Reliable Active-Set Solvers for Real-Time MPC (Daniel Arnström)

Abstract:
In Model Predictive Control (MPC), control problems are formulated as optimization problems, allowing for constraints on actuators and system states to be directly accounted for. Implicitly defining a control law through an optimization problem does, however, make the evaluation of the control law more complex compared with classical PID and LQ controllers. As a result, determining the worst-case computational time for evaluating the control law becomes non-trivial, yet such worst-case bounds are essential for applying MPC to control safety-critical systems in real time, especially when the controller is implemented on limited hardware.
The optimization problems that need to be solved in linear MPC are often quadratic programs (QPs), and the corresponding optimization method that is used is often an active-set method.
In this talk we will present a recently developed complexity-certification framework for active-set QP solvers; this framework determines the exact worst-case computational complexity for a family of active-set solvers, which include the recently developed active-set solver DAQP. In addition to being real-time certifiable, DAQP is efficient, can easily be warm-started, and is numerically stable, all of which are important properties for a solver used in real-time MPC applications.