Dynamical Realizations of Finite Volterra Series
Copyright policy )Dynamical Realizations of Finite Volterra Series
In this paper, realizations of finite Volterra series are viewed as nonlinear analytic input–output systems, with state space described by an analytic manifold. For a minimal realization guaranteed by H. J. Sussmann, the state space, which is unique up to diffeomorphism, is shown to have the homogeneous space structure of a nilmanifold, the quotient of two nilpotent Lie groups. The structure of nilmanifolds as described by A. Malcev is used to show that for these systems, the state space has a vector space structure. As a consequence of this result, it is shown that a minimal realization of a finite Volterra series can be described as a cascade of linear subsystems with polynomial link maps, in which the dimension o f each linear subsystem is independent of the realization considered.
- University of Warwick United Kingdom
input-output map, nilpotent Lie groups, Nilpotent and solvable Lie groups, Volterra series, minimal realization, Realizations from input-output data, General systems theory, Minimal systems representations, Nonlinear systems in control theory, Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics, Control/observation systems governed by ordinary differential equations, cascade of linear subsystems
input-output map, nilpotent Lie groups, Nilpotent and solvable Lie groups, Volterra series, minimal realization, Realizations from input-output data, General systems theory, Minimal systems representations, Nonlinear systems in control theory, Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics, Control/observation systems governed by ordinary differential equations, cascade of linear subsystems
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