Piecewise Lyapunov Function–Based Robust Model Predictive Control for Asymmetric Input‐Saturated Systems with External Disturbances

ABSTRACT Asymmetric input saturation, resulting from physical limits or safety requirements, is prevalent in industrial systems. This poses a significant challenge for control design. However, few studies have been done from the perspective of predictive control for uncertain systems. The conventional symmetric saturation approximation method leads to conservative performance. To address this gap, this paper proposes a novel robust model predictive control (RMPC) scheme for systems with model uncertainty and disturbance under asymmetric saturation. By partitioning the state space according to the control law, the asymmetric input‐saturated system is equivalently transformed into a piecewise model, where each sub‐model has a symmetric deadzone. This allows for full consideration of the actual boundaries of asymmetric saturation. Then, an infinite‐horizon RMPC optimization design is developed, incorporating common or piecewise Lyapunov functions. The stability conditions and constraints are established based on the piecewise model. Due to the exploitation of the asymmetric saturation range, the proposed RMPC approach can achieve less conservative solutions. Finally, recursive feasibility and closed‐loop stability of the proposed optimization problems are ensured through set invariance theory and Lyapunov analysis. The results of simulations, including a double integrator and a reactor‐separator process, confirm that the proposed approach can effectively improve dynamic performance compared to existing methods.