arXiv subjects

Xiushan Jiang

Publications and source records attributed to Xiushan Jiang.

6 recordsLinked to original sources

arXiv2025

Model-free stochastic linear quadratic control for discrete-time systems with multiplicative and additive noises via semidefinite programming

This paper investigates a model-free solution to the stochastic linear quadratic regulation (LQR) problem for linear discrete-time systems with both multiplicative and additive noises. We formulate the stochastic LQR problem as a nonconvex optimization problem and rigorously analyze its dual problem structure. By exploiting the inherent convexity of the dual problem and analyzing Karush-Kuhn-Tucker conditions with respect to optimality in convex optimization, we establish an explicit relationship between the optimal point of the dual problem and the parameters of the associated Q-function. This theoretical insight, combined with the technique of the matrix direct sum, makes it possible to develop a novel model-free sample-efficient, non-iterative semidefinite programming algorithm that directly estimates optimal control gain without requiring an initial stabilizing controller, or noises measurability. The robustness of the model-free SDP method to errors is investigated. Our approach provides a new optimization-theoretic framework for understanding Q-learning algorithms while advancing the theoretical foundations of reinforcement learning in stochastic optimal control. Numerical validation on a pulse-width modulated inverter system demonstrates the algorithm's effectiveness, particularly in achieving a single-step non-iterative solution without hyper-parameter tuning.

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arXiv2025

Primal-dual policy learning for mean-field stochastic LQR problem

Integrating data-driven techniques with mechanism-driven insights has recently gained popularity as a powerful learning approach to solving traditional LQR problems for designing intelligent controllers in complex dynamic systems. However, the theoretical understanding of various reinforcement learning algorithms needs further exploration to enhance their efficiency and safety. In this article, by means of primal-dual optimization tools, we study the partially model-free design of the mean-field stochastic LQR (MF-SLQR) controller using a policy learning approach. Firstly, by designing appropriate optimizing variables, the considered MF-SLQR problem is transformed into a new static nonconvex constrained optimization problem with equivalence preserved in certain senses. After that, the equivalent formulation of the duality results is constructed via finding the solution of the generalized Lyapunov equation. Then, the strong duality is analyzed, based on which we establish a primal-dual algorithm by Karush-Kuhn-Tucker conditions. More importantly, a partially model-free implementation is also presented, which has a direct connection with the classical policy iteration algorithm. Finally, we use a high-dimensional example to validate our methods.

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arXiv2025

Learning-based primal-dual optimal control of discrete-time stochastic systems with multiplicative noise

Reinforcement learning (RL) is an effective approach for solving optimal control problems without knowing the exact information of the system model. However, the classical Q-learning method, a model-free RL algorithm, has its limitations, such as lack of strict theoretical analysis and the need for artificial disturbances during implementation. This paper explores the partially model-free stochastic linear quadratic regulator (SLQR) problem for a system with multiplicative noise from the primal-dual perspective to address these challenges. This approach lays a strong theoretical foundation for understanding the intrinsic mechanisms of classical RL algorithms. We reformulate the SLQR into a non-convex primal-dual optimization problem and derive a strong duality result, which enables us to provide model-based and model-free algorithms for SLQR optimal policy design based on the Karush-Kuhn-Tucker (KKT) conditions. An illustrative example demonstrates the proposed model-free algorithm's validity, showcasing the central nervous system's learning mechanism in human arm movement.

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arXiv2024

Model-free stochastic linear quadratic design by semidefinite programming

In this article, we study a model-free design approach for stochastic linear quadratic (SLQ) controllers. Based on the convexity of the SLQ dual problem and the Karush-Kuhn-Tucker (KKT) conditions, we find the relationship between the optimal point of the dual problem and the Q-function, which can be used to develop a novel model-free semidefinite programming (SDP) algorithm for deriving optimal control gain. This study provides a new optimization perspective for understanding Q-learning algorithms and lays a theoretical foundation for effective reinforcement learning (RL) algorithms. Finally, the effectiveness of the proposed model-free SDP algorithm is demonstrated by two case simulations.

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arXiv2024

Model-free $H_{\infty}$ control of Itô stochastic system via off-policy reinforcement learning

The stochastic $H_{\infty}$ control is studied for a linear stochastic Itô system with an unknown system model. The linear stochastic $H_{\infty}$ control issue is known to be transformable into the problem of solving a so-called generalized algebraic Riccati equation (GARE), which is a nonlinear equation that is typically difficult to solve analytically. Worse, model-based techniques cannot be utilized to approximately solve a GARE when an accurate system model is unavailable or prohibitively expensive to construct in reality. To address these issues, an off-policy reinforcement learning (RL) approach is presented to learn the solution of a GARE from real system data rather than a system model; its convergence is demonstrated, and the robustness of RL to errors in the learning process is investigated. In the off-policy RL approach, the system data may be created with behavior policies rather than the target policies, which is highly significant and promising for use in actual systems. Finally, the proposed off-policy RL approach is validated on a stochastic linear F-16 aircraft system.

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arXiv2023

Model-free Reinforcement Learning for ${H_{2}/H_{\infty}}$ Control of Stochastic Discrete-time Systems

This paper proposes a reinforcement learning (RL) algorithm for infinite horizon $\rm {H_{2}/H_{\infty}}$ problem in a class of stochastic discrete-time systems, rather than using a set of coupled generalized algebraic Riccati equations (GAREs). The algorithm is able to learn the optimal control policy for the system even when its parameters are unknown. Additionally, the paper explores the effect of detection noise as well as the convergence of the algorithm, and shows that the control policy is admissible after a finite number of iterations. The algorithm is also able to handle multi-objective control problems within stochastic fields. Finally, the algorithm is applied to the F-16 aircraft autopilot with multiplicative noise.

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