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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Neural Network-Based Finite-Horizon Optimal Control of Uncertain Affine Nonlinear Discrete-Time Systems
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Neural Network-Based Finite-Horizon Optimal Control of Uncertain Affine Nonlinear Discrete-Time Systems

机译：不确定仿射非线性离散系统的基于神经网络的有限视野最优控制

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摘要

In this paper, the finite-horizon optimal control design for nonlinear discrete-time systems in affine form is presented. In contrast with the traditional approximate dynamic programming methodology, which requires at least partial knowledge of the system dynamics, in this paper, the complete system dynamics are relaxed utilizing a neural network (NN)-based identifier to learn the control coefficient matrix. The identifier is then used together with the actor–critic-based scheme to learn the time-varying solution, referred to as the value function, of the Hamilton–Jacobi–Bellman (HJB) equation in an online and forward-in-time manner. Since the solution of HJB is time-varying, NNs with constant weights and time-varying activation functions are considered. To properly satisfy the terminal constraint, an additional error term is incorporated in the novel update law such that the terminal constraint error is also minimized over time. Policy and/or value iterations are not needed and the NN weights are updated once a sampling instant. The uniform ultimate boundedness of the closed-loop system is verified by standard Lyapunov stability theory under nonautonomous analysis. Numerical examples are provided to illustrate the effectiveness of the proposed method.
机译：本文提出了仿射形式的非线性离散时间系统的有限水平最优控制设计。与传统的近似动态规划方法相比，传统的近似动态规划方法至少需要部分系统动力学知识，在本文中，使用基于神经网络（NN）的标识符来学习控制系数矩阵，从而放松了整个系统动力学。然后将标识符与基于行为者的方案一起使用，以在线和及时的方式学习汉密尔顿-雅各比-贝尔曼（HJB）方程的时变解，称为值函数。 。由于HJB的解决方案是时变的，因此考虑具有恒定权重和时变激活函数的NN。为了适当地满足终端约束，在新的更新定律中引入了附加的误差项，使得终端约束误差也随时间最小化。不需要策略和/或值迭代，并且一旦采样瞬间，NN权重就被更新。在非自治分析下，通过标准Lyapunov稳定性理论验证了闭环系统的一致极限有界性。数值算例说明了该方法的有效性。

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