Synchronization of Time Delayed Fractional Order Chaotic Financial System

The research on a time delayed fractional order financial chaotic system is a hot issue. In this paper, synchronization of time delayed fractional order financial chaotic system is studied. Based on comparison principle of linear fractional equation with delay, by using a fractional order inequality, a sufficient condition is obtained to guarantee the synchronization of master-slave systems. An example is exploited to show the feasibility of the theoretical results

Distributed Aperiodic Time-Triggered and Event-Triggered Consensus: A Scalability Viewpoint

We revisit distributed sampled-data consensus problems from a scalability point of view. Existing solutions in the literature for estimating the maximum sampling interval that preserves stability rely on the Lyapunov functional method. With this method, the overall closed-loop system (i.e. the overall network of agents) is treated as a time-delayed system. Here, a critical point is the scalability of the resulting stability conditions: in fact, the size of the LMIs to be solved depends on the size of the network. In contrast with this method, an easy-to-use and scalable method is presented, with stability conditions that are independent on the size of the network. It is shown that the proposed method can handle linear and Lipschitz nonlinear multiagent systems with both aperiodic time-triggered and event-triggered control in a unified way. Numerical examples show the efficiency of the proposed approach and the tightness of the estimated maximum sampling interval.</p

Distributed Adaptive Consensus Disturbance Rejection: a Directed-spanning-tree Perspective

In this paper, we revisit the problem of consensus disturbance rejection for multiagent systems over a digraph, but from a different perspective, i.e., the perspective of a directed spanning tree (DST). When the minimum nonzero real part of the Laplacian eigenvalues is available, we reproduce the sufficient lower bound for a static homogeneous coupling gain in the literature, by exploring a DST structure of the digraph. The major novelty arises when it is shown that by adaptively tuning the coupling gains along a DST, consensus disturbance rejection can be achieved when the above eigenvalue information is not available. Numerical examples on networks of second-order oscillators and UAVs are included to validate the theoretical results. Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Bart De Schutte

Consensus in high-power multiagent systems with mixed unknown control directions via hybrid Nussbaum-based control

This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.</p

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem

Abstract This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov–Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results