Recursive feasibility without terminal constraints via parent–child MPC architecture

Abstract

This paper introduces a novel hierarchical model predictive control (MPC) framework, called the Parent–Child MPC architecture, designed to ensure recursive feasibility without relying on terminal constraints. The proposed architecture targets nonlinear constrained systems with Lipschitz continuous dynamics, such as quadrotors, helicopters and autonomous bicycles. For such systems, traditional MPC approaches may suffer from computational intractability or conservativeness due to needing terminal constraints. The proposed framework couples a small-horizon, high-fidelity Child MPC with one or more large-horizon, simplified Parent MPC layers. The Parent layers provide robust invariant tubes that replace terminal constraints, enabling scalable planning and stability guarantees. Two case studies, including a linear double integrator system and a nonlinear system, demonstrate the effectiveness of the architecture. Compared to standard robust tube-based MPC, the Parent–Child MPC achieves up to an eight-fold reduction in solver time and a three-fold increase in controllable prediction horizon. It also maintains performance within 3% of robust tube-based MPC. These results highlight the potential of this architecture for real-time control of complex, nonlinear systems under uncertainty.