Volterra Series System Research Articles

A local form of small gain theorem and analysis of feedback Volterra systems

The requirement of evaluating a gain over the entire signal space is one of the restrictions in the traditional small gain theorem. In this paper, a local form of small gain theorem is presented. It yields a bound on the external signal that guarantees that the magnitude of the specified signal along the closed loop stays within a certain region and hence it is useful in addressing the signal magnitude dependent stability problem. The theorem is used to analyze the feedback properties of a Volterra series system as well as an inverse (or pseudo inverse) Volterra system. Improvement over existing results is demonstrated, both theoretically and via numerical examples.

Design method of exact model matching control for finite Volterra series systems

This paper is concerned with exact model matching control (EMM) for finite Volterra series systems. First, we show a structure of a causal controller which can achieve the exact model matching to a reference model and clarify the relationship between the proposed method and the EMM for linear systems. Second, to analyse the stability of the proposed control system, we present an input dependent small gain theorem for the system with an external input, then extend it for the system with two external inputs. With the help of this theorem, we clarify the condition under which the control system is stable for the reference input magnitude within a certain range, and is also robust for small disturbances. Finally, the effectiveness of the proposed method is illustated through numerical simulations.

有限ボルテラ級数システムに対する厳密なモデルマッチング

有限ボルテラ級数システムに対する厳密なモデルマッチング

Adaptive Model Matching for Finite Volterra Series System

In this paper, the model matching problem is investigated and its application to the model reference adaptive control (MRAC) for a class of finite Volterra series system is also considered. At first, a class of finite Volterra series system which has a bilinear realization is treated, and a scheme for matching the input-output relation to a given linear reference model is presented by using a bilinear observer. Secondly, a model reference adaptive control scheme is proposed. Furthermore, the exact model matching problem for an extended class of the finite Volterra series system is also discussed.