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arXiv · 2411.10795

Stochastic Optimal Linear Quadratic Regulation Control of Discrete-time Systems with Delay and Quadratic Constraints

Dawei Liu·Juanjuan Xu·huanshui Zhang
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Abstract

This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases the complexity of the problem. Using Lagrangian duality, the optimal control is obtained by solving the Riccati-ZXL equation in conjunction with a gradient ascent algorithm. Specifically, the parameterized optimal controller and cost function are derived by solving the Riccati-ZXL equation, with a gradient ascent algorithm determining the optimal parameter. The primary contribution of this work is presenting the optimal control as a feedback mechanism based on the state's conditional expectation, wherein the gain is determined using the Riccati-ZXL equation and the gradient ascent algorithm. Numerical examples demonstrate the effectiveness of the obtained results.

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BibTeXRIS

Dawei Liu, Juanjuan Xu, huanshui Zhang. 2024-11-16. Stochastic Optimal Linear Quadratic Regulation Control of Discrete-time Systems with Delay and Quadratic Constraints. https://arxiv.org/abs/2411.10795

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