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Long Wang

Publications and source records attributed to Long Wang.

306 records · Page 17Linked to original sources
arXiv2004

Aggregation of foraging swarms

In this paper we consider a continuous-time anisotropic swarm model with an attraction/repulsion function and study its aggregation properties. It is shown that the swarm members will aggregate and eventually form a cohesive cluster of finite size around the swarm center. We also study the swarm cohesiveness when the motion of each agent is a combination of the inter-individual interactions and the interaction of the agent with external environment. Moreover, we extend our results to more general attraction/repulsion functions. The model in this paper is more general than isotropic swarms and our results provide further insight into the effect of the interaction pattern on individual motion in a swarm system.

q-bio.CB↗
arXiv2004

Self-organization in a group of mobile autonomous agents

This paper considers a discrete time swarm model of a group of mobile autonomous agents with a simple attraction and repulsion function for swarm aggregation and investigates its stability properties. In particular, it is proved that the individuals (members) of the swarm will aggregate and form a cohesive cluster of a finite size depending only on the parameters of the swarm model in a finite time, and the swarm system is completely stable.

math.OC↗
arXiv2004

Swarming Behavior of Multi-Agent Systems

In this paper we consider a continuous-time anisotropic swarm model in $n$-dimensional space with an attraction/repulsion function and study its aggregation properties. It is shown that the swarm members will aggregate and eventually form a cohesive cluster of finite size around the swarm center. Moreover, the numerical simulations show that all agents will eventually enter into and remain in a bounded region around the swarm center. The model is more general than isotropic swarms and our results provide further insight into the effect of the interaction pattern on individual motion in a swarm system.

math.OC↗
arXiv2002

Robust Strictly Positive Real Synthesis for Convex Combination of Sixth-Order Polynomials

For the two sixth-order polynomials $a(s)$ and $b(s),$ Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial $c(s)$ such that $c(s)/a(s)$ and $c(s)/b(s)$ are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

math.OC↗
arXiv2002

Robust D-stability of uncertain MIMO systems: LMI criteria

The focal point of this paper is to provide some simple and efficient criteria to judge the ${\cal D}$-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family. Taking advantage of the uncertain parameter information, we analyze these two classes of uncertain models and give some LMI conditions for the robust stability of the two families. Two examples illustrate the effectiveness of our results.

math.OC↗
arXiv2002

H-infinity Performance of Interval Systems

In this paper, we study $H^{\infty}$ performance of interval systems. We prove that, for an interval system, the maximal $H^{\infty}$ norm of its sensitivity function is achieved at twelve (out of sixteen) Kharitonov vertices.

math.OC↗
arXiv2002

Edge Theorem for Multivariable Systems

This paper studies robustness of multivariable systems with parametric uncertainties, and establishes a multivariable version of Edge Theorem. An illustrative example is presented.

math.OC↗
arXiv2002

Stability of Polytopic Polynomial Matrices

This paper gives a necessary and sufficient condition for robust D-stability of Polytopic Polynomial Matrices. Edge theorem is extended to multi-input-multi-output case.

math.OC↗
arXiv2002

Geometric Characterization of Strictly Positive Real Regions and its Applications

Strict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a fixed polynomial is unbounded, whereas the weak SPR region is bounded. We then prove that the intersection of several weak SPR regions associated with different polynomials can not be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low order and high order polynomial families. Illustrative examples are provided to show the effectiveness of this algorithm.

math.OC↗
arXiv2002

Robust Performance of A Class of Control Systems

Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.

math.OC↗
arXiv2002

Robust SPR Synthesis for Low-Order Polynomial Segments and Interval Polynomials

We prove that, for low-order (n < 5) stable polynomial segments or interval polynomials, there always exists a fixed polynomial such that their ratio is SPR-invariant, thereby providing a rigorous proof of Anderson's claim on SPR synthesis for the fourth-order stable interval polynomials. Moreover, the relationship between SPR synthesis for low-order polynomial segments and SPR synthesis for low-order interval polynomials is also discussed.

math.OC↗
arXiv2002

On the Number of Positive Solutions to a Class of Integral Equations

By using the complete discrimination system for polynomials, we study the number of positive solutions in {\small $C[0,1]$} to the integral equation {\small $ϕ(x)=\int_0^1k(x,y)ϕ^n(y)dy$}, where {\small $k(x,y)=ϕ_1(x)ϕ_1(y)+ϕ_2(x)ϕ_2(y), ϕ_i(x)>0, ϕ_i(y)>0, 0<x,y<1, i=1,2,$} are continuous functions on {\small $[0,1]$}, {\small $n$} is a positive integer. We prove the following results: when {\small $n= 1$}, either there does not exist, or there exist infinitely many positive solutions in {\small $C[0,1]$}; when {\small $n\geq 2$}, there exist at least {\small 1}, at most {\small $n+1$} positive solutions in {\small $C[0,1]$}. Necessary and sufficient conditions are derived for the cases: 1) {\small $n= 1$}, there exist positive solutions; 2) {\small $n\geq 2$}, there exist exactly {\small $m(m\in \{1,2,...,n+1\})$} positive solutions. Our results generalize the existing results in the literature, and their usefulness is shown by examples presented in this paper.

math-ph↗
arXiv2002

Frequency Response of Uncertain Systems: Strong Kharitonov-Like Results

In this paper, we study the frequency response of uncertain systems using Kharitonov stability theory on first order complex polynomial set. For an interval transfer function, we show that the minimal real part of the frequency response at any fixed frequency is attained at some prescribed vertex transfer functions. By further geometric and algebraic analysis, we identify an index for strict positive realness of interval transfer functions. Some extensions and applications in positivity verification and robust absolute stability of feedback control systems are also presented.

math.OC↗