The Study Of Uncertain Nonlinear System Control

Uncertain nonlinear systems are complex, but widely exist in the real world. Researches on the control of uncertain nonlinear systems have both theoretical and practical interests. The major contributions of this dissertation are as follows:(1) The switching adaptive control is studied for a class of uncertain nonlinear system. In the case that there is no a priori knowledge of the upper bound and lower bound of the unknown parameters, the switching adaptive control design approach is presented. The derived switching adaptive controller guarantees the global stability of the closed-loop system and the ultimate convergence of all the states in the closed-loop system, which can tune its parameter on-line in a switching manner via a switching logic. The switching adaptive controller not only has the advantage of learning capabilities in adaptive control but also possess preferably robust.(2) The switching adaptive control is considered for a class of nonlinear system with unknown control directions. In fact, the unknown multiplicative are sometimes not only the unknown of the values but also have no a priori knowledge of the signs. These signs represent motion direction of the system under any control, and knowledge of these signs makes adaptive or robust control design much easier. The objective of this chapter is to develop a switching adaptive control design procedure based on Lyapunov's direct method that does not require a priori knowledge of control directions. The derived switching adaptive controller can change the signs of the adaptive control and tune its parameter on-line in a switching manner via a switching logic, which can guarantees the global stability of the closed-loop system and the ultimate convergence of all the states in the closed-loop system.(3) The stability problem of chained systems with nonlinear disturbance and drift terms is investigated. Nonlinear drift uncertainties can destroy the stability property achieved by previous stabilization algorithms for systems in ideal chained form. Thus, on the basis of Lyapunov's direct method, an adaptive controller is developed by using state scaling technique and the backstepping method, which can steer the systemglobally converge to the origin, while the estimated parameter maintain bounded. In particular, a novel adaptive switching is proposed to overcome the uncontrollability problems associated with chained systems.(4) The stability problem of chained systems with stochastic disturbance is stuided. When the uncertain nonlinear system is considered, the analysis and design can be facilitated by assuming the disturbance satisfying the bounded uncertain or parameterized uncertain, but this assumption cannot depict the real disturbance completely. Hence, it is necessary to study a class of general disturbance-stochastic disturbance. To overcome the quadratic variation terms of stochastic control and the uncontrollability in chained system, a novel control design procedure is constructively proposed, which involves the introduction of a time-varying technique and the application of quartic Lyapunov function. The derived controller can render the closed-loop system asymptotically stable in the large when the stochastic disturbance equal zero at the equilibrium point of the open-loop system, and bounded in probability, otherwise.(5) By using passivity technique and time-varying approach, a saturated time-varying adaptive controller is proposed for the uncertain nonhonolomic mobile robot, which can guarantee all states of the mobile robot are bounded and ultimately converge to zero. The convergence-rates can be significantly improved via using state-scaling technique.