This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems". Indeed, this emerging research area is slowly gaining momentum among electrical engineers while its deeply rooted mathematical concepts also slowly migrate to various engineering disciplines. A very important aspect of research in fractional-order circuits and systems is that it is an interdisciplinary subject. Specifically, it is an area where biochemistry, medicine and electrical engineering over-lap giving rise to many new potential applications. This article aims to provide an overview of the current status of research in this area, highlighting specific problems which need to be addressed particularly by electrical engineers.

Fractional-order circuits and systems: An emerging interdisciplinary research area

In this paper, we study the time-space fractional order (fractional for simplicity) nonlinear subdiffusion and superdiffusion equations, which can relate the matter flux vector to concentration gradient in the general sense, describing, for example, the phenomena of anomalous diffusion, fractional Brownian motion, and so on. The semi-discrete and fully discrete numerical approximations are both analyzed, where the Galerkin finite element method for the space Riemann-Liouville fractional derivative with order 1+@b@?[1,2] and the finite difference scheme for the time Caputo derivative with order @a@?(0,1) (for subdiffusion) and (1,2) (for superdiffusion) are analyzed, respectively. Results on the existence and uniqueness of the weak solutions, the numerical stability, and the error estimates are presented. Numerical examples are included to confirm the theoretical analysis. During our simulations, an interesting diffusion phenomenon of particles is observed, that is, on average, the diffusion velocity for 0<@a<1 is slower than that for @a=1, but the diffusion velocity for 1<@a<2 is faster than that for @a=1. For the spatial diffusion, we have a similar observation.

Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

This paper deals with designing a sliding mode controller (SMC) for a fractional-order chaotic financial system. Using the sliding mode control technique, a sliding surface is determined. The sliding mode control law is derived to make the states of the fractional-order financial system asymptotically stable. The designed control scheme is robust against the system’s uncertainty and guarantees the property of asymptotical stability in the presence of an external disturbance. An illustrative simulation result is given to demonstrate the effectiveness of the proposed sliding mode control design.

Control of a fractional-order economical system via sliding mode

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

This paper presents two different stabilization methods based on the fractional-calculus theory. The first method is proposed via using the fractional differentiator, and the other is constructed based on using the fractional integrator. It has been shown that the proposed techniques can be used to suppress chaotic oscillations in 3-D chaotic systems. To show the practical capability of the methods, some experimental results on the control of chaos in chaotic circuits are presented.

Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations

This paper is devoted to the analysis of fractional order Van der Pol system studied in the literature. Based on the existing theorems on the stability of incommensurate fractional order systems, w...

More Details on Analysis of Fractional-order Van der Pol Oscillator

In this paper, the frequency domain-based numerical methods for simulation of fractional order systems are studied in the sense of stability preservation. First, the stability boundary curve is exactly determined for these methods. Then, this boundary is analyzed and compared with an accurate (ideal) boundary in different frequency ranges. Also, the critical regions in which the stability does not preserve are determined. Finally, the analytical achievements are confirmed via some numerical illustrations.

Stability Preservation Analysis for Frequency-Based Methods in Numerical Simulation of Fractional Order Systems

We propose new insights into the network centrality based not only on the network graph, but also on a more structured model of network uncertainties. The focus of this paper is on the class of uncertain linear consensus networks in continuous time, where the network uncertainty is modeled by structured additive Gaussian white noise input on the update dynamics of each agent. The performance of the network is measured by the expected dispersion of its states in steady state. This measure is equal to the square of the $\mathcal {H}_2$ -norm of the network, and it quantifies the extent by which its state deviates away from the consensus state in steady state. We show that this performance measure can be explicitly expressed as a function of the Laplacian matrix of the network and the covariance matrix of the noise input. We investigate several structures for noise input and provide engineering insights on how each uncertainty structure can be relevant in real-world settings. Then, a new centrality index is defined in order to assess the influence of each agent or link on the network performance. For each noise structure, the value of the centrality index is calculated explicitly, and it is shown how it depends on the network topology as well as the noise structure. Our results assert that agents or links can be ranked according to this centrality index, and their rank can drastically change from the lowest to the highest, or vice versa, depending on the noise structure. This fact hints at emergence of fundamental tradeoffs on network centrality in the presence of multiple concurrent network uncertainties with different structures.

Centrality Measures in Linear Consensus Networks With Structured Network Uncertainties

This paper deals with a fractional calculus based control strategy for chaos suppression in the 3D chaotic systems. It is assumed that the structure of the controlled chaotic system has only one control input. In the proposed strategy, the controller has three tuneable parameters and the control input is constructed as fractional-order integration of a linear combination of linearized model states. The tuning procedure is based on the stability theorems in the incommensurate fractional-order systems. To evaluate the performance of the proposed controller, the design method is applied to suppress chaotic oscillations in a 3D chaotic oscillator and in the Chen chaotic system.

Sadegh Bolouki

Papers

Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations

More Details on Analysis of Fractional-order Van der Pol Oscillator

Stability Preservation Analysis for Frequency-Based Methods in Numerical Simulation of Fractional Order Systems

Centrality Measures in Linear Consensus Networks With Structured Network Uncertainties

Using fractional-order integrator to control chaos in single-input chaotic systems