Sensitivity-Based Distributed Model Predictive Control for Nonlinear Systems under Inexact Optimization

TL;DR

This paper introduces a distributed model predictive control scheme for nonlinear systems that uses a sensitivity-based algorithm, enabling efficient, parallelized optimization with convergence guarantees and real-time applicability.

Contribution

It proposes a novel sensitivity-based distributed MPC algorithm with proven convergence and stability for nonlinear systems, suitable for real-time implementation.

Findings

Algorithm converges to the central solution under certain conditions.

Stability is maintained despite inexact minimization.

Numerical simulations confirm real-time feasibility.

Abstract

This paper presents a distributed model predictive control (DMPC) scheme for nonlinear continuous-time systems. The underlying distributed optimal control problem is cooperatively solved in parallel via a sensitivity-based algorithm. The algorithm is fully distributed in the sense that only one neighbor-to-neighbor communication step per iteration is necessary and that all computations are performed locally. Sufficient conditions are derived for the algorithm to converge towards the central solution. Based on this result, stability is shown for the suboptimal DMPC scheme under inexact minimization with the sensitivity-based algorithm and verified with numerical simulations. In particular, stability can be guaranteed with either a suitable stopping criterion or a fixed number of algorithm iterations in each MPC sampling step which allows for a real-time capable implementation.