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The convergence of policy gradient algorithms in reinforcement learning hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of…
The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control.…
This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for…
In this work, we revisit the Linear Quadratic Gaussian (LQG) optimal control problem from a behavioral perspective. Motivated by the suitability of behavioral models for data-driven control, we begin with a reformulation of the LQG problem…
This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers…
We consider the problem of controlling a linear dynamical system from bilinear observations with minimal quadratic cost. Despite the similarity of this problem to standard linear quadratic Gaussian (LQG) control, we show that when the…
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 studies the data-driven synthesis of linear quadratic integral (LQI) controllers for continuous-time systems. The objective is to achieve optimal state-feedback control with integral action for reference tracking using only…
The Linear Quadratic Gaussian (LQG) problem is a classic and widely studied model in optimal control, providing a fundamental framework for designing controllers for linear systems subject to process and observation noises. In recent years,…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
Linear Quadratic Regulator (LQR) design is one of the most classical optimal control problems, whose well-known solution is an input sequence expressed as a state-feedback. In this work, finite-horizon and discrete-time LQR is solved under…
Linear-Quadratic-Gaussian (LQG) control is concerned with the design of an optimal controller and estimator for linear Gaussian systems with imperfect state information. Standard LQG assumes the set of sensor measurements, to be fed to the…
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, network of agents with identical dynamics is considered. The agents are assumed to be fed by self and neighboring output measurements, while the states are not available for measuring. Viewing distributed estimation as dual…
Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with…
We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed…
This paper first presents necessary and sufficient conditions for the solvability of discrete time, mean-field, stochastic linear-quadratic optimal control problems. Then, by introducing several sequences of bounded linear operators, the…
The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The…
For various typical cases and situations where the formulation results in an optimal control problem, the Linear Quadratic Regulator (LQR) approach and its variants continue to be highly attractive. In certain scenarios, it can happen that…
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,…