Study Of On-line System Identification & Adaptive Control

Based on the backstepping procedure (a kind of recursive algorithm according to the order of the state components), we proposed the adaptive law and control law of the resulting closed-loop systems with constructive method, which can provide solutions for the robust adaptive control problems for a large kind of nonlinear systems with uncertainties (including state-feedback and output-feedback controls). A terse design method is presented to the adaptive tracking system in the article. Also for the discrete-time stochastic bilinear systems, a new adaptive scheme is described, as well as for the discrete-time linear stochastic systems with unknown orders and parameters, an on-line established algorithm which is strong consistency for the estimation of the orders and parameters is presented in the article.The article is consisted of three parts as follows: (1) For the cases of state-feedback and output-feedback, a class of nonlinear systems with general uncertainties and partially unknown parameters is considered respectively, and a robust adaptive state-feedback (or output-feedback) controller is designed for tracking reference signal. The controller is robust to the uncertainties of both the parameters and the states of the system. The global stability of theresulting closed-loop system can be guaranteed and the s -tracking problem has been solved as well. The simulation results have shown that the designed adaptive controller has good track effect, and the used control quantites are in the range of admissible control.(2) The adaptive control problem is studied for discrete-time bilinear stochastic systems with unknown parameters and correlated noise. A new adaptive control scheme, which is the ELS-based adaptive trackers of the studied systems, is proposed according to the certainty equivalence principle. By using the algorithm, the given bounded reference signal can be tracked by the resulting closed-loop system's output, both the global stability and asymptotic optimality of the adaptive tracking algorithm are proved, furthermore, the estimates of the unknown parameters are obtained with the strong consistency and a fast convergence rate. The good tracking effect and parameter estimating performance of the proposed algorithm are presented in two simulation examples.(3) A new recursive estimate algorithm is proposed for unknown time-delay, orders and coefficients of linear discrete-time stochastic control systems (ARMAX model). It is proved that the estimates of the time-delay, orders and coefficients are strongly consistent. Simultaneously, a faster convergent rate of the coefficient estimates to their true values is obtained.