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The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online…
The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all…
A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
Designing controllers to generate various trajectories has been studied for years, while recently, recovering an optimal controller from trajectories receives increasing attention. In this paper, we reveal that the inherent linear quadratic…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
Domain randomization is a simple, effective, and flexible scheme for obtaining robust feedback policies aimed at reducing the sim-to-real gap due to model mismatch. While domain randomization methods have yielded impressive demonstrations…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
We consider the static output feedback control for Linear Quadratic Regulator problems with structured constraints under the assumption that system parameters are unknown. To solve the problem in the model free setting, we propose the…
The Linear Quadratic Regulator (LQR) is a cornerstone of optimal control theory, widely studied in both model-based and model-free approaches. Despite its well-established nature, certain foundational aspects remain subtle. In this paper,…
In this paper, we investigate a data-driven framework to solve Linear Quadratic Regulator (LQR) problems when the dynamics is unknown, with the additional challenge of providing stability certificates for the overall learning and control…
We study the convergence of deterministic policy gradient algorithms in continuous state and action space for the prototypical Linear Quadratic Regulator (LQR) problem when the search space is not limited to the family of linear policies.…
We present a model-based globally convergent policy gradient method (PGM) for linear quadratic Gaussian (LQG) control. Firstly, we establish equivalence between optimizing dynamic output feedback controllers and designing a static feedback…
We revisit in this paper the discrete-time linear quadratic regulator (LQR) problem from the perspective of receding-horizon policy gradient (RHPG), a newly developed model-free learning framework for control applications. We provide a…
We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an input-output-history (IOH) representation of the closed-loop system. First, we show that any dynamic…
Linear-quadratic regulator (LQR) is a landmark problem in the field of optimal control, which is the concern of this paper. Generally, LQR is classified into state-feedback LQR (SLQR) and output-feedback LQR (OLQR) based on whether the full…
In this paper, we investigate a model-free optimal control design that minimizes an infinite horizon average expected quadratic cost of states and control actions subject to a probabilistic risk or chance constraint using input-output data.…
In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…
We develop a dynamic trading strategy in the Linear Quadratic Regulator (LQR) framework. By including a price mean-reversion signal into the optimization program, in a trading environment where market impact is linear and stage costs are…
Direct data-driven optimal control provides an elegant end-to-end paradigm, yet its real-time applicability is often hindered by the growing dimensionality of online decision variables. Recent breakthroughs, notably Data-EnablEd Policy…