PdE-based model reference adaptive control of uncertain heterogeneous multiagent networks

Robust globally stable model reference adaptive control (MRAC) laws recently derived for systems described by parabolic and hyperbolic partial differential equations (PDEs) with spatially-varying coefficients under distributed sensing and actuation are extended to heterogeneous multiagent networks characterized by parameter uncertainty. The extension is carried out using partial difference equations (PdEs) on graphs that preserve parabolic- and hyperbolic-like cumulative network behavior. Unlike in the PDE case, only boundary input is specified for the reference model. The algorithms proposed directly incorporate this boundary reference input into the reference PdE to generate the distributed admissible reference evolution profile followed by the agents. The agent evolution thus depends only on the interaction with the adjacent agents, making the system fully decentralized. Numerical examples are presented as well, including the case of the switched topology associated with a sudden loss of an agent. The resulting PdE MRAC laws inherit the robust linear structure of their PDE counterparts.     

Nonlinear stable adaptive control based upon Elman networks

Elman networks‘ dynamical modeling capability is discussed in this paper firstly. According to Elman networks‘ unique structure ,a weight training algorithm is designed and a nonlinear adaptive controller is constructed. Without the PE presumption, neural networks controller‘s closed-loop properties are studied and the whole Elman networks‘ passivity is demonstrated.     

A distributed approach to capacity allocation in logical networks

We consider a dynamic capacity reallocation scheme in a logically fully-connected telecommunications network. We show that the problem of optimal capacity allocation can be solved in a distributed manner, an essential feature of such a scheme. Our continuous-capacity reallocation scheme can be used as a foundation for a discrete system. This is useful from the perspective of practical implementation.     

A compound adaptive approach to degenerate nonlinear quenching problems

Quenching phenomena play important roles in both steady and unsteady combustion processes. This article studies a compound finite difference method for solving a nonlinear degenerate combustion model problem. The approach combines procedures of semidiscretization, adaptive ODE solver, and highly stable rational approximation for handling the spatial degeneracy and quenching singularity involved. A second‐order adaptive scheme is constructed, which provides monotone convergence of the numerical solution and direct computations of critical quenching values. It has a simple, yet accurate and reliable, structure and is easy to use. We further demonstrate advantages of the scheme by comparing it to existing algorithms. Numerical examples are presented to further strengthen our results. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 29–47, 1999     

Computational study of a nonhierarchical decomposition algorithm

Optimizing the design of complex ground and flight vehicles involves multiple disciplines and multilayered computer codes stitched together from mostly incompativle disciplinary codes. The application of established, large-scale, optimization algorithms to the complete model is nearly impossible. Hierarchical decompositions are inappropriate for these types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategyfor nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two-dimensional quadratic programs. This paper demonstrates the failure of the algorithm for quadratic programs and suggests a number of possible modifications.     

Value iteration and optimization of multiclass queueing networks

This paper considers in parallel the scheduling problem for multiclass queueing networks, and optimization of Markov decision processes. It is shown that the value iteration algorithm may perform poorly when the algorithm is not initialized properly. The most typical case where the initial value function is taken to be zero may be a particularly bad choice. In contrast, if the value iteration algorithm is initialized with a stochastic Lyapunov function, then the following hold: (i) a stochastic Lyapunov function exists for each intermediate policy, and hence each policy is regular (a strong stability condition), (ii) intermediate costs converge to the optimal cost, and (iii) any limiting policy is average cost optimal. It is argued that a natural choice for the initial value function is the value function for the associated deterministic control problem based upon a fluid model, or the approximate solution to Poisson’s equation obtained from the LP of Kumar and Meyn. Numerical studies show that either choice may lead to fast convergence to an optimal policy. This revised version was published online in June 2006 with corrections to the Cover Date.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Asymptotic behavior of solutions of functional difference equations

For linear functional difference equations, we obtain some results on the asymptotic behavior of solutions, which correspond to a Perron-type theorem for linear ordinary difference equations. We also apply our results to Volterra difference equations with infinite delay.     

On the reversibility of queueing networks

This paper relates the reversibility of certain discrete state Markovian queueing networks — the class of quasi-reversible networks — to the reversibility of the underlying switching process. Quasi-reversible networks are characterized by a product form equilibrium state distribution.When the state can be represented by customer totals at each node, the reversibility of the state process is equivalent to the reversibility of the switching process. More complicated quasi-reversible networks require additional conditions, to ensure the reversibility of the network state process.     

Newsvendor equations for production networks

We consider production networks with stochastic activity leadtimes. When activities finish early holding costs are incurred and when end products are delivered late penalty costs are incurred. Objective is to find the activity start and finish times that minimize the total cost. We introduce the concept of a tardy path and derive the optimality equations for each node in the network. We show that under the optimal solution, for a set of nodes the tardiness probability satisfies the Newsvendor equations.     

一类非线性差分方程的振动性

用Riccati变换方法，获得了一类非线性差分方程△[αn△（bn△xn=pnxn-r))] qnf(xn-σ)=0的振动性的一些结果，并对已知结果做了一些有意义的改进。     

Poisson flows in single class open networks of quasireversible queues

This paper analyzes open networks of quasireversible nodes with a single class of customers and in equilibrium. A simple argument shows, under a stability conditions, that a flow on a link of such a network is Poisson if and only if the link is not part of a loop. This loop criterion is shown to apply to the usual quasireversible networks with bounded service rates.     

Almost self-optimizing strategies for the adaptive control of diffusion processes

The ergodic control of a multidimensional diffusion process described by a stochastic differential equation that has some unknown parameters appearing in the drift is investigated. The invariant measure of the diffusion process is shown to be a continuous function of the unknown parameters. For the optimal ergodic cost for the known system, an almost optimal adaptive control is constructed for the unknown system.This research was partially supported by NSF Grants ECS-87-18026, ECS-91-02714, and ECS-91-13029.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.     

OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS

This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.     

OSCILLATION OF CERTAIN NONLINEAR ADVANCED DIFFERENCE EQUATIONS

This paper deals with the oscillatory properties of a class of nonlinear advanced difference equations. Sufficient criteria in the form of infinite sum for the equation to be oscillatory are obtained. In the linear cases, our results coincide with those in the literature.