Adaptive nonlinear H∞ control systems via neural network approximators

A new class of adaptive nonlinear H
_infin
control systems for nonlinear and time-varying processes which include nonlinear parametric models approximated by neural networks (NN), is proposed in this manuscript. Those control schemes are derived as solutions of particular nonlinear H
_infin
control problems, where unknown system parameters, approximation and algorithmic errors in NN, and estimation errors of layer weights in NN, are regarded as exogenous disturbances to processes, and thus, in the resulting control systems, LscrH
₂
gains from those uncertain elements to generalized outputs are made less than gamma(> 0) (prescribed positive constants). The resulting control systems are bounded for arbitrarily large but bounded variations of time-varying parameters and layer weights, and modeling and algorithmic errors in NN approximators