tailieunhanh - Kiểm soát và ổn định thích ứng dự toán cho các hệ thống phi tuyến P7

In Chapter 6 we found that it is possible to define static (non-adaptive) stabilizing controllers, u = V,(X) with u E R”, for a wide variety of nonlineas plants. In addition to being able to define control laws for systems in input-output feedback linearizable and strict-feedback forms, it was shown how nonlinear damping and dynamic normalization may be used to compensate for system uncertainty. In this and subsequent chapters we will h consider using the dynamic (adaptive) controller u = Y, (z, 6) where now e(t) is allowed to vary with time. In general, we will consider two different approaches. | Stable Adaptive Control and Estimation for Nonlinear Systems Neural and Fuzzy Approximator Techniques. Jeffrey T. Spooner Manfredi Maggiore Raul Ordonez Kevin M. Passino Copyright 2002 John Wiley Sons Inc. ISBNs 0-471-41546-4 Hardback 0-471-22113-9 Electronic Chapter Direct Adaptive Control Overview In Chapter 6 we found that it is possible to define static non-adaptive stabilizing controllers u vs z with u E Rm for a wide variety of nonlinear plants. In addition to being able to define control laws for systems in input-output feedback linearizable and strict-feedback forms it was shown how nonlinear damping and dynamic normalization may be used to compensate for system uncertainty. In this and subsequent chapters we will consider using the dynamic adaptive controller u ua z 0 where now 0 t is allowed to vary with time. In general we will consider two different approaches to developing the adaptive control law. The first is a direct adaptive approach in which a set of parameters in the control law is directly modified to form a stable closed-loop system. In an indirect approach components of a stabilizing control law are first estimated and then combined to form the overall control law. For example if for a given scalar error system e a x 3 x u one is able to adaptively approximate a x and 3 x with fF a and Fp respectively then the adaptive control law va Ke F lFp might be suggested as a possible stabilizing controller assuming Ta a and Fp 3. Design tools for the indirect approach will be studied in greater detail in the next chapter. As for the case of static controller development it is useful to study the trajectory of an error system e y Z which quantifies the controller performance. We will be particularly interested in the tracking problem where we wish to drive y r t and the set-point regulation problem where y r with r a constant. Recall that according to Assumption the error system is also chosen such that if e is bounded then it is possible to .