We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile nodes to minimize an uncertainty metric in a given mission space. For multi agent in a one-dimensional mission space, we show that the optimal solution is obtained in terms of a sequence of switching locations and waiting time on these switching points, thus reduci...

This paper proves convergence of a sample-path based stochastic gradient-descent algorithm for optimizing expected-value performance measures in discrete event systems. The algorithm uses increasing precision at successive iterations, and it moves against the direction of a generalized gradient of the computed sample performance function. Two convergence results are established: one, for the ca...

In this paper, we employ two stock pricing models: a Black-Scholes (BS) model and a Variance Gamma (VG) model, and apply the maximum likelihood method (MLE) to estimate corresponding parameters in each model. With the estimated parameters, we conduct Monte Carlo simulations to simulate spot prices and deltas of the European call option at different time spots over different sample paths. We foc...

We formulate the importance sampling problem as a parametric minimization problem under the original measure and use a combination of infinitesimal perturbation analysis (IPA) and stochastic approximation (SA) to minimize the variance of the price estimation. Compared to existing methods, the IPA estimator derived in this paper has significantly smaller estimation variance and doesn’t depend on...

Infinitesimal Perturbation Analysis (IPA) estimators of the response gradient for a discrete event stochastic simulation are typically developed within the framework of Generalized semi-Markov processes (GSMPs). Unfortunately, while mathematically rigorous, GSMPs are not particularly useful for modeling real systems. In this paper we describe a procedure that allows IPA gradient estimation to b...

In this study an analytical method is developed to obtain the response of electro-magneto-thermo-elastic stress and perturbation of a magnetic field vector for a thick-walled spherical functionally graded piezoelectric material (FGPM). The hollow sphere, which is placed in a uniform magnetic field, is subjected to a temperature gradient, inner and outer pressures and a constant electric potenti...

We prove an extension theorem for a small perturbation of the Ornstein-Uhlenbeck operator (L,D(L)) in the space of all uniformly continuous and bounded functions f : H → R, where H is a separable Hilbert space. We consider a perturbation of the form N0φ = Lφ + 〈Dφ,F 〉 where F : H → H is bounded and Fréchet differentiable with uniformly continuous and bounded differential. Hence, we prove that N...

Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbatio...

in this paper robust pid control of fully-constrained cable driven parallel manipulators with elastic cables is studied in detail. in dynamic analysis, it is assumed that the dominant dynamics of cable can be approximated by linear axial spring. to develop the idea of control for cable robots with elastic cables, a robust pid control for cable driven robots with ideal rigid cables is firstly de...