Linear Quadratic Regulator

The Linear Quadratic Regulator (LQR) is a fundamental optimal control technique aiming to find the optimal control law that minimizes a quadratic cost function for linear systems. Current research emphasizes improving LQR's robustness and efficiency, particularly in handling uncertainties, constraints, and high-dimensional systems, often employing machine learning methods like neural networks and reinforcement learning algorithms such as Proximal Policy Optimization and Thompson Sampling to address these challenges. These advancements are significant for various applications, including robotics, autonomous vehicles, and aerospace engineering, by enabling more accurate, adaptable, and computationally efficient control of complex dynamic systems. Furthermore, research is actively exploring efficient algorithms for constrained LQR problems and investigating the theoretical properties of LQR learning, such as convergence rates and sample complexity.