Fast Gradient Method for Model Predictive Control with Input Rate and Amplitude Constraints⁎This research is supported by the Engineering and Physical Sciences Research Council (EPSRC) with a Diamond CASE studentship. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Kempf, Idris; Goulart, Paul; Duncan, Stephen
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 6542
• Page End: 6547
• Publication Date: 2020
• Subjects: Model Predictive Control (MPC) -- Fast Gradient Method -- Dykstra's Method -- Alternating Direction of Multipliers Method (ADMM) -- Projection -- Rate Constraints; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.070
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs. Instead of augmenting the decision variables of the underlying finite-horizon optimal control problem to accommodate the input rate constraints, we propose to solve this problem using the fast gradient method, where the projection step is solved using Dykstra's algorithm. We show that, relative to the Alternating Direction of Method Multipliers (ADMM), this approach greatly reduces the computation time while halving the memory usage. Our algorithm is implemented in C and its performance demonstrated using several examples.