D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the orthogonal and the nonorthogonal amplify-and-forward (NAF) protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Moreover our code construction for the OAF protocol incurs less delay. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. The variable-NSDF protocol is shown to improve on the DMT of the best previously known static protocol when the number of relays is greater than two. Also included is a DMT optimal code construction for the NAF protocol.

Learning Optimal Discriminant Functions through a Cooperative Game of Automata

The problem of learning correct decision rules to minimize the probability of misclassification is a long-standing problem of supervised learning in pattern recognition. The problem of learning such optimal discriminant functions is considered for the class of problems where the statistical properties of the pattern classes are completely unknown. The problem is posed as a game with common payoff played by a team of mutually cooperating learning automata. This essentially results in a probabilistic search through the space of classifiers. The approach is inherently capable of learning discriminant functions that are nonlinear in their parameters also. A learning algorithm is presented for the team and convergence is established. It is proved that the team can obtain the optimal classifier to an arbitrary approximation. Simulation results with a few examples are presented where the team learns the optimal classifier.

An Optimal g-Guidance Scheme for Satellite Launch Vehicles

A closed-loop steering logic based on an optimal (2-guidance is developed here. The guidance system drives the satellite launch vehicle along a two- or three- dimensional trajectory for placing the payload into a specified circular orbit. The modified g-guidance algorithm makes use of the optimal required velocity vector, which minimizes the total impulse needed for an equivalent two-impluse transfer from the present state to the final orbit. The required velocity vector is defined as velocity of the vehicle on the hypothetical transfer orbit immediately after the application of the first impulse. For this optimal transfer orbit, a simple and elegant expression for the Q-matrix is derived. A working principle for the guidance algorithm in terms of the major and minor cycles, and also for the generation of the steering command, is outlined.

An Online Implementable Differential Evolution Tuned Optimal Guidance Law

This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly. The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.

Optimal dynamic inversion-based semi-active control of benchmark bridge using MR dampers

A new two-stage state feedback control design approach has been developed to monitor the voltage supplied to magnetorheological (MR) dampers for semi-active vibration control of the benchmark highway bridge. The first stage contains a primary controller, which provides the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion (ODI) approach has been developed to obtain the amount of voltage to be supplied to each of the MR dampers such that it provides the required force prescribed by the primary controller. ODI is formulated by optimization with dynamic inversion, such that an optimal voltage is supplied to each damper in a set. The proposed control design has been simulated for both phase-I and phase-II study of the recently developed benchmark highway bridge problem. The efficiency of the proposed controller is analyzed in terms of the performance indices defined in the benchmark problem definition. Simulation results demonstrate that the proposed approach generally reduces peak response quantities over those obtained from the sample semi-active controller, although some response quantities have been seen to be increasing. Overall, the proposed control approach is quite competitive as compared with the sample semi-active control approach.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters I. Algorithm

The simultaneous state and parameter estimation problem for a linear discrete-time system with unknown noise statistics is treated as a large-scale optimization problem. The a posterioriprobability density function is maximized directly with respect to the states and parameters subject to the constraint of the system dynamics. The resulting optimization problem is too large for any of the standard non-linear programming techniques and hence an hierarchical optimization approach is proposed. It turns out that the states can be computed at the first levelfor given noise and system parameters. These, in turn, are to be modified at the second level.The states are to be computed from a large system of linear equations and two solution methods are considered for solving these equations, limiting the horizon to a suitable length. The resulting algorithm is a filter-smoother, suitable for off-line as well as on-line state estimation for given noise and system parameters. The second level problem is split up into two, one for modifying the noise statistics and the other for modifying the system parameters. An adaptive relaxation technique is proposed for modifying the noise statistics and a modified Gauss-Newton technique is used to adjust the system parameters.

Optimal simultaneous maximum a posterioriestimation of states, noise statistics and parameters II. Numerical performance

A very general and numerically quite robust algorithm has been proposed by Sastry and Gauvrit (1980) for system identification. The present paper takes it up and examines its performance on a real test example. The example considered is the lateral dynamics of an aircraft. This is used as a vehicle for demonstrating the performance of various aspects of the algorithm in several possible modes.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Optimal irrigation planning in river basin development: The case of the Upper Cauvery river basin

The study deals with the irrigation planning of the Cauvery river basin in peninsular India which is extensively developed in the downstream reaches and has a high potential for development in the upper reaches. A four-reservoir system is modelled on a monthly basis by using a mathematical programming (LP) formulation to find optimum cropping patterns, subject to land, water and downstream release constraints, and applied to the Cauvery basin. Two objectives, maximizing net economic benefits and maximizing irrigated cropped area, considered in the model are analysed in the context of multiobjective planning and the trade-offs discussed.

Active vibration suppression of non-linear beams using optimal dynamic inversion

Euler–Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

Optimal popular matchings

In this paper we consider the problem of computing an “optimal” popular matching. We assume that our input instance View the MathML source admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n2+m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.

Optimal maintenance and replacement via a semi-Markov decision model

Optimal bang-coast maintenance policies for a machine, subject to failure, are considered. The approach utilizes a semi-Markov model for the system. A simplified model for modifying the probability of machine failure with maintenance is employed. A numerical example is presented to illustrate the procedure and results.

Constrained linear filter and its relation to singular optimal control

This paper presents an analysis of an optimal linear filter in the presence of constraints on the moan squared values of the estimates from the viewpoint of singular optimal control. The singular arc has been shown to satisfy the generalized Legcndrc-Clebseh condition and Jacobson's condition. Both the cases of white measurement noise and coloured measurement noise are considered. The constrained estimate is shown to be a linear transformation of the unconstrained Kalman estimate.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example