H-infinity mixed-sensitivity optimization for infinite dimensional plants subject to convex constraints.

摘要

This dissertation focuses on Hinfinity near-optimal finite-dimensional compensator design for linear time invariant (LTI) infinite-dimensional plants subject to convex constraints. Infinite-dimensional (or distributed parameter) systems are systems whose models contain combinations of partial differential equations (PDEs) and/or time delays. This dissertation presents a systematic design methodology for such systems, based on Hinfinity mixed-sensitivity optimization, subject to convex constraints on the closed loop maps: The infinite-dimensional plant is approximated by a finite dimensional approximant. The celebrated the Youla-Bongiorno-Jabr-Kucera Q-Parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixed-sensitivity Hinfinity optimization that is convex in the Youla Q-Parameter. For unstable plants, the same parameterization can be used but the coprime factors need to be approximated by their finite dimensional approximants. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, the infinite-dimensional convex optimization problem is transformed to a finite-dimensional convex optimization problem involving a search over a finite-dimensional parameter space. This is significant because (1) analytic methods for problems with Hinfinity mixed-sensitivity objectives subject to convex constraints are currently unavailable and (2) very efficient interior point methods exist to solve such (nonlinear convex) optimization problems.; In addition to solving weighted mixed-sensitivity Hinfinity control system design problems, subgradient concepts are used to directly accommodate time and frequency domain specifications (e.g. peak value of control action, overshoot at the output, peak magnitude) in the design process. As such, a systematic control system design methodology is provided for a large class of infinite-dimensional plants. Several illustrative examples for thermal, structural, and aircraft systems are provided. In short, the approach taken permits a designer to address control system design problems for which no direct method exists.