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To further understand the underlying mechanism of various reinforcement learning (RL) algorithms and also to better use the optimization theory to make further progress in RL, many researchers begin to revisit the linear-quadratic regulator…
Most of the policy evaluation algorithms are based on the theories of Bellman Expectation and Optimality Equation, which derive two popular approaches - Policy Iteration (PI) and Value Iteration (VI). However, multi-step bootstrapping is…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
This paper introduces and analyzes an improved Q-learning algorithm for discrete-time linear time-invariant systems. The proposed method does not require any knowledge of the system dynamics, and it enjoys significant efficiency advantages…
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in…
Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…
Following the recent resurgence in establishing linear control theoretic benchmarks for reinforcement leaning (RL)-based policy optimization (PO) for complex dynamical systems with continuous state and action spaces, an optimal control…
In this paper, we propose a novel equilibrium solution notion for the time-inconsistent stochastic linear-quadratic optimal control problem. This notion is called the mixed equilibrium solution, which consists of two parts: a…
This paper presents a novel model-free and fully data-driven policy iteration scheme for quadratic regulation of linear dynamics with state- and input-multiplicative noise. The implementation is similar to the least-squares temporal…
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…
Traditional stochastic optimal control methods that attempt to obtain an optimal feedback policy for nonlinear systems are computationally intractable. In this paper, we derive a decoupling principle between the open loop plan, and the…
This paper studies optimal consensus tracking problem of heterogeneous linear multi-agent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution of a multi-player…
We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the…
This paper considers linear-quadratic (LQ) stochastic leader-follower Stackelberg differential games for jump-diffusion systems with random coefficients. We first solve the LQ problem of the follower using the stochastic maximum principle…
Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties…
Unlike traditional model-based reinforcement learning approaches that estimate system parameters from data, non-model-based data-driven control learns the optimal policy directly from input-state data without any intermediate model…
In this paper, we investigate the optimal output tracking problem for linear discrete-time systems with unknown dynamics using reinforcement learning and robust output regulation theory. This output tracking problem only allows to utilize…
This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its…
This paper studies the data-driven synthesis of linear quadratic integral (LQI) controllers for continuous-time systems. The objective is to achieve optimal state-feedback control with integral action for reference tracking using only…