tailieunhanh - Kiểm soát và ổn định thích ứng dự toán cho các hệ thống phi tuyến P8

In the previous chapter we explained_how to develop stable direct adaptive controllers of the form u = .F(z, O), where .F is an approximator and 8 E RP is a vector of adjustable parameters. The approximator may be defined using knowledge of the system dynamics or using a generic universal approximator. We found that as long as there exists a parameter set for the approximator such that an appropriate static stabilizing controller may be represented, then the parameters of the approximator may be adjusted on-line to achieve stability using either the a-modification or the e-modification. In this chapter we will. | 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 Indirect Adaptive Control Overview In the previous chapter we explained how to develop stable direct adaptive controllers of the form u F z 0 where F is an approximator and 0 E Rp is a vector of adjustable parameters. The approximator may be defined using knowledge of the system dynamics or using a generic universal approximator. We found that as long as there exists a parameter set for the approximator such that an appropriate static stabilizing controller may be represented then the parameters of the approximator may be adjusted on-line to achieve stability using either the a-modification or the e-modification. In this chapter we will explain how to design indirect adaptive controllers. Unlike the direct adaptive control approach we will design an indirect adaptive controller by first identifying individual types of uncertainty within the system. A separate adaptive approximator will then be used to compensate for each of the uncertainties. The indirect adaptive control law is then formed by combining the results of each of the approximations. We will begin our treatment of indirect adaptive control by studying the control of systems which contain uncertainties that are in the span of the input. In this situation the uncertainties are said to satisfy matching conditions. Both additive and multiplicative uncertainties will be considered so that the error dynamics become e a t x T 3 x A i x 4- Il rr iz where A t E Rm is a vector of possibly time-varying additive uncertainties and II E Rmxm is a nonsingular matrix of static time-invariant multiplicative uncertainties. It will be assumed that the error system is defined to satisfy Assumption so that boundedness of e implies boundedness of x.