We are interested here in the problem of global decentralized adaptive regulation (of the plant output to zero) of square multivariable linear time-invariant systems without any restrictions on relative degrees nor matching assumptions. The first solution to this problem was recently reported by the author using Morse's new dynamic certainty equivalent adaptive controller to prove that global stabilization is possible if the unmodelled interconnections do not induce "amplification of the energy of the signals in all channels". In this paper we show that, to preserve global convergence, it is actually enough to have only one "non amplifying channel". Instrumental for the establishment of our result is the fundamental S-procedure losslessness theorem of Megretsky and Treil, together with some basic loop-transformations and D-scalings. Keywords: Adaptive Control, Decentralized Control, Passive Systems. 1 Introduction Several fundamental problems in identification and adaptive control of ...

Promulgated by some with religious-like fervor, viewed with skepticism by others, adaptive control has for almost forty years been one of the most alluring, intriguing, and often misunderstood areas within the field of automatic control. In truth, despite its present shortcomings fe.g., its failure to adequately address performance issuesg adaptive control has come quite a long way since first conceived. Once amounting to little more than a collection of seemingly unrelated heuristic ideas, adaptive control now rests on a bona fide foundational theory which serves to explain basic concepts and constructions in a principled manner. An early advance contributing to the theory's development was the formulation and resolution of the now classical siso "model reference control problem." The main obstacle to the problem's resolution was dealing with nominal process models of high "relative degree." The assault on the relative degree problem involved many people and took place over a period of several years. The problem's first solution appeared in the late 1970s and used what is now called "integrator backstepping." A second solution emerged about two years later and relied on the idea of "error normalization." The latter approach led to an overall control algorithm which was far simpler in form than that provided by backstepping. As a result the backstepping approach was totally eclipsed by the error normalization approach and remained so for more than a decade. Ironically, integrator backstepping has quite recently enjoyed renewed and considerable attention because of its apparently unique ability to deal with certain types of nonlinearities in both adaptive and nonadaptive systems. The aims of this paper are to explain what backstepping is, to chronicle the events leadin...

estimation and control for a class of

We propose a new method for the design of adaptation algorithms that guarantees a certain prescribed level of performance and applicable to systems with nonconvex parameterization. The main idea behind the method is two-fold. First, we augment the tuning error function and design the adaptation scheme in the form of ordinary differential equations. The resulting augmentation is allowed to depend on state derivatives. Second, we find a suitable realization of the designed adaptation scheme in an algebraic-integral form. Due to their explicit dependence on the state of the original system, such adaptation schemes are referred to as adaptive algorithms in finite form, in contrast to (conventional) algorithms in differential form. Sufficient conditions for the existence of finite form realizations are proposed. It is shown that our method to design algorithms in finite form is applicable to a broad class of nonlinear systems including systems with nonconvex parameterization and low-triangular systems.

Abstract — In this paper the relative degree limitation for adaptive observer-based synchronization schemes is overcome. The scheme is extended to nonpassifiable systems. Two synchronization methods are described and justified based on augmented error adaptive observer and high-order tuners. The solution is based on modern theory of nonlinear adaptive control, particularly on nonlinear observer structure and new classes of adaptation algorithms. Conditions of parametric convergence of the parameter estimation are established for the noiseless case. Robustness of the scheme to the bounded measurement error is established. The results are illustrated by example of application the proposed adaptive synchronization of chaotic Lorenz systems.