Quadratic Lyapunov Functions and State Feedback via InteriorPoint Optimization

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9222391 Boyd One of the most useful qualities of a properly designed feedback control system is robustness, i.e., the ability of the closed- loop system to continue working well despite large variations in the (open-loop) plant dynamics. This property is also the source of some of the hardest problems in control system analysis and synthesis. For example, the problem of determining a feedback law that is guaranteed to work well when connected to any plant model from a given set of models-the robust synthesis problem-is in general quite difficult. A recent advance is an analytic solution to a specific type of robust synthesis problem. This analytic solution can be derived in several different frameworks: Hoo-optimal control, linear-quadratic game-theoretic control, or linear exponential quadratic Gaussian (LEQG) optimal control. In contrast, this research centers around a method that couples Lyapunov theory with (numerical) convex optimization (but is closely connected with the analytic solution method mentioned above). In particular, newly developed interior point optimization methods will be applied to some convex and quasiconvex problems that arise in control theory (analysis and synthesis). Preliminary investigations suggest that the impact of interior point methods on Lyapunov function and state feedback search problems will be as profound as it has been on linear and quadratic programming. The goal of the research is to develop the foundations for method of control system robustness analysis and robust controller synthesis that substitutes convex optimization for the computations required in the analytic solution mentioned above, but in return solves a much larger class of problems. Moreover, with interior point optimization methods, the increase in computation effort over that required for the analytic solution, may be quite modest. ***