Constrained optimal control for a class of nonlinear systems with uncertainties

Jie Ding, S. Balakrishnan
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Abstract

Approximate dynamic programming formulation (ADP) implemented with an Adaptive Critic (AC) based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in the ADP and the AC solutions are escalating, there is a dire need to consider enabling factors for their possible implementations. A typical AC structure consists of two interacting NNs which is computationally expensive. In this paper, a new architecture, called the "Cost Function Based Single Network Adaptive Critic (J-SNAC)" is presented that eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. Many real-life problems have controller limits. In this paper, a non-quadratic cost function is used that incorporates the control constraints. Necessary equations for optimal control are derived and an algorithm to solve the constrained-control problem with J-SNAC is developed. A benchmark nonlinear system is used to illustrate the working of the proposed technique. Extensions to optimal control constrained problems in the presence of uncertainties are also considered.
一类不确定非线性系统的约束最优控制
基于自适应批评(AC)的神经网络结构实现的近似动态规划公式(ADP)已发展成为求解Hamilton-Jacobi-Bellman (HJB)方程的一种强大技术。随着对ADP和AC解决方案的兴趣不断升级,迫切需要考虑其可能实施的使能因素。典型的交流结构由两个相互作用的神经网络组成,计算成本很高。本文提出了一种新的体系结构,称为“基于成本函数的单网络自适应批评(J-SNAC)”,它消除了典型AC结构中的一个网络。这种方法适用于工程中广泛的非线性系统。许多现实生活中的问题都有控制器的限制。本文采用了包含控制约束的非二次代价函数。推导了最优控制的必要方程,并提出了一种求解J-SNAC约束控制问题的算法。以一个非线性系统为例说明了该方法的有效性。同时也考虑了存在不确定性的最优控制约束问题的扩展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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