Adaptive suboptimal tracking for a first-order object under Lipschitz uncertainty

Adaptive suboptimal tracking for a first-order discrete object under Lipschitz uncertainty and bounded external perturbations is studied. The new nonlinear control law, due to L.L. Xie and L. Guo based on nonparametric estimation of the stationary uncertainty is applied to control the object with a known linear part. This control law admits uncertainty with the Lipschitz constant L < 3/2 + root2.. The upper estimate for the quality criterion, which is equal to the upper limit of the modulus of deviation of the output of the object from a given signal, is derived as a function of the Lipschitz constant and norm of the external perturbation. Unknown parameters in the closed-loop are estimated by the method of recurrent objective inequalities. The adaptive control is suboptimal due to the use of cone estimates for the vector of unknown parameters.