Stable MPC Design for Hybrid Mixed Logical Dynamical Systems: $l_{\infty}$-based Lyapunov Approach
For control engineers working on hybrid systems, this provides a computationally simpler stability guarantee, but the approach is incremental as it adapts existing Lyapunov-based MPC techniques to MLD systems.
The paper proposes exponential stability conditions for hybrid systems in Mixed Logical Dynamical form with Model Predictive Control, using an infinity-norm-based Lyapunov function to avoid terminal equality constraints. The method reduces computational complexity and achieves stability independent of prediction horizon, demonstrated on a car suspension system.
There are two main challenges in control of hybrid systems which are to guarantee the closed-loop stability and reduce computational complexity. In this paper, we propose the exponential stability conditions of hybrid systems which are described in the Mixed Logical Dynamical (MLD) form in closed-loop with Model Predictive Control (MPC). To do this, it is proposed to use the decreasing condition of infinity norm based Lyapunov function instead of imposing the terminal equality constraint in the MPC formulation of MLD system. The exponential stability conditions have a better performance from both implementation and computational points of view. In addition, the exponential stability conditions of the equilibrium point of the MLD system do not depend on the prediction horizon of MPC problem which is the main advantage of the proposed method. On the other hand, by using the decreasing condition of the Lyapunov function in the MPC setup, the suboptimal version of the control signal with reduced complexity is obtained. In order to show the capabilities of the proposed method, the stabilization problem of the car suspension system is studied.