Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

A generalized multi-period mean-variance portfolio optimization with Markov switching parameters

In this paper, we deal with a generalized multi-period mean-variance portfolio selection problem with market parameters Subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447-457]). We present necessary and Sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period meal-variance problem, based on a set of interconnected Riccati difference equations, and oil a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for Fisk control over bankruptcy Ill a dynamic portfolio selection problem with Markov jumps selection problem. (C) 2008 Elsevier Ltd. All rights reserved.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Perforin and interferon-gamma activities independently control tumor initiation, growth, and metastasis

Perforin (pfp) and interferon-gamma (IFN-gamma) together in C57BL/6 (B6) and BALB/c mouse strains provided optimal protection in 3 separate tumor models controlled by innate immunity. Using experimental (B6, RM-1 prostate carcinoma) and spontaneous (BALB/c, DA3 mammary carcinoma) models of metastatic cancer, mice deficient in both pfp and IFN-gamma were significantly less proficient than pfp- or IFN-gamma -deficient mice in preventing metastasis of tumor cells to the lung. Pfp and IFN-gamma -deficient mice were as susceptible as mice depleted of natural killer (NK) cells in both tumor metastasis models, and IFN-gamma appeared to play an early role in protection from metastasis, Previous experiments in a model of fibrosarcoma induced by the chemical carcinogen methylcholanthrene indicated an important role for NK1.1(+) T cells, Herein, both pfp and IFN-gamma played critical and independent roles in providing the host with protection equivalent to that mediated by NK1.1+ T cells, Further analysis demonstrated that IFN-gamma, but not pfp, controlled the growth rate of sarcomas arising in these mice. Thus, this is the first study to demonstrate that host IFN-gamma, and direct cytotoxicity mediated by cytotoxic lymphocytes expressing pfp independently contribute antitumor effector functions that together control the initiation, growth, and spread of tumors in mice, (C) 2001 by The American Society of Hematology.

Optimal reserve management and sovereign debt

Most models currently used to determine optimal foreign reserve holdings take the level of international debt as given. However, given the sovereign`s willingness-to-pay incentive problems, reserve accumulation may reduce sustainable debt levels. In addition, assuming constant debt levels does not allow addressing one of the puzzles behind using reserves as a means to avoid the negative effects of crisis: why do not sovereign countries reduce their sovereign debt instead? To study the joint decision of holding sovereign debt and reserves, we construct a stochastic dynamic equilibrium model calibrated to a sample of emerging markets. We obtain that the reserve accumulation does not play a quantitatively important role in this model. In fact, we find the optimal policy is not to hold reserves at all. This finding is robust to considering interest rate shocks, sudden stops, contingent reserves and reserve dependent output costs. (c) 2008 Elsevier B.V. All rights reserved.

The role of vaccines in the control of STDs: HPV vaccines

Prophylactic vaccines for genital human papillomavirus (HPV) infection have been shown to be feasible in animal models, and suitable vaccine material based on virus-like particles can be produced in bulk at reasonable cost. Initiation of phase III clinical trials will follow definition of trial outcome measures through further epidemiological studies, and development-of assays of host protective immunity. Vaccines could in principle eliminate HPV-related disease, as the human race is the only natural host for the relevant papillomaviruses (PVs). Therapeutic vaccines for genital HPV infection are also possible, but have not yet been demonstrated as feasible in practice because the choice of vaccine antigens is difficult, the method of their optimal delivery is uncertain, and the nature of the relevant antiviral immunity is unknown. PV species specificity will require trials to be conducted in man, which will slow definition of an ideal vaccine.

Multiplex semi-nested RT-PCR with exogenous internal control for simultaneous detection of bovine coronavirus and group A rotavirus

Neonatal calf diarrhea is a multi-etiology syndrome of cattle and direct detection of the two major agents of the syndrome, group A rotavirus and Bovine coronavirus (BCoV) is hampered by their fastidious growth in cell culture. This study aimed at developing a multiplex semi-nested RT-PCR for simultaneous detection of BCoV (N gene) and group A rotavirus (VP1 gene) with the addition of an internal control (mRNA ND5). The assay was tested in 75 bovine feces samples tested previously for rotavirus using PAGE and for BCoV using nested RT-PCR targeted to RdRp gene. Agreement with reference tests was optimal for BCoV (kappa = 0.833) and substantial for rotavirus detection (kappa = 0.648). the internal control, ND5 mRNA, was detected successfully in all reactions. Results demonstrated that this multiplex semi-nested RT-PCR was effective in the detection of BCoV and rotavirus, with high sensitivity and specificity for simultaneous detection of both viruses at a lower cost, providing an important tool for studies on the etiology of diarrhea in cattle. (C) 2010 Elsevier B.V. All rights reserved.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

