Parameter optimization in linear systems with arbitrarily constrained controller structure

TLDR: In this paper, an algorithm for optimization of constant parameters in the controller for a time invariant linear system is given, which can be applied to linear controllers of arbitrary structure with any degree of decentralization in the distribution of information.

Abstract: An algorithm is given for optimization of constant parameters in the controller for a time invariant linear system. The algorithm may be applied to linear controllers of arbitrary structure with any degree of decentralization in the distribution of information. Most important, it is not necessary to provide an initial controller of the specified structure which stabilizes the system. Rather, the structural constraints are initially relaxed to whatever degree necessary to obtain a stabilizing controller. The algorithm then gradually restores the constraints, converges to a local optimum solution, when one exists, and stabilizes any open loop system possessing a controllable unstable subspace. The necessary conditions while the optimum parameters must satisfy are developed for the arbitrarily constrained controller. The method of satisfying these necessary conditions involves use of a standard conjugate direction search together with a combined multiplier and penalty method for invoking the structural constraints. While attention is focused on the deterministic control problem, it is noted that systems with driving disturbances and measurement uncertainty may be handled with no significant modification of the algorithm. The result is a very practical tool for system design via parameter optimization.