A complete parameterization of CLF-based controls via satisficing theory
Control laws based on control Lyapunov functions (clfs) offer many benefits: they are guaranteed to stabilize the closed-loop system, they may possess robust gain margins, or they may provide inverse-optimality. This thesis describes how the theory of satisficing is used to completely parametrize the class of clf-based control laws. A robust parameterization is also presented that completely parametrizes clf-based control laws that possess favorable gain margins, and it is shown that such robust satisficing controls are inverse-optimal. This parameterization is also extended to systems with exogenous disturbances via input-to-state clfs. The structure of these satisficing controls is illuminated by examining state-dependent sets in the control space, and it is shown how these parameterizations can be harnessed to provide superior performance. Several examples illustrate the efficacy of the satisficing parameterization in improving performance and in guaranteeing stability and robustness.