N-Player Stochastic Differential Games

Conditions are described which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. It was found that when the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary

A new approach to service provisioning in ATM networks

The authors formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. The authors derive the network's adjustment scheme and the users' decision rule and establish their optimality. Since the approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network

Capacity of classes of Gaussian channels. Part I - Discrete-time

Capacity of discrete time Gaussian channel

Nonlinear programming and optimal control

Generalization of nonlinear programming problem - optimization problem

Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations

Analysis of Solar Energy Aggregation under Various Billing Mechanisms

Ongoing reductions in the cost of solar photovoltaic (PV) systems are driving their increased installations by residential households. Various incentive programs such as feed-in tariff, net metering, net purchase and sale that allow the prosumers to sell their generated electricity to the grid are also powering this trend. In this paper, we investigate sharing of PV systems among a community of households, who can also benefit further by pooling their production. Using cooperative game theory, we find conditions under which such sharing decreases their net total cost. We also develop allocation rules such that the joint net electricity consumption cost is allocated to the participants. These cost allocations are based on the cost causation principle. The allocations also satisfy the standalone cost principle and promote PV solar aggregation. We also perform a comparative analytical study on the benefit of sharing under the mechanisms favorable for sharing, namely net metering, and net purchase and sale. The results are illustrated in a case study using real consumption data from a residential community in Austin, Texas.Comment: 12 page

Qualitative Criterion for Interception in a Pursuit/Evasion Game

A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exist is that, after some initial time, the future cone of the target be contained within the future cone of the interceptor. The sufficient condition may be regarded as a kind of Nash equillibrium.Comment: 8 pages; revsions and corrigend

Stochastic Dynamic Optimization Approaches and Computation

This description of stochastic dynamical optimization models is intended to exhibit some of the connections between various formulations that have appeared in the literature, and indicate some of the difficulties that must be overcome when trying to adapt solution methods that have been successfully applied to one class of problems to an apparently related but different class of problems. The emphasis is on solvable models. The authors begin with the least dynamical versions of stochastic optimization models, one- and two-stage models then consider discrete time models, and conclude with continuous time models