Control of discrete-time systems via online learning and estimation

Online learning state trajectory control for discrete-time systems is considered herein. An improvement to a method previously developed that learns the control input as a function of the desired states for state trajectory tracking control is investigated. The improved method consists of letting the learned control effort be split into a nominal map and a learned adjustment in addition to online estimation of control parameters such as the system´s Jacobian and controllability matrix. The method employs the technique known as block-input state realization to transform the system to one with equal number of states and inputs. A neural network structure called the nodal link perceptron network learns the adjustment of the nominal map as a function of the desired states while the Jacobian matrix and the controllability matrix are estimated online via a modified Broyden method to achieve the overall control input. The proposed controller is explored through three different simulations. The method can successfully deal with the nonlinearities and uncertainties inherent in complex systems. This method serves as a model free alternative for intelligent control of complex and uncertain systems