Neural network L₂ gain controller for a nonlinear system with uncertainty

A neural network controller with L₂-gain was developed for an affine nonlinear system with parameter uncertainty. The controller stabilizes the closed-loop control system with a finite L₂-gain. The general structure of the storage function was formulated based on a Fourier neural network system's fitting capacity, which was satisfied by a Hamiltonian-Jacobi inequality (HJI). Moreover, by employing the optimization of a genetic algorithm to the weighting of the neural network system, the neural network system with its anti-disturbance system was able to meet the criteria of L₂-gain performance. For an L₂-gain input signal, the closed-loop control system needs to stabilize finite L₂ gain to input-output mapping and have the parameters of L₂ gain as small as possible. In a stirred-tank chemical reactor control example, simulation results demonstrated that the proposed method is feasible and can meet the criteria of L₂-gain performance.