We have recently applied the principles of continuum mechanics to develop a new leader-follower model for the collective motion of a multiagent system (MAS). Agents are modeled as particles of a continuum body that can deform in Rn (n = 1, 2, 3) under a specific class of mappings, called the homogeneous transformation. This paper shows how a desired homogeneous deformation is uniquely specified based on the trajectories chosen by p +1 (p ≤ n) leaders, and it is acquired by the remaining agents, called followers, through local communication. Under this setup, every follower interacts with p + 1 local agents with fixed communication weights that are uniquely determined based on the initial positions of the agents. Although asymptotic convergence of the agents' transient positions to the desired final positions (prescribed by a homogeneous transformation) can be assured by applying the proposed paradigm, follower agents deviate from the desired positions during evolution. The main objective of this paper is to assure that the transient error, the difference between the actual and desired positions of each follower, converges to zero during evolution. For this purpose, each leader chooses a time-dependent polynomial vector of order (h -1) (h ∈ N) for its trajectory connecting two consecutive way points, and each follower applies continuous time or discrete time linear time invariant dynamics to update its state based on the states of p + 1 local agents. The second objective of this paper is to develop a paradigm for the homogeneous deformation of an MAS that is robust to communication failure. For this purpose, we will show how followers can acquire desired positions prescribed by a homogeneous mapping to preserve volumetric ratios under either fixed or switching communication topologies, where there is no restriction on the number of the agents, if every follower communicates with mi ≥ p + 1 local agents. In addition, agents' collective motion can be stably continued even if some followers give up communication with other agents at some time during evolution.

This paper attempts to provide an analytically based visualization tool for investigating the existence of singularity induced bifurcations along with corresponding singular sets of operating points in power systems. This tool is based on the solution of a set of parameter dependent differential-algebraic equations (DAE's) for analyzing power system phenomena. The focus of this work is on the information obtained when visualizing limits (and neighboring areas) imposed by singularity-induced bifurcations. This tool is an enhanced feature of the Voltage Stability Toolbox (VST) through which various properties of these stability limits can be easily further investigated.

To study the steady state behavior of small integrated AC/DC power systems, a new realization of AC equivalent approach to AC/DC power flow is proposed in this paper. Depending on control modes, the converter AC terminal buses are modeled as constant voltage bus (slack bus) and nonlinear load bus (PI bus). As a result the whole system and corresponding Jacobian matrix become area-decoupled. In this paper we study two control modes through analysis of multiple load flow solutions thus providing a quantitative and qualitative assessment of feasible and controllable system operating points.

This paper provides an of overview of local bifurcation theory and its application to power system voltage stability analysis. The qualitative behavior of power system dynamics as modeled by differential-algebraic equations is discussed, followed by a summary of the concepts and tools for the analysis of local bifurcation from equilibria. Computational methods for locating and classifying bifurcation points as they have been applied in power system analysis are reviewed. Several examples are given.

New algorithms are presented for deriving joint kinematic relations and these are integrated with Poincare's form of Lagrange's equations to generate the dynamical equations of motion for rigid multibody chains. Software is described which performs all of the required symbolic constructions. Examples are given.>