State space sets with common optimal feedback laws for nonlinear MPC

TL;DR

This paper explores extending the concept of shared optimal feedback laws from linear to nonlinear MPC, proposing an algorithm to unify domains and reduce computational effort in solving optimal control problems.

Contribution

It introduces a novel algorithm for nonlinear MPC that unites state space domains with common optimal feedback laws, enhancing computational efficiency.

Findings

Unified domains increase reuse of feedback laws

Significant reduction in OCP computations demonstrated

Algorithm applicable to nonlinear MPC scenarios

Abstract

In model predictive control (MPC), an optimal control problem (OCP) is solved for the current state and the first input of the solution, the optimal feedback law, is applied to the system. This procedure requires to solve the OCP in every time step. Recently, a new approach was suggested for linear MPC. The parametric solution of a linear quadratic OCP is a piecewise-affine feedback law. The solution at a point in state space provides an optimal feedback law and a domain on which this law is the optimal solution. As long as the system remains in the domain, the law can be reused and the calculation of an OCP is avoided. In some domains the optimal feedback laws are identical. By uniting the corresponding domains, bigger domains are achieved and the optimal feedback law can be reused more often. In the present paper, we investigate in how far this approach can be extended from linear to nonlinear MPC, we propose an algorithm and we illustrate the achieved savings with an example.