A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.

Partial Integrated Guidance and Control of Surface-to-Air Interceptors for High Speed Targets

An important limitation of the existing IGC algorithms, is that they do not explicitly exploit the inherent time scale separation that exist in aerospace vehicles between rotational and translational motions and hence can be ineffective. To address this issue, a two-loop partial integrated guidance and control (PIGC) scheme has been proposed in this paper. In this design, the outer loop uses a recently developed, computationally efficient, optimal control formulation named as model predictive static programming. It gives the commanded pitch and yaw rates whereas necessary roll-rate command is generated from a roll-stabilization loop. The inner loop tracks the outer loop commands using the Dynamic inversion philosophy. Uncommonly, Six-Degree of freedom (Six-DOF) model is used directly in both the loops. This intelligent manipulation preserves the inherent time scale separation property between the translational and rotational dynamics, and hence overcomes the deficiency of current IGC designs, while preserving its benefits. Comparative studies of PIGC with one loop IGC and conventional three loop design were carried out for engaging incoming high speed target. Simulation studies demonstrate the usefulness of this method.

Modified ILMI algorithm for practical PID/PD implementation on a Micro Air Vehicle

This paper extends the iterative linear matrix inequality algorithm (ILMI) for systems having non-ideal PI, PD and PID implementations. The new algorithm uses the practical implementation of the feedback blocksto form the equivalent static output feedback plant. The LMI based synthesis techniques are used in the algorithm to design a multi-loop, multi-objective fixed structure control. The benefits of such a control design technique are brought out by applying it to the lateral stabilizing and tracking feedback control problem of a 30cm wingspan micro air vehicle.

Star Camera Calibration Combined with Independent Spacecraft Attitude Determination

A methodology for determining spacecraft attitude and autonomously calibrating star camera, both independent of each other, is presented in this paper. Unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters (like principal point offset, focal length etc.), the proposed method has the advantage of computing spacecraft attitude independently of camera calibrating parameters except lens distortion. In the proposed method both attitude estimation and star camera calibration is done together independent of each other by directly utilizing the star coordinate in image plane and corresponding star vector in inertial coordinate frame. Satellite attitude, camera principal point offset, focal length (in pixel), lens distortion coefficient are found by a simple two step method. In the first step, all parameters (except lens distortion) are estimated using a closed-form solution based on a distortion free camera model. In the second step lens distortion coefficient is estimated by linear least squares method using the solution of the first step to be used in the camera model that incorporates distortion. These steps are applied in an iterative manner to refine the estimated parameters. The whole procedure is faster enough for onboard implementation.

Positional Consensus in Multi-Agent Systems using a Broadcast Control Mechanism

In this paper a strategy for controlling a group of agents to achieve positional consensus is presented. The proposed technique is based on the constraint that every agents must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming formulation that is computationally less intensive than earlier proposed methods. Moreover, we introduce a random perturbation input in the control command that helps us to achieve perfect consensus even for a large number of agents, which was not possible with the existing strategy in the literature. Moreover, we extend the method to achieve positional consensus at a pre-specified location. The effectiveness of the approach is illustrated through simulation results.

