Bang-bang control of a flexible-link manipulator with actuator saturation using neural network

In this paper, a methodology of finding a minimum time and non-linear state feedback control of a flexible-link manipulator with saturated control is proposed. Since the difficulty which is involved in minimization of the cost function is solving GHJB equation, having proper cost function can solve regulation and bang-bang control problem for non-linear systems. To show this, we present a proper non-quadratic cost function and solve corresponding optimal control problem by approximation the solution of GHJB. Since solving GHJB is difficult, we use neural network to approximate the solution of GHJB equation. The controller, which is found by that method, has better performance in contrast LQR method for linearized systems because it does not ignore the inherent nonlinearity of non-linear systems. The simulation results confirm that deflection modes are damped faster and cost function has a good upper band.