Robust Predictive Control for Uncertain Nonlinear Systems via Funnel Synthesis

Abstract

This thesis studies robust predictive control for uncertain nonlinear systems, with an emphasis on constrained control synthesis through convex optimization-based approaches. Ensuring constraint satisfaction and robustness under disturbances and model uncertainty is a central challenge in the design of control systems for safety-critical applications. The control framework consists of two modules: a trajectory generation module that computes a nominal state and an open-loop input, and a state feedback module that compensates for deviations from the nominal. The combined input is applied to the system to ensure robustness and constraint satisfaction. This thesis develops novel methods and theoretical results that enable the design of such systems under broader classes of nonlinearities and uncertainties, while improving computational efficiency and enhancing the accuracy of constraint satisfaction. A central element is funnel synthesis, in which time-varying invariant funnels and associated feedback controllers are synthesized around nominal trajectories. New formulations are introduced using time-varying incremental quadratic constraints, enabling the handling of nonlinearities beyond Lipschitz continuity. The funnel invariance condition is derived via a differential linear matrix inequality using Lyapunov theory. To solve the continuous-time funnel synthesis problem, an optimal control framework supporting higher-order funnel representations is proposed. Three convex approaches are developed to address continuous-time constraint satisfaction (CTCS) for funnel synthesis. The first introduces intermediate constraint-checking points without increasing the number of decision variables. The second reformulates continuous-time linear matrix inequalities as nodal constraints via an exterior penalty on constraint violations, evaluated at discrete time points and solved using a subgradient-based successive convexification algorithm. The third approach, based on a matrix copositivity condition, achieves CTCS without additional intermediate checking points or constraint reformulation, offering a structured but conservative alternative. Finally, joint synthesis algorithms are proposed to compute both the nominal trajectory and the associated funnel within a unified framework, reducing the conservatism that arises when they are optimized separately. The proposed methods are demonstrated on systems including a unicycle, a 6-degree-of-freedom (6-DoF) free-flyer, a 6-DoF quadrotor, and a powered descent guidance scenario for a 6-DoF rocket.