The effect of resource aggregation at different scales: Optimal foraging behavior of Cotesia rubecula

Resources can be aggregated both within and between patches. In this article, we examine how aggregation at these different scales influences the behavior and performance of foragers. We developed an optimal foraging model of the foraging behavior of the parasitoid wasp Cotesia rubecula parasitizing the larvae of the cabbage butterfly Pieris rapae. The optimal behavior was found using stochastic dynamic programming. The most interesting and novel result is that the effect of resource aggregation within and between patches depends on the degree of aggregation both within and between patches as well as on the local host density in the occupied patch, but lifetime reproductive success depends only on aggregation within patches. Our findings have profound implications for the way in which we measure heterogeneity at different scales and model the response of organisms to spatial heterogeneity.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

A hedging point strategy - balancing effluent quality, economy and robustness in the control of wastewater treatment plants

An operational space map is an efficient tool to compare a large number of operational strategies to find an optimal choice of setpoints based on a multicriterion. Typically, such a multicriterion includes a weighted sum of cost of operation and effluent quality. Due to the relative high cost of aeration such a definition of optimality result in a relatively high fraction of the effluent total nitrogen in the form of ammonium. Such a strategy may however introduce a risk into operation because a low degree of ammonium removal leads to a low amount of nitrifiers. This in turn leads to a reduced ability to reject event disturbances, such as large variations in the ammonium load, drop in temperature, the presence of toxic/inhibitory compounds in the influent etc. Hedging is a risk minimisation tool, with the aim to "reduce one's risk of loss on a bet or speculation by compensating transactions on the other side" (The Concise Oxford Dictionary (1995)). In wastewater treatment plant operation hedging can be applied by choosing a higher level of ammonium removal to increase the amount of nitrifiers. This is a sensible way to introduce disturbance rejection ability into the multi criterion. In practice, this is done by deciding upon an internal effluent ammonium criterion. In some countries such as Germany, a separate criterion already applies to the level of ammonium in the effluent. However, in most countries the effluent criterion applies to total nitrogen only. In these cases, an internal effluent ammonium criterion should be selected in order to secure proper disturbance rejection ability.

Review and future directions in the modelling and control of continuous drum granulation

Many granulation plants operate well below design capacity, suffering from high recycle rates and even periodic instabilities. This behaviour cannot be fully predicted using the present models. The main objective of the paper is to provide an overview of the current status of model development for granulation processes and suggest future directions for research and development. The end-use of the models is focused on the optimal design and control of granulation plants using the improved predictions of process dynamics. The development of novel models involving mechanistically based structural switching methods is proposed in the paper. A number of guidelines are proposed for the selection of control relevant model structures. (C) 2002 Published by Elsevier Science B.V.

An optimal level of technology reliance on foreign partners in a global sourcing partnership: components procurement, technology management and market performance

Existing studies on global sourcing strategy have implicitly adopted a cJosed-systems perspective in which sourcing activities are managed within a multinational company across national boundaries. Produd and process innovations and components procurement that are jointly managed by a consortium of cooperating firms have not been examined. In this paper, we empiricallyexamine the issues concerning sourcing partnerships in an open-systems perspective. Findings suggest that even in a sourcing partnership arrangement with a foreign supplier, the principal firm's ability to procure and control the supply of major components has a positive bearing on its market performance.

Adaptable control for electrical generation at irregural wind speeds

The main aims of this work are the development and the validation of one generic algorithm to provide the optimal control of small power wind generators. That means up to 40 kW and blades with fixed pitch angle. This algorithm allows the development of controllers to fetch the wind generators at the desired operational point in variable operating conditions. The problems posed by the variable wind intensity are solved using the proposed algorithm. This is done with no explicit measure of the wind velocity, and so no special equipment or anemometer is required to compute or measure the wind velocity.

Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations.