Related papers: Linearly-constrained Linear Quadratic Regulator fr…
The linear quadratic regulator (LQR) problem is a cornerstone of automatic control, and it has been widely studied in the data-driven setting. The various data-driven approaches can be classified as indirect (i.e., based on an identified…
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
In this paper we study the linear quadratic regulation (LQR) problem for dynamical systems coupled over large-scale networks and obtain locally computable low-complexity solutions. The underlying large or even infinite networks are…
The solution of a constrained linear-quadratic regulator problem is determined by the set of its optimal active sets. We propose an algorithm that constructs this set of active sets for a desired horizon N from that for horizon N-1. While…
Consider a linear quadratic regulator (LQR) problem being solved in a model-free manner using the policy gradient approach. If the gradient of the quadratic cost is being transmitted across a rate-limited channel, both the convergence and…
A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by…
This paper is concerned with a kind of linear-quadratic (LQ) optimal control problem of backward stochastic differential equation (BSDE) with partial information. The cost functional includes cross terms between the state and control, and…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
Learning-based control methods for industrial processes leverage the repetitive nature of the underlying process to learn optimal inputs for the system. While many works focus on linear systems, real-world problems involve nonlinear…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
Consider a discrete-time Linear Quadratic Regulator (LQR) problem solved using policy gradient descent when the system matrices are unknown. The gradient is transmitted across a noisy channel over a finite time horizon using analog…
Distributed optimal control is known to be challenging and can become intractable even for linear-quadratic regulator problems. In this work, we study a special class of such problems where distributed state feedback controllers can give…
We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic…
We study the convergence of model-based policy gradient for the deterministic, scalar, discounted linear-quadratic regulator when the controller is an overparameterized one-hidden-layer ReLU network without biases. Although the optimal LQR…
Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the…
This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…