5,979 research outputs found
Entropy increase in switching systems
The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipative affine maps has a pullback attractor consisting of singleton component sets. This entails that the complexity of the control sequence and switched dynamics, as quantified by the topological entropy, coincide. In this paper we extend the previous framework to pullback attractors with nontrivial components sets in order to gain further insights in that relation. This calls, in particular, for distinguishing two distinct contributions to the complexity of the switched dynamics. One proceeds from trajectory segments connecting different component sets of the attractor; the other contribution proceeds from trajectory segments within the component sets. We call them âmacroscopicâ and âmicroscopicâ complexity, respectively, because only the first one can be measured by our analytical tools. As a result of this picture, we obtain sufficient conditions for a switching system to be more complex than its unswitched subsystems, i.e., a complexity analogue of Parrondoâs paradox
Resonance and marginal instability of switching systems
We analyse the so-called Marginal Instability of linear switching systems,
both in continuous and discrete time. This is a phenomenon of unboundedness of
trajectories when the Lyapunov exponent is zero. We disprove two recent
conjectures of Chitour, Mason, and Sigalotti (2012) stating that for generic
systems, the resonance is sufficient for marginal instability and for
polynomial growth of the trajectories. We provide a characterization of
marginal instability under some mild assumptions on the sys- tem. These
assumptions can be verified algorithmically and are believed to be generic.
Finally, we analyze possible types of fastest asymptotic growth of
trajectories. An example of a pair of matrices with sublinear growth is given
Fuzzy switching systems: minimizing discontinuities and ripple magnitude and energy
This paper presents an efficient and effective method to determine optimal switching instants of fuzzy switching systems such that both the ripple magnitude and energy of the fuzzy switching systems are minimized. The method is based on optimal switching control techniques, where an optimal enhancing control method is used. This method has several advantages over the traditional methods. Firstly, it does not require the process of linearization. Secondly, it guarantees to achieve optimality. For illustration, a practical example of an optimal pulse width modulated fuzzy control of a switched-capacitor DC/DC power converter is presented
Modelling legacy telecommunications switching systems for interaction analysis
No abstract avaliabl
- âŠ