MIMO Control System Design for Aircraft Via Convex Optimization

This paper shows how convex optimization may be used to solve control system design problems for multiple-input muItiple-output(MIMO) linear time invariant(LTI) finite dimensional plants. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity ℋ ^∞ optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated optimization problem from an infinite dimensional optimization problem involving a search over stable real-rational transfer function matrices in "ℋ ^∞ to a finite dimensional optimization problem involving a search over a finite-dimensional space. It is shown how cutting plane (CP) and interior point (IP) methods may be used to solve the resulting finite dimensional convex optimization problem efficiently. In addition to solving multivariable weighted mixed sensitivity ℋ ^∞ control system design problems, it is shown how subgradient concepts may be used to directly accommodate time-domain overshoot specifications in the design process. As such, we provide a systematic design methodology for a large class of difficult MIMO control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. The method presented is applied to an unstable MIMO HiMAT (highly maneuverable advanced technology) fighter.