The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min-max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton-Jacobi-Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution.

中文翻译：

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具有不确定模型的系统的鲁棒最小-最大最优控制设计：一种神经动态规划方法。

本研究的主要成果是设计一种基于人工神经网络（ANN）的次优控制器，以解决一类不确定系统的有限水平优化问题。优化问题考虑了Bolza形式的凸性能指标。动态不确定性限制被认为是受建模不确定性以及外部有界扰动影响的线性系统。所提出的控制器基于动态神经程序近似解决方案实现了最小-最大方法。人工神经网络对值函数进行近似，以获得汉密尔顿-雅各比-贝尔曼（HJB）方程解的估计。ANN中权重的显式自适应定律是从HJB解的近似获得的。基于李雅普诺夫理论的稳定性分析表明，近似值函数可作为李雅普诺夫函数的候选者，并得出平衡点的实际稳定性。仿真示例说明了次优控制器的特性。通过使用不同控制器获得的性能指标的比较评估了扰动和次优解决方案的效果。