Study On Direct Adaptive Control Methods For Switched Systems

As one important type of hybrid systems, switched systems consist of subsystems and a switching signal. Switched systems have wide applications and thus lots of results have been reported. At present, most works are about certain switched systems. Since uncertainties always exist in practice, the adaptive control problem of switched systems attracts more and more attention and gradually becomes a hot topic in control society. However, uncertain parameters make it difficult to apply the traditional adaptive control method to the switched systems because it increases the complexity in analysis and design. There are many problems to be solved, such as how to incorporate the uncertain parameters into the construction of Lyapunov functions of switched systems, how to eliminate the effect of switching signal and how to design the switching signal together with the controllers. Effective and systematic methods about these problems have not been available, and results are quite limited.This dissertation studies the direct adaptive control problem of a class of uncertain switched systems with linear unknown parameters. Sufficient conditions of partial stability and hyperstability are given for switched systems. Then, based on these results, design schemes and procedures are given using the Lyapunov stability method and hyperstability method respectively. Both arbitrary switching and designed switching are considered. Further, these ideas of designing adaptive controllers for switched systems are applied to the switched model of robot manipulators, where adaptive tracking controllers are designed. Adaptive friction compensation and adaptive disturbance attenuation problems are discussed. At last, in order to enhance the performance of adaptive control, a finite time parameter estimator is proposed. The transient period is dramatically reduced via resetting the control parameter with the estimated real value. The main contributions are as follows.1. Partial stability is studied for general nonlinear switched systems. For a given switching signal, sufficient conditions are given for the switched systems to be partial stable using the multiple Lyapunov functions method. As a special case, when the "partial" state contains all the state elements, this partial stability condition is identical to that of the multiple Lyapunov functions method.2. The model reference adaptive control problem is considered for nonlinear switched systems with linear unknown parameters. The boundedness of system signal and the convergence of tracking error are proved using the Lyapunov method and the piecewise adaptive laws. Asymptotical tracking is achieved without demanding the persistent excitation (PE) of the input signal and the measurability of differentiation between subsystems.3. The stabilization problem is addressed for the switched systems with subsystems that cannot be stabilized. The multiple Lyapunov functions method and the max-min switching law are used. Signal boundedness and state convergence are ensured by the proposed controller and adaptive law.4. Using the concept of cross-supply rates, we give a sufficient condition for a switched system to be hyperstable. Also, the condition and method of designing the switching signal are given to make a switched system hyperstable when all the subsystems are not positive real. In addition, the result is used to design model reference adaptive controller for linear switched systems.5. A switched model is built for the robot manipulator with shifting loads. To accomplish the tracking task, an adaptive friction compensation controller and an adaptive H? controller are presented for the switched robot model. Simulation verifies the superiority of the proposed controllers comparing to the controller designed using the non-switched model.6. A finite time parameter estimator is designed for the switched adaptive control systems, and the robustness of the estimated real value is analyzed with respect to the disturbance. The adaptive law is given for the circumstance that the input signal is not exciting, where the performance of the estimator is analyzed. Simulation explains how to use the estimated real value to enhance the control performance. No other methods are found in designing parameter estimator for switched systems hither to now.