Related papers: Learning the Riccati solution operator for time-va…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
In this paper, a cooperative Linear Quadratic Regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the…
This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…
In this letter, we explore the communication-control co-design of discrete-time stochastic linear systems through reinforcement learning. Specifically, we examine a closed-loop system involving two sequential decision-makers: a scheduler…
Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…
We develop a model-free learning algorithm for the infinite-horizon linear quadratic regulator (LQR) problem. Specifically, (risk) constraints and structured feedback are considered, in order to reduce the state deviation while allowing for…
In this paper, we propose and analyze a new method for online linear quadratic regulator (LQR) control with a priori unknown time-varying cost matrices. The cost matrices are revealed sequentially with the potential for future values to be…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
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…
With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying…
This paper studies a continuous-time stochastic linear-quadratic (SLQ) optimal control problem on infinite-horizon. A data-driven policy iteration algorithm is proposed to solve the SLQ problem. Without knowing three system coefficient…
The purpose of this paper is to close the remaining gaps in the understanding of the role that the constrained generalized continuous algebraic Riccati equation plays in singular linear-quadratic (LQ) optimal control. Indeed, in spite of…
Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often…
Formation control problems can be expressed as linear quadratic discrete-time games (LQDTG) for which Nash equilibrium solutions are sought. However, solving such problems requires solving coupled Riccati equations, which cannot be done in…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…
This paper develops a controller synthesis algorithm for distributed LQG control problems under output feedback. We consider a system consisting of three interconnected linear subsystems with a delayed information sharing structure. While…
The problem of data-driven recursive computation of receding horizon LQR control through a randomized combination of online/current and historical/recorded data is considered. It is assumed that large amounts of historical input-output data…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
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.…