Mehraeen Shahab, Jagannathan Sarangapani
Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA 70803, USA.
IEEE Trans Neural Netw. 2011 Nov;22(11):1757-69. doi: 10.1109/TNN.2011.2160968. Epub 2011 Sep 29.
In this paper, the direct neural dynamic programming technique is utilized to solve the Hamilton-Jacobi-Bellman equation forward-in-time for the decentralized near optimal regulation of a class of nonlinear interconnected discrete-time systems with unknown internal subsystem and interconnection dynamics, while the input gain matrix is considered known. Even though the unknown interconnection terms are considered weak and functions of the entire state vector, the decentralized control is attempted under the assumption that only the local state vector is measurable. The decentralized nearly optimal controller design for each subsystem consists of two neural networks (NNs), an action NN that is aimed to provide a nearly optimal control signal, and a critic NN which evaluates the performance of the overall system. All NN parameters are tuned online for both the NNs. By using Lyapunov techniques it is shown that all subsystems signals are uniformly ultimately bounded and that the synthesized subsystems inputs approach their corresponding nearly optimal control inputs with bounded error. Simulation results are included to show the effectiveness of the approach.
本文利用直接神经动态规划技术，对一类内部子系统和互联动态未知的非线性互联离散时间系统进行前向求解哈密顿-雅可比-贝尔曼方程，以实现分散近最优调节，同时假设输入增益矩阵已知。尽管未知互联项被认为是弱的且是整个状态向量的函数，但在仅局部状态向量可测的假设下尝试进行分散控制。每个子系统的分散近最优控制器设计由两个神经网络（NN）组成，一个动作NN旨在提供近最优控制信号，一个评判NN评估整个系统的性能。两个NN的所有参数均在线调整。利用李雅普诺夫技术表明，所有子系统信号均一致最终有界，且合成的子系统输入以有界误差趋近其相应的近最优控制输入。给出了仿真结果以表明该方法的有效性。
