Contributions to robust control of systems with parametric uncertainties

The robustness of a control system for a plant with parametric uncertainties is, in a broad sense, its capability of maintaining desired control performance in spite of possible discrepancy between nominal and actual values of plant parameters. It is practically very important to analyze how robust control systems are and to synthesize control systems that achieve good robustness. Robust control addresses these problems. The purpose of this dissertation is to present several novel methods and results related to robust control of systems with parametric uncertainties. Two separate topics are treated in this dissertation. The first topic is probabilistic robust control analysis and synthesis for linear systems. In the probabilistic robust control framework, uncertain plant parameters are characterized as random variables with known joint probability density function and the robustness of a control system is quantified by the probability that the system satisfies desired performance specifications. Under the assumption that the uncertain parameters are jointly Gaussian, we present an analysis method to analytically approximate the probability that the system is asymptotically stable and meets a quadratic performance specification. We also present a synthesis method to maximize this approximate probability. The second topic is robust stabilization of unstable periodic orbits in nonlinear dynamic systems possessing parametric uncertainties. The challenge is to achieve robust stability of orbital motion when both the period and the location of the periodic orbit are uncertain. We address this problem by extending the method of Generalized Sampled-Data Hold Function control of linear periodic systems in two ways. First, a change of independent variable is introduced, from time to a new angular variable, making the control logic event-driven rather than time-driven. Second, an adaptation strategy is introduced, whereby the uncertain parameters are estimated online, the reference periodic orbit is computed based on the parameter estimates, and event-driven control is implemented to stabilize the motion about the parameter-dependent reference periodic orbit. This adaptive event-driven strategy is applied to the robust stabilization of an unstable Halo orbit in the Earth-Sun system under uncertainty of the mass parameter.