Abstract
This talk will describe a novel approach for computationally tractable, data-driven, optimisation-based control for applications in which safety is critical. Starting with a brief introduction to the main concepts and challenges, the discussion will motivate recent work on Model Predictive Control (MPC) and the convex-concave procedure for finding locally optimal solutions of nonconvex problems. We will consider how to use differences of convex (DC) functions to derive convex conditions that allow control system performance to be optimized as a sequence of convex sub-problems.
Using sequences of sets (tubes) to bound predicted trajectory, the method provides guaranteed robustness to uncertainty, and it allows warm-starting and early-termination at feasible suboptimal solutions. Key properties and theoretical results, including feasibility, convergence, optimality and closed loop stability will be discussed. The talk will explain how DC representations can be computed directly from data and how model estimation can be performed online simultaneously with control to define safe learning-based control algorithms. We will discuss data-driven techniques using neural networks, machine learning and sum-of-squares polynomials to obtain systematic DC decompositions of nonlinear system dynamics.
We will discuss three diverse applications of these techniques: transitioning tiltwing aircraft between vertical and horizontal filght, controlling batch-fed bioreactors, and deep brain stimulation.
Biographical Information
I studied engineering as an undergraduate (MEng in Engineering Science) and completed a doctorate (DPhil) at the University of Oxford, graduating in 1993 and 1998. Between these I did a master’s degree (SM) at Massachusetts Institute of Technology, graduating in 1995. Since 2002 I have been with the Engineering Science Department and a Fellow of St John’s College. I am Professor of Engineering Science a member of the Oxford Control Group. My research is about designing feedback controllers for uncertain systems in order to optimize performance subject to constraints. I am interested in the fundamental properties of optmization-based control strategies such as feasibility and closed-loop stability, as well as issues such as convexity and efficiency of computation, stochastic uncertainty and online model adaptation. Current and past applications I have considered include power management in EVs and hybrid electric aircraft, trajectory optimization in VTOL aircraft, deep brain stimulation (DBS) in medical applications, and bioprocess control.