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

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...

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Bibliographic Details
Published inIEEE control systems letters Vol. 7; pp. 235 - 240
Main Authors Skibik, Terrence, Nicotra, Marco M.
Format Journal Article
LanguageEnglish
Published IEEE 2023
Subjects
Asymptotic stability
Costs
Heuristic algorithms
Numerical stability
optimal control
Optimization
Predictive control
real-time systems
stability analysis
Stability criteria
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Summary: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.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2022.3186631