Related papers: Model-Free $\delta$-Policy Iteration Based on Damp…
H{\infty} control of nonlinear continuous-time system depends on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which has been proved impossible to obtain a closed-form solution due to the nonlinearity of HJI equation. In order…
This paper addresses the model-free nonlinear optimal problem with generalized cost functional, and a data-based reinforcement learning technique is developed. It is known that the nonlinear optimal control problem relies on the solution of…
We study policy iteration (PI) for deterministic infinite-horizon discounted optimal control problems, whose value function is characterized by a stationary Hamilton--Jacobi--Bellman (HJB) equation. At the PDE level, PI is fundamentally…
The $H_\infty$ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear $ H_\infty $ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs…
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…
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case.…
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…
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…
The uncertainties in plant dynamics remain a challenge for nonlinear control problems. This paper develops a ternary policy iteration (TPI) algorithm for solving nonlinear robust control problems with bounded uncertainties. The controller…
We propose a physics-informed neural network policy iteration (PINN-PI) framework for solving stochastic optimal control problems governed by second-order Hamilton--Jacobi--Bellman (HJB) equations. At each iteration, a neural network is…
We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic…
In optimal control problem, policy iteration (PI) is a powerful reinforcement learning (RL) tool used for designing optimal controller for the linear systems. However, the need for an initial stabilizing control policy significantly limits…
Policy iteration (PI) is a recursive process of policy evaluation and improvement for solving an optimal decision-making/control problem, or in other words, a reinforcement learning (RL) problem. PI has also served as the fundamental for…
Policy iteration (PI) is a widely used algorithm for synthesizing optimal feedback control policies across many engineering and scientific applications. When PI is deployed on infinite-horizon, nonlinear, autonomous optimal-control…
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…
This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…
An off policy reinforcement learning based control strategy is developed for the optimal tracking control problem to achieve the prescribed performance of full states during the learning process. The optimal tracking control problem is…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
This paper studies the adaptive optimal control problem for a class of linear time-delay systems described by delay differential equations (DDEs). A crucial strategy is to take advantage of recent developments in reinforcement learning and…
The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically,…