1997年12月1日 · In this paper we study the convergence of the Galerkin approximation method applied to the generalized Hamilton-Jacobi-Bellman (GHJB) equation over a compact set containing the origin. The GHJB equation gives the cost of an arbitrary control law and can be used to improve the performance of this control.

2017年12月4日 · In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman ( GHJB ) equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems.

Hamilton–Jacobi–Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed re-cursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian

2022年10月21日 · 推导HJB方程的第一步就是使得 u(t) 遵循最优反馈函数，即如下原则： 从最优轨迹族 ( x ( t ) , t ) ∈ R n + 1 (x (t),t)\in \mathbb R^ {n+1} (x(t),t) ∈ Rn+1上任意一点出发的轨线，它后续的性能指标必然是最优的。 u¯(t), t ∈ [t, t + Δt] u∗(t), t ∈ [t + Δt,tf] u …

2024年5月6日 · HJB方程提供了求解 动态规划 问题的一个有效工具，尤其是在连续时间、连续状态空间的环境中。 其基本思想是将原问题转化为寻找一个价值函数（也称作代价函数或泛函），该函数表示从当前状态出发到某个终止条件下的最优成本或收益。 HJB方程确保了这个价值函数满足一定的动态一致性条件。 对于一个标准的连续时间最优控制问题，其基本要素包括： X \mathcal {X} X。 U \mathcal {U} U。 f : X × U × R → X f: \mathcal {X} \times \mathcal {U} \times …

In this article, the HJB equation will first be derived. A simple application will be presented, in addition to its use in solving the linear quadratic control problem. Finally, a brief overview of some solution methods and applications presented in the literature will be given.

哈密顿-雅可比-贝尔曼方程（Hamilton-Jacobi-Bellman equation，简称HJB方程）是一个偏微分方程，是最优控制的核心。 HJB方程式的解是针对特定动态系统及相关代价函数下，有最小代价的实值函数。

In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton–Jacobi–Bellman (GHJB) equation which appears in optimization problems.

2021年4月24日 · 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.

1996年6月1日 · We state sufficient conditions for the convergence of Galerkin approximations to the GHJB equation. The sufficient conditions derived in this paper include standard completeness assumptions and the asymptotic stability of the associated vector field.