A Simple and Fast Coordinate-Descent Augmented-Lagrangian Solver for Model Predictive Control

Abstract

This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by coordinate descent (CD), whose computation cost depends linearly on the prediction horizon and quadratically on the state and input dimensions. CDAL is simple to implement and does not require constructing explicitly the matrices of the quadratic programming problem to solve. To favor convergence speed, CDAL employs a reverse cyclic rule for the CD method, the accelerated Nesterov's scheme for updating the dual variables, and a simple diagonal preconditioner. We show that CDAL competes with other state-of-the-art first-order methods, both in case of unstable linear time-invariant and prediction models linearized at runtime. All numerical results are obtained from a very compact, library-free, C implementation of the proposed CDAL solver.