The field of control systems is witnessing significant developments in data-driven control and adaptive Linear Quadratic Regulator (LQR) methods. Researchers are exploring innovative approaches to improve the stability and performance of systems using input-output data matrices and robust linear regression techniques. Notably, the use of Moore-Penrose inverses and primal-dual estimation procedures are being employed to guarantee stability and obtain unbiased gradient estimates. Furthermore, epoch-based approaches and direct Model-Reference Adaptive Control (MRAC) are being leveraged to overcome drawbacks in existing adaptive LQR methods. These advancements have the potential to enhance the efficiency and robustness of control systems in various applications.

Noteworthy papers include: The paper on Input-Output Data-Driven Representation, which shows that latent poles in data-driven representations are guaranteed to be stable using Moore-Penrose inverses. The paper on Sample-Efficient Model-Free Policy Gradient Methods, which establishes convergence guarantees with a sample complexity of order O(1/epsilon) for solving the LQR problem in unknown stochastic linear systems. The paper on Adapt and Stabilize, Then Learn and Optimize, which proposes a new algorithm that overcomes existing drawbacks in adaptive LQR methods with a provable high-probability regret bound.