Guaranteed cost model predictive control approaches for linear systems subject to multiplicative uncertainties with applications to autonomous vehicles - Massera Filho, Carlos Alberto de Magalhães (2019)
The Linear Quadratic Regulator (LQR) is an optimal control approach which aims to drive states of a linear system to its origin through the minimization of a quadratic cost functional. Such an approach has been widely successful for both theoretical and practical applications. However, when such controllers are subject to uncertainties, optimal closed-loop performance cannot be obtained since robustness properties are no longer guaranteed. Guaranteed Cost Controllers (GCC) presents robust asymptotic stability and provides a guaranteed upper bound to a quadratic cost function. Such method addresses the lack of performance guarantees of the LQR. Meanwhile, Model Predictive Control (MPC) is a class of optimization-based control algorithms that use an explicit model of the controlled system to predict its future states. The MPC can be as a generalization of the LQR for constrained linear systems. Therefore, it equally suffers from a lack of robustness guarantees when the system is subject to uncertainties. Robust MPC (RMPC) approaches were proposed to address MPCs poor closed-loop performance subject to uncertainties. Its objective is to obtain a control input sequence that simultaneously minimizes a cost function and guarantees the feasibility of system states and control inputs, for a system subject to the worst-case disturbance within an uncertainty set. Autonomous vehicles have gained increasing interest from both the industry and research communities in recent years. An essential aspect in the design of automotive control systems is to ensure the controller is stable and has acceptable performance within the entire operational envelope which it is designed to operate. In the case of autonomous vehicles, where there is no human driver as a fallback, it is of utmost importance to ensure the safe operations of the control system and its capability to avoid saturating the handling limits of the vehicle. In this thesis, we propose Guaranteed Cost Controller approaches for both unconstrained and constrained linear systems subject to multiplicative structured norm-bounded uncertainties and present the application of such a controller to the lateral control problem of autonomous vehicles up to the tire saturation limits.