Hierarchical robust nonlinear switching control design for propulsion systems

The desire for developing an integrated control system-design methodology for advanced propulsion systems has led to significant activity in modeling and control of flow compression systems in recent years. In this dissertation we develop a novel hierarchical switching control framework for addressing the compressor aerodynamic instabilities of rotating stall and surge. The proposed control framework accounts for the coupling between higher-order modes while explicitly addressing actuator rate saturation constraints and system modeling uncertainty.; To develop a hierarchical nonlinear switching control framework, first we develop generalized Lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the Lyapunov function and the system dynamics are removed. In particular, local and global stability theorems are given using lower semicontinuous Lyapunov functions. Furthermore, generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized Lyapunov level surfaces. The proposed results provide transparent generalizations to standard Lyapunov and invariant set theorems.; Using the generalized Lyapunov and invariant set theorems, a nonlinear control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear control strategy is developed that stabilizes a given nonlinear system by stabilizing a collection of nonlinear controlled subsystems. The switching nonlinear controller architecture is designed based on a generalized lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized system equilibria. The proposed framework provides a rigorous alternative to designing gain scheduled feedback controllers and guarantees local and global closed-loop system stability for general nonlinear systems. Furthermore, the hierarchical switching control framework is extended to include inverse optimality notions. Specifically, the hierarchical controller is parameterized with respect to a given system equilibrium manifold wherein an inverse optimal morphing strategy is constructed to coordinate the hierarchical switching. The overall approach is quite different from the quasivariational inequality methods for optimal switching systems developed in the literature in that our results provide hierarchical homotopic feedback controllers guaranteeing closed-loop stability via an underlying Lyapunov function. Finally, the proposed control framework is extended to account for system parametric uncertainty wherein the hierarchical switching architecture is parameterized over a set of moving nominal system equilibria.