Control of Distributed Parameter Systems Subject to Convex Constraints: Applications to Irrigation Systems and Hypersonic Vehicles

This paper addresses designing finite dimensional linear time invariant (LTI) controllers for infinite dimensional LTI plants subject to H-infinity mixed-sensitivity performance objectives and convex constraints. Specifically, we focus on designing control systems for two classes of systems which are generally described by hyperbolic partial differential equations: (1) Irrigation systems and (2) Hypersonic Vehicles with flexible dynamics. The distributed parameter plant is first approximated by a finite dimensional approximant. The Youla parameterization is then used to parameterize the set of all stabilizing LTI controllers and a weighted mixed-sensitivity H-infinity optimization is formulated. After transforming the infinite dimensional problem to a finite-dimensional optimization problem, convex is optimization is used to obtain the solution. Subgradient concepts are used to directly accommodate time-domain specifications. Illustrative examples for irrigation systems and hypersonic vehicles are provided.