Design method of adaptive nonlinear H∞ control systems via neural network approximators

A class of adaptive nonlinear H_∞ control systems for nonlinear and time-varying processes which include nonlinear parametric models approximated by multi-layer neural networks, is proposed. Those control schemes are derived as solutions of particular nonlinear H_∞ control problems, where unknown system parameters and approximate and algorithmic errors in neural networks are regarded as exogenous disturbances to the processes, and thus, in the resulting control systems, the L₂ gains from those virtual disturbances to generalized outputs are made less than the prescribed positive constants γ(> 0). The proposed control systems are shown to be bounded for arbitrarily large but bounded variations of time-varying parameters and approximate and algorithmic errors in neural network approximators