Intelligent Backstepping Control And Analysis For Nonlinear Systems

In last two decades, nonlinear control theory becomes one of focuses in control community. In particular, some important results in the nonlinear control have been obtained based on backstepping technique. However, there still exist some open problems needed to be further investigated. This dissertation uses backstepping technique as a basic tool, and focuses on the extension of this tool to the other areas of nonlinear control systems. Some important control theory, such as adaptive neural network approximation theory, stability theory of time-delay functional differential equations, decentralized control theory of interconnected large-scale systems, stability theory of stochastic differential equations and learning control theory of time-varying systems are combined with backstepping technique to address the problems of state-feedback control and output-feedback control for several classes of nonlinear systems. The main contributions are outlined as follows:1. A novel technique, called the signal replacement technique, is introduced in this dissertation. In the procedure of controller design, as system signals are unmeasured or unutilized, for example, the unavailable time-delay states or outputs in controller design for time-delay systems, and the unutilized interconnected signals in decentralized controller design for interconnected systems, considering the system states or outputs will eventually track the reference signals, we replace these unavailable signals with the reference signals and then employ adaptive robust technique to deal with the placement errors. Thus, the control objective can be achieved. Most works of this dissertation are based on this technique.2. Under assumption that nonlinear functions satisfy Lipschitz condition, both delay-dependent state-feedback and output-feedback control schemes are designed for a class of nonlinear time-delay systems with lower-triangle structure, where backstepping technique is combined with the signal replacement technique. By constructing a Lyapunov-Krasovskii functional, it is proved that all closed-loop signals are uniformly bounded and the tracking error asymptotically converges to zero.3. The existing adaptive backstepping neural network control theory is extended to nonlinear time-delay systems. Firstly, based on the signal replacement technique and the linearly parameterized neural network approximation theory, a new delay-dependent adaptive neural network control scheme is designed for nonlinear time-delay systems with strict-feedback forms. Then, adaptive backstepping neural network control theory is further extended to nonlinear time-delay systems with output-feedback form. The designed controllers ensure that the tracking error converges to a small residual set around zero in the root mean squared sense.4. The existing adaptive backstepping neural network control theory is extended to nonlinear interconnected systems. Under assumption that each subsystem controller obtains information of all subsystem reference signals, and based on the signal replacement technique, i.e. replacing the interconnected output signals with the reference signals, two kinds of adaptive decentralized control approaches are designed for two classes of nonlinear systems, respectively in the case that the states is measured or unmeasured. The arbitrary small tracking errors of subsystems can be achieved by tuning the design parameters.5. State-feedback stabilization is addressed for a class of p-odd power stochastic nonlinear system by using adding a power integrator technique. By constructing a high-order Lyapunov function, it is proved that the designed stabilization algorithm can achieve the closed-loop asymptotical stability in probability sense.6. A simplified adaptive backstepping stabilization method is designed for time-delay nonlinear output-feedback systems and stochastic nonlinear output-feedback systems, respectively. Only a neural network is employed to compensate for all unknown nonlinear functions, and thus the controller is more simplified. The designed control schemes respectively guarantee the asymptotical stability of two kinds of closed-loop systems.7. This dissertation considers the problem of adaptive leaning tracking control for nonlinear systems with periodic time-varying parameters. A kind of periodic learning control strategy is designed for nonlinearly parameterized systems with periodic time-varying parameters and periodic time-varying delays. By constructing a Lyapunov-Krasovskii-like composite energy function, it is proved that the systems output can exactly track the given periodic reference signal in the sense of L_T~2 - norm.