Feiran Zhao

Manuel Klädtke, Feiran Zhao, Florian Dörfler et al.

This paper proposes an explainability concept for direct data-driven linear quadratic regulation (LQR) with quadratic regularization. Our perspective follows the parametric effect of regularization, an analysis approach that translates regularization costs from auxiliary variables to system quantities, enabling intuitive interpretations. The framework further enables the elimination of auxiliary variables, thereby reducing computational complexity. We demonstrate the effectiveness of our approach and the identified effect of regularization via simulations.

Thierry Schwaller, Feiran Zhao, Florian Dörfler

The data-driven linear quadratic regulator (ddLQR) is a widely studied control method for unknown dynamical systems with disturbance. Existing approaches, both indirect, i.e., those that identify a model followed by model-based design, and direct, which bypasses the identification step, often rely on the certainty-equivalence principle and therefore do not explicitly account for model uncertainty. In this paper, we propose a Bayesian formulation for both indirect and direct ddLQR that incorporates posterior uncertainty into the control design. The resulting expected cost decomposes into a certainty-equivalence term and a variance-dependent term, providing a principled interpretation of regularization. We further show that the indirect and direct formulations are equivalent under this perspective. The resulting direct method admits a tractable semidefinite program whose size is independent of the data length. Numerical simulations demonstrate improved optimality gap and closed-loop stability, particularly in low-data regimes.

Feiran Zhao, Florian Dörfler

Unknown linear time-varying (LTV) systems require the control policy to adapt from online closed-loop data as dynamics evolve. Existing methods usually update the policy by solving a one-shot optimization problem, which can be computationally demanding and sensitive to noisy model estimates. In this paper, we propose a policy gradient adaptive control (PGAC) method for LTV system control with unknown model parameters. Specifically, PGAC integrates online policy optimization into feedback by updating the state-feedback policy with one-step gradient descent of the linear quadratic regulator cost at each time instant. This incremental update is computationally light and naturally limits policy variations caused by noisy data. To explicitly compute the policy gradient online, we estimate local models from recent closed-loop trajectories using normalized sliding-window least-squares. We provide stability and convergence certificates of PGAC for two classes of LTV systems. For slowly time-varying systems, we prove that the closed-loop system achieves practical exponential stability without a dwell-time condition. For piecewise-constant LTV systems, we establish practical stability through a dwell-time contraction argument. We also provide average frozen-time optimality-gap bounds of the policy sequence for both classes. Finally, we validate the effectiveness of our method via numerical case studies of both LTV and nonlinear systems.

Han Wang, Feiran Zhao, Florian Dorfler

This paper develops a data-enabled primal-dual framework for learning optimal control policies for unknown linear discrete-time systems from online data. The proposed approach views the data-dependent control synthesis problem as a time-varying semidefinite program (SDP) whose coefficients are recursively updated from online closed-loop measurements. Instead of repeatedly solving a full SDP as new data arrive, the policy is updated online through lightweight primal-dual iterations, each consisting of a linear equation solve and a projection onto the positive semidefinite cone. The framework applies to both direct and indirect data-driven formulations and covers a broad class of control objectives, including LQR, $H_\infty$ control, and safety-critical control. To characterize the coupling between online optimization and closed-loop data generation, we introduce two data-dependent quantities: the Sim-to-Real Gap, which measures the mismatch between noisy and noiseless data-induced SDPs, and the Difference-of-Signal, which measures the temporal variation of the SDP coefficients. Under persistency of excitation, suitable SDP regularity conditions, and sufficiently slow data variation, we establish a local linear tracking result up to residual terms governed by the latter two quantities. A global ergodic convergence bound is also derived for arbitrary initialization. Numerical examples on LQR, $H_\infty$ control, and safe exploration demonstrate that the proposed method can efficiently improve control performance from online data while accommodating SDP constraints beyond the well-explored LQR policy-gradient formulations.

Feiran Zhao, Keyou You

Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it as a discrete-time infinite-horizon LQR problem with a state predictive variance constraint. To solve it, we parameterize the policy with a feedback gain pair and leverage primal-dual methods to optimize it by solely using data. We first study the optimization landscape of the Lagrangian function and establish the strong duality in spite of its non-convex nature. Alongside, we find that the Lagrangian function enjoys an important local gradient dominance property, which is then exploited to develop a convergent random search algorithm to learn the dual function. Furthermore, we propose a primal-dual algorithm with global convergence to learn the optimal policy-multiplier pair. Finally, we validate our results via simulations.