Related papers: A Q-learning algorithm for discrete-time linear-qu…
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…
We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$…
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the deterministic case is to provide the desired feedback controls for linear quadratic…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters.…
In this paper, we will deal with a Linear Quadratic Optimal Control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability…
This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases the…
In this paper, we solve the long-standing fundamental problem of irregular linear--quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding…
In this paper, the finite horizon asymmetric information linear quadratic (LQ) control problem is investigated for a discrete-time mean field system. Different from previous works, multiple controllers with different information sets are…
Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online…
We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an…
We present a continuous-time equivalent to the well-known iterative linear-quadratic algorithm including an implementation of a backtracking line-search policy and a novel regularization approach based on the necessary conditions in the…
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…
Q-learning is a popular reinforcement learning algorithm. This algorithm has however been studied and analysed mainly in the infinite horizon setting. There are several important applications which can be modeled in the framework of finite…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
In this paper, we propose Q-learning algorithms for continuous-time deterministic optimal control problems with Lipschitz continuous controls. Our method is based on a new class of Hamilton-Jacobi-Bellman (HJB) equations derived from…
This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic…
In control and engineering community, models generally contain a number of parameters which are unknown or roughly known. A complete knowledge of these parameters is critical to describe and analyze the dynamics of the system. This paper…
This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…