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We study in this paper the linear quadratic optimal control (linear quadratic regulation, LQR for short) for discrete-time complex-valued linear systems, which have shown to have several potential applications in control theory. Firstly, an…
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…
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…
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…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…
In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random…
We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
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…
We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear…
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…
We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…
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…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
We present a method for optimal control with respect to a linear cost function for positive linear systems with coupled input constraints. We show that the optimal cost function and resulting sparse state feedback for these systems can be…
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, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations,…
This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…