Strategic Information Acquisition: Applications to Herding and Auctions

The information that the economic agents have and regard relevant to their decision making is often assumed to be exogenous in economics. It is assumed that the agents either poses or can observe the payoff relevant information without having to exert any effort to acquire it. In this thesis we relax the assumption of ex-ante fixed information structure and study what happens to the equilibrium behavior when the agents must also decide what information to acquire and when to acquire it. This thesis addresses this question in the two essays on herding and two essays on auction theory. In the first two essays, that are joint work with Klaus Kultti, we study herding models where it is costly to acquire information on the actions that the preceding agents have taken. In our model the agents have to decide both the action that they take and additionally the information that they want to acquire by observing their predecessors. We characterize the equilibrium behavior when the decision to observe preceding agents' actions is endogenous and show how the equilibrium outcome may differ from the standard model, where all preceding agents actions are assumed to be observable. In the latter part of this thesis we study two dynamic auctions: the English and the Dutch auction. We consider a situation where bidder(s) are uninformed about their valuations for the object that is put up for sale and they may acquire this information for a small cost at any point during the auction. We study the case of independent private valuations. In the third essay of the thesis we characterize the equilibrium behavior in an English auction when there are informed and uninformed bidders. We show that the informed bidder may jump bid and signal to the uninformed that he has a high valuation, thus deterring the uninformed from acquiring information and staying in the auction. The uninformed optimally acquires information once the price has passed a particular threshold and the informed has not signalled that his valuation is high. In addition, we provide an example of an information structure where the informed bidder initially waits and then makes multiple jumps. In the fourth essay of this thesis we study the Dutch auction. We consider two cases where all bidders are all initially uninformed. In the first case the information acquisition cost is the same across all bidders and in the second also the cost of information acquisition is independently distributed and private information to the bidders. We characterize a mixed strategy equilibrium in the first and a pure strategy equilibrium in the second case. In addition we provide a conjecture of an equilibrium in an asymmetric situation where there is one informed and one uninformed bidder. We compare the revenues that the first price auction and the Dutch auction generate and we find that under some circumstances the Dutch auction outperforms the first price sealed bid auction. The usual first price sealed bid auction and the Dutch auction are strategically equivalent. However, this equivalence breaks down in case information is acquired during the auction.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Non-linear systems with quadratic and cubic damping - an analytical approach

The possible equivalence of second-order non-linear systems having quadratic and cubic damping with third-order linear systems is studied in this paper. It is shown that this equivalence can be established through transformation techniques under certain constraints on the form of the non-linearity of the given system.

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.

Moiré Displacement Transducer for N/C Systems

Noncontact method of sensing accurately the magnitude and direction of displacements is essential in systems such as the numerically controlled machines. A displacement transducer, using Moiré transmission gratings is described. The notable feature of this instrument is that it requires only gratings of small lengths, even for measurement of large displacements.

Compact AM Signals for Maximum Clutter Rejection

The transmitted signal is assumed to consist of a close succession of rectangular pulses of equal width. A matched filter scheme is employed and a theory is developed for a computer-aided optimization of the envelope of monotone compact signals for maximum rejection of dense clutter of any given distribution in range. Specific results are presented and indeterminate cases are discussed.

Microwave modulation by amorphous-semiconductor switches

Microwave modulation has been achieved by using thin-film amorphous-semiconductor switches made of ternary chalcogenides. X-band microwaves were modulated by a threshold switch at frequencies varying from 100 Hz to 1 MHz, with modulation efficiencies comparable to siliconp¿i¿n diodes. The insertion loss was 0.5 to 0.6 dB and the isolation was 18 dB at 100 mA operating current. Possible applications this method are discussed.

Dominating search: Google before the law

For many, particularly in the Anglophone world and Western Europe, it may be obvious that Google has a monopoly over online search and advertising and that this is an undesirable state of affairs, due to Google's ability to mediate information flows online. The baffling question may be why governments and regulators are doing little to nothing about this situation, given the increasingly pivotal importance of the internet and free flowing communications in our lives. However, the law concerning monopolies, namely antitrust or competition law, works in what may be seen as a less intuitive way by the general public. Monopolies themselves are not illegal. Conduct that is unlawful, i.e. abuses of that market power, is defined by a complex set of rules and revolves principally around economic harm suffered due to anticompetitive behavior. However the effect of information monopolies over search, such as Google’s, is more than just economic, yet competition law does not address this. Furthermore, Google’s collection and analysis of user data and its portfolio of related services make it difficult for others to compete. Such a situation may also explain why Google’s established search rivals, Bing and Yahoo, have not managed to provide services that are as effective or popular as Google’s own (on this issue see also the texts by Dirk Lewandowski and Astrid Mager in this reader). Users, however, are not entirely powerless. Google's business model rests, at least partially, on them – especially the data collected about them. If they stop using Google, then Google is nothing.