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In decentralized control systems with linear dynamics, quadratic cost, and Gaussian disturbance (also called decentralized LQG systems) linear control strategies are not always optimal. Nonetheless, linear control strategies are appealing…
Linear time-invariant control systems can be considered as finitely generated modules over the commutative principal ideal ring $\mathbb{R}[\frac{d}{dt}]$ of linear differential operators with respect to the time derivative. The Kalman…
The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control.…
Consider a network of multiple independent stochastic linear systems where, for each system, a scheduler collocated with the sensors arbitrates data transmissions to a corresponding remote controller through a shared contention-based…
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing…
In this paper we consider the distributed linear quadratic control problem for networks of agents with single integrator dynamics. We first establish a general formulation of the distributed LQ problem and show that the optimal control gain…
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…
The convergence of policy gradient algorithms in reinforcement learning hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of…
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…
The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (risky) events. The…
Distributional linear quadratic regulator (LQR) is a new framework that integrates the distributional reinforcement learning and classical LQR, which offers a new way to study the random return instead of the expected cost. Unlike iterative…
Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of…
This paper is concerned with linear-quadratic-Gaussian (LQG) control for a field-mediated feedback connection of a plant and a coherent (measurement-free) controller. Both the plant and the controller are multimode open quantum harmonic…
This paper presents a simulation-based comparison between the two controllers, Proportional Integral Derivative (PID), a classical controller and Linear Quadratic Regulator (LQR), an optimal controller, for a linearized quadrotor model. To…
In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first…
The Linear Quadratic Gaussian (LQG) problem is a classic and widely studied model in optimal control, providing a fundamental framework for designing controllers for linear systems subject to process and observation noises. In recent years,…
We consider solutions to the linear quadratic Gaussian (LQG) regulator problem via policy gradient (PG) methods. Although PG methods have demonstrated strong theoretical guarantees in solving the linear quadratic regulator (LQR) problem,…
A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their…
Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…