Robust Adaptive Control of Linearizable Nonlinear Single Input Systems

The design of stabilizing controllers for nonlinear plants with unknown nonlinearities is a challenging problem. The inability to identify exactly the nonlinearities on-line or off-line motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities. The price paid in such case, could be lack of theoretical guarantees for global stability, and/or zero tracking or regulation error at steady state. In this paper a nonlinear robust adaptive control algorithm is designed and analyzed for a class of single-input nonlinear systems with unknown nonlinearities. The controller guarantees closed loop semiglobal stability and convergence of the tracking error to a small residual set. The region of attraction for semiglobal stability depends on the number of nodes and weights in the single layer neural network used to estimate the unknown plant nonlinearities. The size of the residual set depends on design parameters and can be calculated apriori. Two examples are used to demonstrate the performance and properties of the proposed scheme.