【摘要】 为了求解线性二次型的动态优化控制问题,提出了一种基于随机神经网络Boltzmann机求解线性二次型动态优化控制问题的方法,将系统的性能指标转化成Boltzmann机的能量函数,将控制序列与网络的神经元相对应,Boltzmann机的稳态对应的就是最优的控制序列.理论研究表明,对于任意时变多变量的线性二次型,都能找到一个相应的。Boltzmann机,它的能量函数与二次型的性能指标等价.仿真试验表明,应用Boltzmann机可实现任意时变多变量系统的线性二次型动态优化控制.更多还原

【Abstract】 In order to solve linear quadratic(LQ) optimal control problem of discrete-time system, the authors present a promising alternative based on random neural network-Boltzmann machines. By the method, the LQ performance index is transformed into the energy function of Boltzmann machine, and the control sequence is transformed into the neuron state vector of Boltzmann machines. Solving LQ dynamic optimization problem is equivalent to operating associated Boltzmann machines from its initial state to the terminal state that represents the optimal control sequence. The theoretical study indicates that we are able to find a relevant Boltzmann machines whose energy function is corresponding to the LQ performance index. Emulation experiment shows boltzmann machines can implement linear quadratic optimal control of any multivariable time-variant system.更多还原