By Howard Kaufman
Suitable both as a reference or as a textual content for a graduate direction in adaptive keep watch over platforms, this e-book is a self-contained compendium of simply implementable adaptive regulate algorithms which were built and utilized through the authors for over 10 years. those algorithms don't require specific method parameter identity and feature been effectively utilized to a wide selection of engineering difficulties together with versatile constitution keep an eye on, blood strain regulate and robotics. normally, those algorithms are appropriate for a large category of a number of input-output regulate platforms containing major uncertainty in addition to disturbances.
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Additional info for Direct Adaptive Control Algorithms: Theory and Applications
139). The system is stable if the equation can only be satisfied for a positive semidefinite matrix Q(t) , . 140) may have more than one equilibrium point, and one must differentiate between local stability around an equilibrium point and global stability that includes the entire state-space. Without loss of generality, it is assumed that the origin is an equilibrium point. 140) is negative definite. The system is stable if the derivative is negative semidefinite , . 141) is (locally) globally uniformly asymptotically stable if there exists a (locally) positive definite function 44 2.
They also incorporated , ,  Ioannou's fixed sigma-algorithm  into the basic algorithm. This results in a robust MRAC law for ASPR multi-input multi-output plants. Later, Bayard, Ih, and Wang  extended the MRAC algorithm by introducing "branch" noise filters into the adaptive controller which suppress measurement noise while ensuring global stability of the adaptive algorithm. Such branch filters allow filtering of the output error without introducing phase lag into the adaptive loop.
The trajectory x(t) may approach the limit point P in a different way, namely, x(t) may enter Se(P) and leave it immediately, an infinite number of times. 152) could remain finite. However, by Assumptions lor 2, the trajectories cannot pass an infinite distance in a finite amount of time. 146). This is a very general result, and allows for analysis of complex nonlinear systems even when one cannot find the "best" Lyapunov functions. In particular cases, one must analyze the meaning of the set n, because it could turn out to be a collection of equilibrium points, limit cycles, etc ..