Related papers: Accelerated Optimization Landscape of Linear-Quadr…
Real-time optimal control remains a fundamental challenge in robotics, especially for nonlinear systems with stringent performance requirements. As one of the representative trajectory optimization algorithms, the iterative Linear Quadratic…
Feedback control problems involving autonomous quadratic systems are prevalent, yet there are only a limited number of software tools available for approximating their solution due to the complexity of the problem. This paper represents a…
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…
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,…
The linear-quadratic regulator (LQR) is an efficient control method for linear and linearized systems. Typically, LQR is implemented in minimal coordinates (also called generalized or "joint" coordinates). However, other coordinates are…
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 propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and…
The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback problem has no explicit-form solution. It is suggested to…
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…
This paper focuses on adaptive control of the discrete-time linear quadratic regulator (adaptive LQR). Recent literature has made significant contributions in proving non-asymptotic convergence rates, but existing approaches have a few…
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…
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…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
This article presents a method to automatically generate energy-optimal trajectories for systems with linear dynamics, linear constraints, and a quadratic cost functional (LQ systems). First, using recent advancements in optimal control, we…
In this paper, we introduce a reduced order model-based reinforcement learning (MBRL) approach, utilizing the Iterative Linear Quadratic Regulator (ILQR) algorithm for the optimal control of nonlinear partial differential equations (PDEs).…
This paper presents a state and state-input constrained variant of the discrete-time iterative Linear Quadratic Regulator (iLQR) algorithm, with linear time-complexity in the number of time steps. The approach is based on a projection of…
We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…
We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss principle of least constraint and solving it using dynamic programming. Our approach builds…
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 propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…