相关论文: Solving the Model Unavailable MARE using Q-Learnin…
Reinforcement learning improves the reasoning ability of large language models but remains costly and sample-inefficient, as many rollouts provide weak learning signals. Difficulty-aware data selection methods attempt to address this by…
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the…
We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional…
A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward…
The State-Dependent Riccati Equation (SDRE) technique generalizes the classical algebraic Riccati formulation to nonlinear systems by designing an input to the system that optimally(suboptimally) regulates system states toward the origin…
In this paper we mainly propose efficient and reliable numerical algorithms for solving stochastic continuous-time algebraic Riccati equations (SCARE) typically arising from the differential statedependent Riccati equation technique from…
This paper considers a stochastic linear quadratic problem for discrete-time systems with multiplicative noises over an infinite horizon. To obtain the optimal solution, we propose an online iterative algorithm of reinforcement learning…
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
Using the tools of optimal control, semiconvex duality and \maxp algebra, this work derives a unifying representation of the solution for the matrix differential Riccati equation (DRE) with time-varying coefficients. It is based upon a…
Q-learning is a promising method for solving optimal control problems for uncertain systems without the explicit need for system identification. However, approaches for continuous-time Q-learning have limited provable safety guarantees,…
Reinforcement learning (RL) is a classical tool to solve network control or policy optimization problems in unknown environments. The original Q-learning suffers from performance and complexity challenges across very large networks. Herein,…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…
The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
Reinforcement learning (RL) is a class of artificial intelligence algorithms being used to design adaptive optimal controllers through online learning. This paper presents a model-free, real-time, data-efficient Q-learning-based algorithm…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
Differential Riccati equations (DREs) are semilinear matrix- or operator-valued differential equations with quadratic non-linearities. They arise in many different areas, and are particularly important in optimal control of linear quadratic…
Domain incremental learning (DIL) poses a significant challenge in real-world scenarios, as models need to be sequentially trained on diverse domains over time, all the while avoiding catastrophic forgetting. Mitigating representation…
An online policy learning problem of linear control systems is studied. In this problem, the control system is known and linear, and a sequence of quadratic cost functions is revealed to the controller in hindsight, and the controller…