Real-Time Non-Smooth MPC for Switching Systems: Application to a Three-Tank Process

TL;DR

This paper develops a real-time non-smooth model predictive control method for switching systems, demonstrated on a three-tank process, avoiding mixed-integer formulations and ensuring efficient, mode-consistent control in hardware experiments.

Contribution

It introduces a non-smooth MPC scheme combining Filippov modeling, finite elements, and complementarity constraints, specifically tailored for a three-tank system without mixed-integer optimization.

Findings

Successful real-time control of a three-tank system with switching dynamics.

Efficient handling of switching events and mode transitions in hardware.

Performance remains robust under model mismatch and within real-time constraints.

Abstract

Real-time model predictive control of non-smooth switching systems remains challenging due to discontinuities and the presence of discrete modes, which complicate numerical integration and optimization. This paper presents a real-time feasible non-smooth model predictive control scheme for a physical three-tank process, implemented without mixed-integer formulations. The approach combines Filippov system modeling with finite elements and switch detection for time discretization, leading to a finite-dimensional optimal control problem formulated as a mathematical program with complementarity constraints. The mathematical program is solved via a homotopy of smooth nonlinear programs. We introduce modeling adjustments that make the three-tank dynamics numerically tractable, including additional modes to avoid non-Lipschitz points and undefined function values. Hardware experiments demonstrate efficient handling of switching events, mode-consistent tracking across reference changes, correct boundary handling, and constraint satisfaction. Furthermore, we investigate the impact of model mismatch and show that the tracking performance and computation times remain within real-time limits for the chosen sampling time. The complete controller is implemented using the non-smooth optimal control framework NOSNOC