An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

Time-distributed optimization (TDO) is an approach for reducing the computational burden of model predictive control (MPC) and a generalization real-time iteration scheme. When using TDO, iterations are distributed over time by maintaining running solution estimate updating it at each sampling instant. In this article, TDO applied to input-constrained linear-quadratic MPC studied in detail, analytic bound number per instant required guarantee closed-loop stability derived. Further, shown that TDO-based can be guaranteed multiple mechanisms, including increasing solver iterations, preconditioning optimal problem, adjusting cost matrices, length receding horizon. These results linear system setting also provide insights guidelines could more broadly applicable, example, nonlinear MPC.