Related papers: Sparse Linear-Quadratic Feedback Design Using Affi…
The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…
Sparse learning is an important topic in many areas such as machine learning, statistical estimation, signal processing, etc. Recently, there emerges a growing interest on structured sparse learning. In this paper we focus on 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…
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…
We provide a modified augmented Lagrange method coupled with a Tikhonov regularization for solving ill-posed state-constrained elliptic optimal control problems with sparse controls. We consider a linear quadratic optimal control problem…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…
In this paper, we consider the adaptive linear quadratic Gaussian control problem, where both the linear transformation matrix of the state $A$ and the control gain matrix $B$ are unknown. The proposed adaptive optimal control only assumes…
We propose a new risk-constrained reformulation of the standard Linear Quadratic Regulator (LQR) problem. Our framework is motivated by the fact that the classical (risk-neutral) LQR controller, although optimal in expectation, might be…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
In this paper we present and analyze a weighted residual a posteriori error estimate for an optimal control problem. The problem involves a nondifferentiable cost functional, a state equation with an integral fractional Laplacian, and…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
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…
We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and…
This paper presents a pioneering approach to solving the linear quadratic regulation (LQR) and linear quadratic tracking (LQT) problems with constrained inputs using a novel off-policy continuous-time Q-learning framework. The proposed…
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the L1/Lq norm with q > 1 is attractive in many applications of…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…
We consider transport processes that are modeled by first order hyperbolic partial differential equations. Our goal is to find a full state feedback that makes a given reference profile locally asymptotically stable. To accomplish this we…