Optimal non-linear reinforcement schemes for stochastic automata

Two optimal non-linear reinforcement schemes—the Reward-Inaction and the Penalty-Inaction—for the two-state automaton functioning in a stationary random environment are considered. Very simple conditions of symmetry of the non-linear function figuring in the reinforcement scheme are shown to be necessary and sufficient for optimality. General expressions for the variance and rate of learning are derived. These schemes are compared with the already existing optimal linear schemes in the light of average variance and average rate of learning.

Optimal design of multiproduct batch chemical plant using NSGA-II

The optimal design of a multiproduct batch chemical plant is formulated as a multiobjective optimization problem, and the resulting constrained mixed-integer nonlinear program (MINLP) is solved by the nondominated sorting genetic algorithm approach (NSGA-II). By putting bounds on the objective function values, the constrained MINLP problem can be solved efficiently by NSGA-II to generate a set of feasible nondominated solutions in the range desired by the decision-maker in a single run of the algorithm. The evolution of the entire set of nondominated solutions helps the decision-maker to make a better choice of the appropriate design from among several alternatives. The large set of solutions also provides a rich source of excellent initial guesses for solution of the same problem by alternative approaches to achieve any specific target for the objective functions

Optimal Risk Adoption: A Real Options Approach

This study develops a real options approach for analyzing the optimal risk adoption policy in an environment where the adoption means a switch from one stochastic flow representation into another. We establish that increased volatility needs not decelerate investment, as predicted by the standard literature on real options, once the underlying volatility of the state is made endogenous. We prove that for a decision maker with a convex (concave) objective function, increased post-adoption volatility increases (decreases) the expected cumulative present value of the post-adoption profit flow, which consequently decreases (increases) the option value of waiting and, therefore, accelerates (decelerates) current investment.

Bank Run Risk and Optimal Reserves

We characterize the optimal reserves, and the generated probability of a bank run, as a function of the penalty imposed by the central bank, the probability of depositors’ liquidity needs, and the return on outside investment opportunities.

Wave algorithms:Optimal database search and catalysis

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.

Optimal reactive power dispatch based on voltage stability criteria in a large power system with AC/DC and FACTs devices

An algorithm for optimal allocation of reactive power in AC/DC system using FACTs devices, with an objective of improving the voltage profile and also voltage stability of the system has been presented. The technique attempts to utilize fully the reactive power sources in the system to improve the voltage stability and profile as well as meeting the reactive power requirements at the AC-DC terminals to facilitate the smooth operation of DC links. The method involves successive solution of steady-state power flows and optimization of reactive power control variables with Unified Power Flow Controller (UPFC) using linear programming technique. The proposed method has been tested on a real life equivalent 96-bus AC and a two terminal DC system under normal and contingency conditions.

A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

Robust/optimal temperature profile control using neural networks

An approximate dynamic programming (ADP) based neurocontroller is developed for a heat transfer application. Heat transfer problem for a fin in a car's electronic module is modeled as a nonlinear distributed parameter (infinite-dimensional) system by taking into account heat loss and generation due to conduction, convection and radiation. A low-order, finite-dimensional lumped parameter model for this problem is obtained by using Galerkin projection and basis functions designed through the 'Proper Orthogonal Decomposition' technique (POD) and the 'snap-shot' solutions. A suboptimal neurocontroller is obtained with a single-network-adaptive-critic (SNAC). Further contribution of this paper is to develop an online robust controller to account for unmodeled dynamics and parametric uncertainties. A weight update rule is presented that guarantees boundedness of the weights and eliminates the need for persistence of excitation (PE) condition to be satisfied. Since, the ADP and neural network based controllers are of fairly general structure, they appear to have the potential to be controller synthesis tools for nonlinear distributed parameter systems especially where it is difficult to obtain an accurate model.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optinial dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator).

Optimal advertisement-innovation mix for maximizing the discounted flow of profit

Due to boom in telecommunications market, there is hectic competition among the cellular handset manufacturers. As cellular manufacturing industry operates in an oligopoly framework, often price-rigidity leads to non-price wars. The handset manufacturing firms indulge in product innovation and also advertise their products in order to achieve their objective of maximizing discounted flow of profit. It is of interest to see what would be the optimal advertisement-innovation mix that would maximize the discounted How of profit for the firms. We used differential game theory to solve this problem. We adopted the open-loop solution methodology. We experimented for various scenarios over a 30 period horizon and derived interesting managerial insights.

Optimal resource partitioning in conflicts based on Lanchester (n, 1) attrition model

This paper develops a model for military conflicts where the defending forces have to determine an optimal partitioning of available resources to counter attacks from an adversary from n different fronts. The problem of optimally partitioning the defending forces against the attacking forces is addressed. The Lanchester square law model is used to develop the dynamical equations governing the variation in force strength. Two different allocation schemes-Time-ZeroAllocation (TZA) and Continuous Constant Allocation (CCA) are considered and the optimal solutions for both are obtained analytically. These results generalize other results available in the literature. Numerical examples are given to support the analytical results.

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

Optimal Blood Glucose Regulation using Single Network Adaptive Critics

Diabetes is a serious disease during which the body's production and use of insulin is impaired, causing glucose concentration level toincrease in the bloodstream. Regulating blood glucose levels as close to normal as possible, leads to a substantial decrease in long term complications of diabetes. In this paper, an intelligent neural network on-line optimal feedback treatment strategy based on nonlinear optimal control theory is presented for the disease using subcutaneous treatment strategy. A simple mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system is considered based on the Bergman's minimal model. A glucose infusion term representing the effect of glucose intake resulting from a meal is introduced into the model equations. The efficiency of the proposed controllers is shown taking random parameters and random initial conditions in presence of physical disturbances like food intake. A comparison study with linear quadratic regulator theory brings Out the advantages of the nonlinear control synthesis approach. Simulation results show that unlike linear optimal control, the proposed on-line continuous infusion strategy never leads to severe hypoglycemia problems.

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A sub-space based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

A mathematical programming approach to optimal Markovian switching of Poisson arrival streams to queueing systems

Motivated by certain situations in manufacturing systems and communication networks, we look into the problem of maximizing the profit in a queueing system with linear reward and cost structure and having a choice of selecting the streams of Poisson arrivals according to an independent Markov chain. We view the system as a MMPP/GI/1 queue and seek to maximize the profits by optimally choosing the stationary probabilities of the modulating Markov chain. We consider two formulations of the optimization problem. The first one (which we call the PUT problem) seeks to maximize the profit per unit time whereas the second one considers the maximization of the profit per accepted customer (the PAC problem). In each of these formulations, we explore three separate problems. In the first one, the constraints come from bounding the utilization of an infinite capacity server; in the second one the constraints arise from bounding the mean queue length of the same queue; and in the third one the finite capacity of the buffer reflect as a set of constraints. In the problems bounding the utilization factor of the queue, the solutions are given by essentially linear programs, while the problems with mean queue length constraints are linear programs if the service is exponentially distributed. The problems modeling the finite capacity queue are non-convex programs for which global maxima can be found. There is a rich relationship between the solutions of the PUT and PAC problems. In particular, the PUT solutions always make the server work at a utilization factor that is no less than that of the PAC solutions.