Related papers: Linear Quadratic Regulators: A New Look
We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
Achieving optimal steady-state performance in real-time is an increasingly necessary requirement of many critical infrastructure systems. In pursuit of this goal, this paper builds a systematic design framework of feedback controllers for…
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, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
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 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…
This paper presents a novel value iteration (VI) algorithm for finding the optimal control for a kind of infinite-horizon stochastic linear quadratic (SLQ) problem with unknown systems. First, an off-line algorithm is estabilished to obtain…
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 concerns a class of uncertain linear quantum systems subject to quadratic perturbations in the system Hamiltonian. A small gain approach is used to evaluate the performance of the given quantum system. In order to get improved…
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes…
This paper is concerned with optimal control problems for control systems in continuous time, and interacting particle system methods designed to construct approximate control solutions. Particular attention is given to the linear quadratic…
We propose a provably stabilizing and tractable approach for control of constrained linear systems under intermittent observations and unreliable transmissions of control commands. A smart sensor equipped with a Kalman filter is employed…
We study the quadratic regulator problem on a finite time horizon for the wave equation with high internal damping controlled on the boundary by square integrable controls. The approach in this paper transforms the wave equation with high…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that…
As the benchmark of data-driven control methods, the linear quadratic regulator (LQR) problem has gained significant attention. A growing trend is direct LQR design, which finds the optimal LQR gain directly from raw data and bypassing…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
We revisit in this paper the discrete-time linear quadratic regulator (LQR) problem from the perspective of receding-horizon policy gradient (RHPG), a newly developed model-free learning framework for control applications. We provide a…