Radial basis function approach to closed-loop time-optimal control

This paper presents a method for designing closed-loop time-optimal controllers. The fact that the gradient of the isochrone surface is coincident with the direction of the co-state vector for any given state is exploited to arrive at a feedback time-optimal controller. A radial basis function based neural network is used to represent the isochrone surface, which then provides us with a closed form expression for the gradients of the isochrone surface as a function of the system states. Numerical simulation of the proposed technique for a second order system indicates a control profile that is characterized by chattering. A boundary layer is used to minimize the chattering of the control.