By Reverse Push The Technical Design H_ ¡Þ And Adaptive Control System

Based on dissipative theory, the problems of H_∞ control and adaptive control for complex dynamic systems are investigated by using backstepping technique. Among these problems we studied are constructive H_∞ control design for linear multivariablesystems, H_∞ control for a class of multivariable-input nonlinear systems and adaptivecontrol for a class of multivariable-input nonlinear systems with uncertainties .The control problems are solved to some extent and some new results are obtained by developing some new techniques. The main contents and results are as follows:1. A new approach to H_∞ control of linear multivariable systems is proposed by using an orthogonal transformation and backstepping-like technique. One key advantage of the proposed approach is that the H_∞ controller for the multivariable systems can be constructively obtained.2. The problem of the H_∞ control for multi-input cascade nonlinear systems isinvestigated. We obtain a result that if the H_∞ control problem for the firstsubsystem is solvable, the problem of the H_∞ control for the overall system can besolved based on backstepping recursive design method. The resulting state feedback control law can make the closed-loop system internally stable and satisfy theH_∞ performance.3. The robust control problem of multi-input cascade nonlinear systems with unmodelled terms is investigated. The control design is based on backstepping recursive design technique. All signals of of the resulting closed-loop system are globally bounded, and the states of the resulting closed-loop system can converge to a residual set. A simulation example is also presented to illustrate the designprocedure and controller performance.4. An adaptive design procedure is proposed for a broader class of multi-input cascade nonlinear systems. The derived adaptive controller guarantees the global boundedness property for all signals and at the same time , steers the states to the origin. The adaptive control design is based on backstepping recursive design technique. The number of parameter estimates is minimal, that is, equal to the number of unknown parameters. The adaptive systems designed by this procedure possess stronger stability than those using overparamtrization.5. An adaptive controller for multi-input cascade nonlinear system with unmodelled terms is given, the control design is based on backstepping recursive design method. All signals of the closed-loop system are globally bounded, and the states of the first subsystem can converge to a neighborhood of the origin..6. A robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances. The controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique. For each auxiliary system, an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics, and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well. It is shown that the resulting closed-loop systems guarantee a satisfactory transient and asymptotic performance. A simulation example is also presented to illustrate the design procedure and controller performance.