Topics considered here include: examples of optimal control problems; dynamic programming and the Hamilton-Jacobi-Bellman equation; verification theorems; the Pontryagin Maximum Principle Principle. The examples include many with an economic flavor, but others too (including the Hopf-Lax solution formula for ut + H(Du) = 0 with H convex). There’s much more here than we’ll have time to do in lec...

The focus of this paper is the traffic shaping at the access of an network node. We propose a novel algorithm that dynamically shapes the incoming traffic, based on service curves equations, in order to meet the QoS constraints in terms of buffer size or delay. We first estimate arrival parameters within various time intervals in order to make the incoming traffic fit into a token bucket traffi...

Submit Manuscript | http://medcraveonline.com Abbreviations: ECoG: Electro Cortico Graphic; BdSEM: Bayesian Differential Structural Equation Modeling; ODEs: Ordinary Differential Equations; ROI: Region Of Interest; fMRI: functional Magnetic Resonance Imaging; MCMC: Markov Chain Monte Carlo; FDA: Functional Data Analysis; STG: Superior Temporal Gyrus; PostSTG: Posterior STG; MidSTG: Middle STG; ...

This papers describes a computer environment that supports the simultaneous electrical and thermal interactions at device and chip level. A circuit simulator and a finite element thermal simulator are coupled through an application program interface that synchronizes the transfer of information between two simulators. Temperature dependent thermal conductivity of silicon is taken into account b...

The solution phase transport and direct electrode kinetics of electro-enzymes are described in terms of a simple model in which the steady state reaction/diffusion equation for enzyme is solved subject to physically realistic boundary conditions. Two physically realizable situations are described: the semi infinite and the membrane bounded case. Limiting expressions for the reaction flux are de...

Abstract: A well-known advantage of bond graph models of electro-mechanical systems is that they can be manipulated manually or with the aid of computer programs to yield first order state equations useful for numerical studies. A causal analysis can show in advance whether derivative causality will cause practical difficulties in the equation formulation which might be best circumvented by mod...

We develop a discrete analogue of the Hamilton–Jacobi theory in the framework of the discrete Hamiltonian mechanics. We first reinterpret the discrete Hamilton–Jacobi equation derived by Elnatanov and Schiff in the language of discrete mechanics. The resulting discrete Hamilton– Jacobi equation is discrete only in time, and is shown to recover the Hamilton–Jacobi equation in the continuous-time...

In this paper we consider the optimal control problem for a insurance company. Our objective is to maximize the expectation of discounted dividends and its terminal value which represents the company liquidation value upon the time of bankruptcy. The surplus of the insurance company is governed by the Brownian motion with a constant drift and a diffusion term. The company can manage its risk ex...

We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measu...