the indicated iteration occurs over the choice of the compensator dynamic-structure, the paradigm stated above can in principle be realised. In this Part 1 of this series of papers the optimal constrained-structure dynamic output feedback problem is formulated in general terms. A method for reducing optimal constrained-structure dynamic output feedback problems to optimal static output feedback problems is developed. This reduction procedure is concretely illustrated for nine special cases of the general optimal constrained-structure dynamic output feedback problem. Taken together, these nine special cases contain most cases of interest in applications. Finally, the utility of these results in applications is described in some detail. Here we consider implementation issues such as operational/physical constraints, operating-point variations, and processor throughput/memory limitations, and describe how anti-windup/bumpless transfer, gain-scheduling, and digital processor implementation can be facilitated by apriori constraining the controller dynamic-structure in an appropriate fashion. In Part 2 of this series of papers a general theory of optimal static output feedback compensation is developed.