Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection and feedback connection. In each case, the corresponding generating series is produced, when one exists, and conditions for convergence of the corresponding Fliess operator are given. ...

This paper presents an approach to design a pressure tracking controller for a pneumatic cylinder system in which the connection port comprises a non-negligible restriction. The pressure chamber of this system is difficult to control because a double restriction is formed by the servovalve and the connection port. The model of this system can be approximated using singular perturbation approach...

This paper presents novel analysis results for input-to-state stability (ISS) that utilise dynamic programming techniques to characterise minimal ISS gains and transient bounds. These characterisations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimisation problems in nonlinear dissipative systems theory (including L2...

We explore the connection between the higher moments of the current (or voltage) distribution in a random linear resistor network, and the resistance of a nonlinear random resistor network. We find that the two problems are very similar, and that an infinite set of exponents are required to fully characterise each problem. These exponent sets are shown to be identical on a particular hierarchic...

Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection and feedback connection. In each case, the corresponding generating series is produced, when one exists, and conditions for convergence of the corresponding Fliess operator are given. ...

Given two analytic nonlinear input-output systems represented as Fliess operators, four system interconnections are considered in a unified setting: the parallel connection, product connection, cascade connection, and feedback connection. In each case, the corresponding generating series is produced and conditions for the convergence of the corresponding Fliess operator are given. In the proces...

Using the recent statistical mechanical theory for nonlinear irreversible processes of Grabert, Graham and Green, we re-examine the fluctuations in an electric circuit containing a nonlinear dissipative resistance. We explicitly establish the relationship between the nonlinear thermal fluctuations and the deterministic irreversible transport law. In particular, we verify their choice of the met...

In this paper we discuss in detail the nonlinear equations of the mean–field approximation and their connection to the exact many–body Schrödinger equation. Then we analyze the mean–field approach and the nonlinear dynamics of a trapped condensate of weakly–interacting bosons.

With the purpose of analyzing non-stationary time series, this paper innovates the nonlinear cointegration discriminate analysis by introducing support vector machine and innovated feature-weighting model to overcome existing limitations of two methods, that is, the statistical approach and the neural network used by the nonlinear cointegration theory. Then, the application of the innovated met...