Model-based robust and stochastic control, and statistical inference for uncertain dynamical systems

This thesis develops various methods for the robust and stochastic model-based control of uncertain dynamical systems. Several different types of uncertainties are considered, as well as different mathematical formalisms for quantification of the effects of uncertainties in dynamical systems. For deterministic uncertain models and robust control, uncertainties are described as sets of unknowns and every element from a set is presumed to be realizable. Stability and performance characteristics and controlled system behaviors are required to be satisfied for any element in the set of uncertain models. This thesis extends and expands robust control theory to tackle control problems for specific classes of structured uncertain linear and nonlinear systems that include cone-invariant systems, descriptor systems, and Wiener systems. The resultant analysis and control methods are proposed in terms of conic programming that includes linear programming and semidefinite programming (SDP). For stochastic uncertain models and stochastic control, uncertainties are described in terms of probability distribution functions. Stability and performance characteristics and controlled system behaviors are required to be satisfied with a desired probabilistic confidence. This thesis develops analysis and control schemes based on a spectral methods known as generalized polynomial chaos that can be used to approximate the propagation of uncertainties through dynamical systems. The proposed analysis and design methods are shown to be computationally efficient and accurate alternatives to sampling-based methods, especially when the methods are incorporated into model-based real-time control such as model predictive control. In addition to accounting for uncertainties and disturbances, the occurrence of a system component fault or failure can significantly degrade the ability of the control system to satisfy the desired stability and performance criteria. This thesis presents an application of the robust control formalism to passively ensure the reliability of a closed-loop system. For an active and intelligent control under presumed fault scenarios, this thesis considers Bayesian inference and information theory that are suited for real-time model checking and selection. To maximize the performance of statistical inference decision-making in the presence of stochastic uncertainties, design methods for optimal probing input signals are proposed in terms of the solutions of mathematical programs. Due to excitation nature of probing inputs, the resultant mathematical programs are nonconvex and a sequential SDP and convex relaxation methods are proposed to cope with such computational challenges. For real-time model checking and selection of complex distributed systems, this thesis develops methods of distributed hypothesis testing that are based on belief propagation and optimization in graphical models. The proposed methods are scalable and guarantee a consensus of distributed statistical inference decision-making