Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQualitative stability of nonlinear networked systems
115
0
0.0
(
0
)
Added by
Marco Tulio Angulo
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70s, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
rate research
Read More
The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions structural accessibility and structural observability for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems.
We study in this paper certain properties of the responses of dynamical systems to external inputs. The motivation arises from molecular systems biology. and, in particular, the recent discovery of an important transient property, related to Webers law in psychophysics: fold-change detection in adapting systems, the property that scale uncertainty does not affect responses. FCD appears to play an important role in key signaling transduction mechanisms in eukaryotes, including the ERK and Wnt pathways, as well as in E.coli and possibly other prokaryotic chemotaxis pathways. In this paper, we provide further theoretical results regarding this property. Far more generally, we develop a necessary and sufficient characterization of adapting systems whose transient behaviors are invariant under the action of a set (often, a group) of symmetries in their sensory field. A particular instance is FCD, which amounts to invariance under the action of the multiplicative group of positive real numbers. Our main result is framed in terms of a notion which extends equivariant actions of compact Lie groups. Its proof relies upon control theoretic tools, and in particular the uniqueness theorem for minimal realizations.
In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: 1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology, quite different from the familiar notion of consensus or formation controllability; 2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; 3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient. For a networked system with single-input/single-output (SISO) LTI nodes, we present precise necessary and sufficient conditions for the controllability of a general network topology.
A new approach for robust Hinfty filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting Hinfty filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.
The issues of robust stability for two types of uncertain fractional-order systems of order $alpha in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust stability is given; for the norm-bounded uncertainty case, a sufficient and necessary condition of robust stability is presented. Both of these conditions can be checked by solving sets of linear matrix inequalities. Two numerical examples are presented to confirm the proposed conditions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
