Stable and robust LQR design via scenario approach. (July 2021)

• Record Type: Journal Article
• Authors: Scampicchio, Anna; Aravkin, Aleksandr; Pillonetto, Gianluigi
• Is Part Of: Automatica. Volume 129(2021)
• Publication Date: 2021-07
• Subjects: Optimal control -- LQR design -- Reinforcement learning -- Lyapunov stability -- Scenario approach -- Population growth models; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109571
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: Linear Quadratic Regulator (LQR) design is one of the most classical optimal control problems, whose well-known solution is an input sequence expressed as a state-feedback. In this work, finite-horizon and discrete-time LQR is solved under stability constraints and uncertain system dynamics. The resulting feedback controller balances cost value and closed-loop stability. Robustness of the solution is modeled using the scenario approach, without requiring any probabilistic description of the uncertainty in the system matrices. The new methods are tested and compared on the Leslie growth model, where we control population size while minimizing a suitable finite-horizon cost function.