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Selected Abstracts

Direct adaptive control for non-linear uncertain systems with exogenous disturbances

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2002
Wassim M. Haddad
Abstract A direct adaptive non-linear control framework for multivariable non-linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non-linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the plant. In the case of bounded energy L2 disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input,output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A subspace approach to balanced truncation for model reduction of nonlinear control systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2002
Sanjay Lall
Abstract In this paper, we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computations, and we show that when it is applied to linear systems it results in the usual balanced truncation. For nonlinear systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input,output map of the system. An important feature of this approach is that the resulting reduced-order model is nonlinear, and has inputs and outputs suitable for control. We perform an example reduction for a nonlinear mechanical system. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Model reduction of interconnected linear systems

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2009
H. Sandberg
Abstract The problem of model reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different model reduction methods are introduced and compared in this paper. Both methods are extensions to the well-known balanced truncation method. Compared with earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. The so-called structured Hankel singular values are used in the methods, and indicate how important states in the subsystems are with respect to a chosen input,output map for the entire interconnected system. It is shown how these structured Hankel singular values can be used to select an approximation order. Finally, the two methods are applied to a model of a mechanical device. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Z+ fading memory and extensions of input,output maps

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2001
Irwin W. Sandberg
Abstract An Erratum for this article has been published in the International Journal of Circuit Theory and Applications 30(4) 2002, 179. Much is known about time-invariant non-linear systems with inputs and outputs defined on Z+ that possess approximately-finite memory. For example, under mild additional conditions, they can be approximated arbitrarily well by the maps of certain interesting simple structures. An important fact that gives meaning to results concerning such systems is that the approximately-finite-memory condition is known to be often met. Here we consider the known proposition that if a causal time-invariant discrete-time input,output map H has fading memory on a set of bounded functions defined on all of the integers Z, then H can be approximated arbitrarily well by a finite Volterra series operator. We show that in a certain sense, involving the existence of extensions of system maps, this result too has wide applicability. Copyright © 2001 John Wiley & Sons, Ltd. [source]