Multilayer Recurrent Neural Networks for Online Robust Pole Assignment

In this brief, two multilayer recurrent neural networks are presented for robust pole assignment based on a new problem formulation. One is called state-independent annealing neural network and the other is called state-dependent annealing neural network. The proposed recurrent neural networks are composed of three layers and are shown to be capable of synthesizing linear control systems via robust pole assignment in real time. The state-dependent annealing neural network is proven to converge for any design parameters. Moreover, the neural network converges exponentially to an optimal solution of the robust pole assignment problem and the perturbed closed-loop control system based on the neural network is globally exponentially stable with appropriate design parameters. These desirable properties make it possible to apply the neural network to slowly time-varying linear control systems. Simulation results are shown to illustrate the effectiveness, advantages, and operating characteristics of the proposed neural network approach.