论文信息 - Hankel operators and Gramians for nonlinear systems

Hankel operators and Gramians for nonlinear systems

In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel mapping introduced by Fliess (1974). In this paper, a definition of a system Hankel operator is developed for causal L/sub 2/-stable input-output systems. If a generating series representation of the input-output system is given then an explicit representation of the corresponding Hankel operator is possible. If, in addition, an affine state space model is available with certain stability properties then a unique factorization of the Hankel operator can be constructed with direct connections to well known and new nonlinear Gramian extensions.

W.S. Gray | J. Scherpen | W. Gray | J.M.A. Scherpen

[1] J. M. A. Scherpen,et al. Balancing for nonlinear systems , 1993 .

[2] Jacquelien M.A. Scherpen,et al. On Similarity Invariance of Balancing for Nonlinear Systems , 1995 .

[3] M. Fliess. Réalisation locale des systèmes non linéaires, algèbres de Lie filtrées transitives et séries génératrices non commutatives , 1983 .

[4] Françoise Lamnabhi-Lagarrigue,et al. An algebraic approach to nonlinear functional expansions , 1983 .

[5] Alberto Isidori,et al. Nonlinear control systems: an introduction (2nd ed.) , 1989 .

[6] W. Gray,et al. Sufficient conditions for minimality of a nonlinear realization via controllability and observability functions , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[7] Tosio Kato. Perturbation theory for linear operators , 1966 .

[8] A. P. Robertson,et al. Topological Vector Spaces , 1980 .

[9] J. Batt,et al. Nonlinear compact mappings and their adjoints , 1970 .

[10] M. Fliess,et al. Fonctionnelles causales non linaires et indtermines non commutatives , 1981 .

[11] Thomas Kailath,et al. Linear Systems , 1980 .

[12] Leonard M. Silverman,et al. Singular value analysis of deformable systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[13] B. Moore. Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .