Related papers: Stable and Robust LQR Design via Scenario Approach
This manuscript surveys reinforcement learning from the perspective of optimization and control with a focus on continuous control applications. It surveys the general formulation, terminology, and typical experimental implementations of…
This letter presents a robust data-driven receding-horizon control framework for the discrete time linear quadratic regulator (LQR) with input constraints. Unlike existing data-driven approaches that design a controller from initial data…
We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this…
In a recent paper we have shown that data collected from linear systems excited by persistently exciting inputs during low-complexity experiments, can be used to design state- and output-feedback controllers, including optimal Linear…
This paper considers the discrete-time, stochastic LQR problem with $p$ steps of disturbance preview information where $p$ is finite. We first derive the solution for this problem on a finite horizon with linear, time-varying dynamics and…
Reinforcement learning (RL) has been successfully used to solve many continuous control tasks. Despite its impressive results however, fundamental questions regarding the sample complexity of RL on continuous problems remain open. We study…
We present and solve a Linear Quadratic Regulator (LQR) for the boundary control of the beam equation. We use the simple technique of completing the square to get an explicit solution. By decoupling the spatial frequencies we are able to…
This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is…
Presented is an algorithm to synthesize the optimal infinite-horizon LQR feedback controller for continuous-time systems. The algorithm does not require knowledge of the system dynamics but instead uses only a finite-length sampling of…
This paper presents a constrained iterative Linear Quadratic Regulator (iLQR) framework for nonlinear optimal control problems with box constraints on both states and control inputs. We incorporate logarithmic barrier functions into the…
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…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown $\tilde{O}(T^{2/3})$ regret and…
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…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a…
This paper discusses learning a structured feedback control to obtain sufficient robustness to exogenous inputs for linear dynamic systems with unknown state matrix. The structural constraint on the controller is necessary for many…
It is well-known that linear quadratic regulators (LQR) enjoy guaranteed stability margins, whereas linear quadratic Gaussian regulators (LQG) do not. In this letter, we consider systems and compensators defined over directed acyclic…
We consider the continuous-time Linear-Quadratic-Regulator (LQR) problem in terms of optimizing a real-valued matrix function over the set of feedback gains. The results developed are in parallel to those in Bu et al. [1] for discrete-time…
Linear quadratic regulator (LQR) is one of the most popular frameworks to tackle continuous Markov decision process tasks. With its fundamental theory and tractable optimal policy, LQR has been revisited and analyzed in recent years, in…
It is well known that highly volatile control laws, while theoretically optimal for certain systems, are undesirable from an engineering perspective, being generally deleterious to the controlled system. In this article we are concerned…