Research On The Control Of Uncertain Nonlinear Systems Based On On-line Approximation

With the development of technology, the control problems of the systems with uncertainty, nonlinearity, time-varying and those systems with time-delay attract the people's attention, especially the control problem of systems with a high degree of uncertainty in recent years. The control problem of two types of uncertain nonlinear systems is considered in this paper and the main contents of this paper as following:i) The tracking control problem of a class of affine systems in the control input represented by the input-output models with uncertainty is considered. Combining the technique of on-line approximate and the feedback linearization technique, a robust adaptive controller design method is developed. Further more, the control problem of this kind of system with time-delay is considered. The upper bound of the time-delay item is assumed to be known and we use it to cancel the time-delay item in the system by robust control design method. Then, the feedback controller is given by Lyapunov controller design procedure for this system with time-delay.ii) The tracking control problem of the system in i) is considered under the situation whose control gain of the system is totally unknown. Combining the Nussbaum gain technique and on-line approximate theory, based on Lyapunov method, we give a controller and the closed-loop system is guaranteed uniformly ultimately bounded. For the system with time-delay, Lyapunov-Krasovskii method is applied to eliminate the effect of time-delay. And then combining on-line approximation theory and the Nussbaum gain technique, uniformly ultimately bounded controller is given.iii) On the basis of the above work, we developed an adaptive controller design procedure for a class of non-affine systems in control input represented input-output models. First of all, non-affine system is transformed into affine system in control input by using the Lagrange mean value theorem. And then, a controller is given for this affine system.iv) The tracking control problem of a class of pure-feedback system with uncertainty is considered. Dynamic surface control design technique is used to avoid the problem of "explosion of complexity" in the traditional backstepping algorithm and overcome the circular construction of controller from function approximator in the backstepping design. Combining backstepping technique and on-line approximation theorem, a uniformly ultimately bounded controller based on the Lyapunov stability theory is given.v) A robust adaptive controller design procedure is developed for a class of non-affine pure-feedback systems with time-delay. First of all, the Lagrange mean value theorem is used to transform non-affine system into affine system in control input. Then, a controller design procedure is proposed for this affine system. In order to reduce the system requirement, we assume that the sign of control gain of the transformed system is unknown and the Nussbaum control gain technique is adopted in the controller design procedure since that the sign of control gain is unknown. The effects of unknown time-delays are eliminated by using Lyapunov-Krasovskii method in the design procedure. The proposed control scheme guarantees that the closed-loop system is uniformly ultimately bounded.vi) Some simulation examples are presented to demonstrate the effectiveness of the controller design method.