Sampled-data primal–dual gradient dynamics in model predictive control

Ryuta Moriyasu

doi:10.1016/j.automatica.2025.112621

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Sampled-data primal–dual gradient dynamics in model predictive control

2025-09-22

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Ryuta Moriyasu

Sho Kawaguchi

Kenji Kashima *

DOI：10.1016/j.automatica.2025.112621

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Abstract

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Model predictive control (MPC) can incur computational burden that exceeds what the application warrants, sometimes even for linear systems. Recently, a rapid computation method that guides the input toward convergence with the optimal control problem solution by employing primal–dual gradient (PDG) dynamics has been proposed for linear MPCs. However, stability has been ensured under the assumption that the controller is a continuous-time system, leading to potential instability when the controller undergoes discretization and is implemented as a sampled-data system. In this paper, we propose a discrete-time dynamical controller incorporating specific modifications to the PDG approach and present stability conditions. Additionally, we introduce an extension to enhance control performance that was traded off in the original. Numerical examples substantiate that our proposed method, which can be executed in only 1μs on a commodity laptop, not only ensures stability considering sampled-data implementation but also substantially enhances the control performance.

Keywords:

Model predictive control

Primal–dual gradient

Sampled-data system

Stability

Dissipativity

Fast computation