Fast MPC Solvers for Systems with Hard Real-Time Constraints

Abstract

Model predictive control (MPC) is an advanced control technique that offers an elegant framework to solve a wide range of control problems (regulation, tracking, supervision, etc) and handle constraints on the plant. The control objectives and constraints are usually formulated as an optimization problem that the MPC controller has to solve (either offline or online) to return the control command for the plant. This master thesis proposes a novel primal-dual interior-point (PDIP) method for solving quadratic programming problems with linear inequality constraints that typically arise from MPC applications. Convergence of PDIP is studied both in primal and dual framework. We show that the solver converges quadratically to a suboptimal solution of the MPC problem. PDIP solvers rely on two phases: the damped and the pure Newton phases. Compared to state-of-the-art PDIP method, this new solver replaces the initial (linearly convergent) damped Newton phase (usually used to compute a medium-accuracy solution) with a dual solver based on Nesterov's fast gradient scheme (DFG) that converges super-linearly to a medium-accuracy solution. The switching strategy to the pure Newton phase, compared to the state of the art, is computed in the dual space to exploit the dual information provided by the DFG in the first phase. Removing the damped Newton phase has the additional advantage that this solver saves the computational effort required by backtracking line search. The effectiveness of the proposed solver is demonstrated by simulating it on a 2-dimensional discrete-time unstable system.