Plug-and-Play Distributed Control of Large-Scale Nonlinear Systems.

A method to design plug-and-play (PnP) distributed controllers for large-scale nonlinear systems represented by interconnected Takagi-Sugeno fuzzy models with nonlinear consequent is presented in this article. From the combination of techniques to use multiple fuzzy summations and to explore the chordal decomposition of the interconnection graph associated with the large-scale nonlinear system, sufficient conditions for distributed stabilization are derived in terms of linear matrix inequalities (LMIs). Conditions specially designed to allow seamless subsystems plugging-in and unplugging operations from the large-scale system, without requiring the redesign of all previously tuned distributed controllers, are provided.

Phase coherence is not related to topology.

Phase coherence is an important measure in nonlinear science. Whereas there is no generally accepted definition for phase and therefore for phase coherence, many works associate this feature with topological aspects of the systems, such as having a well-defined rotating center. Given the relevance of this concept for synchronization problems, one aim of this paper is to argue by means of a couple of counterexamples that phase coherence is not related to the topology of the attractor.

Phase definition to assess synchronization quality of nonlinear oscillators.

This paper proposes a phase definition, named the vector field phase, which can be defined for systems with arbitrary finite dimension and is a monotonically increasing function of time. The proposed definition can properly quantify the dynamics in the flow direction, often associated with the null Lyapunov exponent. Numerical examples that use benchmark periodic and chaotic oscillators are discussed to illustrate some of the main features of the definition, which are that (i) phase information can be obtained either from the vector field or from a time series, (ii) it permits not only detection of phase synchronization but also quantification of it, and (iii) it can be used in the phase synchronization of very different oscillators.

Evaluation of dynamical models: dissipative synchronization and other techniques.

Some recent developments for the validation of nonlinear models built from data are reviewed. Besides giving an overall view of the field, a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model, which is very useful in validating models that should reproduce dominant dynamical features, like bifurcations, of the original system. In order to assess the discriminating power of the procedure, four well-known benchmarks have been used: namely, Duffing-Ueda, Duffing-Holmes, and van der Pol oscillators, plus the Hénon map.

Using data-driven discrete-time models and the unscented Kalman filter to estimate unobserved variables of nonlinear systems.

This paper addresses the problem of state estimation for nonlinear systems by means of the unscented Kalman filter (UKF). Compared to the traditional extended Kalman filter, the UKF does not require the local linearization of the system equations used in the propagation stage. Important results using the UKF have been reported recently but in every case the system equations used by the filter were considered known.