Analysis of Time-Distributed Model Predictive Control When Using a Regularized Primal–Dual Gradient Optimizer

Abstract

Time-distributed Optimization (TDO) is a method for reducing the computational cost of Model Predictive Control (MPC) where optimization iterations are distributed over time by maintaining a running solution estimate that is updated at each sampling instant. In this letter, TDO is applied to linear MPC with state and input constraints using a regularized primal-dual gradient descent method as the optimizer. A detailed analysis of the rate of convergence shows how different design choices, i.e., maximum number of iterations, value of the regularization term, and prediction horizon length, affect the stability of TDO-MPC. Additionally, it is shown that significant stability improvements can be achieved by using the Closed-Loop Paradigm to improve the conditioning number of the optimal control problem. Numerical simulations on an open-loop unstable system demonstrate the overall impact on stability and constraint satisfaction of each design choice.