Neural network optimal control for discrete-time nonlinear systems with known internal dynamics

A neural network (NN) optimal control for discrete-time nonlinear dynamic systems with known internal dynamics is designed. The control is described by an algebraic equation with a variable structure. This algebraic equation is derived analytically. A functional block diagram of the controlled system is given and analyzed. Software and hardware implementation aspects of the controller are discussed. The controller does not need any training and has moderate complexity. The discrete-time state variable trajectories of the controlled system are shown to be globally asymptotically stable and convergent to unique steady states. It is proved that these trajectories converge to steady-state neighborhood in a finite number of steps. Sliding mode analysis of controller operation is fulfilled. A correctness of controller operation in the case of disturbances of its nonlinearities is analyzed. Using the controller for a special case of optimal tracking control is discussed. Results of presented computer simulations of optimal control of discrete-time two-dimensional and three-dimensional affine nonlinear systems and optimal tracking control of permanent-magnet motor of linear type applied for accurate positioning and nonlinear cooling continuous stirred tank reactor confirm theoretical statements of the paper and illustrate a performance of the controller.