Convex Lifting Based Inverse Parametric Optimization for Implicit Model Predictive Control: A Case Study

Abstract

In this paper we revisit the problem of finding an equivalent inverse optimality formulation to a given linear model predictive control (MPC) problem using the technique of inverse parametric convex programming based on convex lifting. In particular, we show that the parametric solution to a typical QP-based MPC problem can be used to formulate an equivalent LP problem with a significantly reduced space of decision variables and a new set of constraints, the solution of which in both explicit and implicit fashion implies a lower online implementation effort. This is also demonstrated in a practical case study focused on active vibration control, using various optimization methods to solve both the nominal and the reformulated MPC problem. The obtained results suggest a potential of the convex lifting based inverse optimality technique for example in embedded MPC applications where, based on hardware specifications, either explicit or implicit solution is more suitable.