Abstract:

A systematic procedure for synthesis of neural network adaptive synergetic control is proposed for a class of affine multivariable extremum seeking system. By employing the synergetic control, the synergetic convergence among the states can be realized, and the invariance against system parameter variation and external perturbation can also be achieved. By using the system’s states and intput, the search variables from the extremum seeking control, and the known model parameters as the inputs, two three-layer neural networks are designed to estimate the dynamic process of the states extrema and unknown parameters, respectively. At the same time, an adjustable parameter is used to minify the estimation errors of the three-layer neural networks. The detailed theoretical analysis proves that all errors of the closed-loop system exponentially converge to a small tunable neighborhood of the origin by appropriately choosing design constants. Simulation results show the effectiveness of the proposed control method.