Neural network optimal adaptive control for affine continuous-time nonlinear systems with unknown internal dynamics

A neural network (NN) optimal adaptive control for affine nonlinear continuous-time system with unknown internal dynamics is presented. The optimal adaptive control is given by a nonlinear differential equation with variable structure. A block-diagram of the controlled system is designed and investigated. Hardware and software implementation possibilities of the network are discussed. The NN does not need any learning and has moderate complexity. The trajectories of optimal adaptive control and system state variable are globally stable and convergent to unique steady states. It is shown that these trajectories are convergent to the steady states in finite time. Sliding modes of the trajectories are investigated. An accuracy of the network operation in the presence of disturbances of its nonlinearities is analyzed. Using the network for partial case of optimal tracking control is investigated. Computer simulations of the network operation that confirm theoretical derivations and illustrate high performance of the network showing its practical applications are provided.