Autonomy Talks - Andrea Zanelli: Efficient inexact numerical methods for nonlinear MPC

Autonomy Talks - 15/11/2021

Speaker: Dr. Andrea Zanelli, Institute for Dynamic Systems and Control, ETH Zürich

Title: Efficient inexact numerical methods for nonlinear model predictive control with feasibility guarantees with applications to autonomous racing

Abstract: Model predictive control is an optimization-based control strategy that can inherently address multivariate, nonlinear and constrained control problems. However, it requires that a nonconvex program is solved within the time available between subsequent sam- pling instants. Although considerable progress has been made since its early application in the late 1970s in the process industry, MPC still requires a computational effort that is prohibitive for many applications due to fast dynamics or the low computational power available. For this reason, despite MPC being nowadays the state-of-the-art control strat- egy in many applications, its applicability to a broader range of systems, still hinges on the development of efficient methods for numerical optimization.
In this talk, we propose inexact methods that can speed up the computations asso- ciated with the solution of the underlying nonconvex programs. Although drawing from rather diverse areas, from an abstract point of view, such methods exploit a common idea. In fact, in many cases, carefully chosen perturbations to exact solutions and formulations do not jeopardize fundamental properties such as stability and recursive feasibility and can be leveraged to alleviate the computational burden of MPC.
The second method discussed in the talk aims at reducing the computational footprint of robust MPC with ellipsoidal uncertainty. An inexact sequential quadratic programming strategy is proposed that can efficiently compute suboptimal, but feasible solutions to the robustified nonconvex programs. Convergence properties and asymptotic behavior of the approximate solutions are investigated and the computational benefits of the algorithm are assessed in a numerical benchmark where speedups of up to 3 orders of magnitude can be obtained.