A fast circuit module for digital systems

This paper describes anAnd-or-Invert module developed for theOldap computer designed and being built at the Tata Institute of Fundamental Research. To obtain the maximum speed out of available transistors, the circuit makes use of antisaturation and anti-cut-off techniques. The effect of different components on the transient response of the circuit is described. Detailed results of DC tolerance analysis and noise margins are included. The module which uses only indigenous components should be useful in any general digital system where speed is an important requirement.     

A Jordan surface theorem for three-dimensional digital spaces

Many applications of digital image processing now deal with three-dimensional images (the third dimension can be time or a spatial dimension). In this paper we develop a topological model for digital three space which can be useful in this context. In particular, we prove a digital, three-dimensional, analogue of the Jordan curve theorem. (The Jordan curve theorem states that a simple closed curve separates the real plane into two connected components.) Our theorem here is a digital topological formulation of the Jordan-Brouwer theorem about surfaces that separate three-dimensional space into two connected components.     

Robust digital controllers for uncertain chaotic systems: A digital redesign approach

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems––chaotic systems.     

A branch-cut-and-price algorithm for optimal decoding in digital communication systems

Journal of Global Optimization - Channel coding aims to minimize the errors that occur during the transmission of digital information from one place to another. Low-density parity-check codes can...     

Modelling and system identification of active magnetic bearing systems

Active magnetic bearing (AMB) systems have recently attracted much attention in the rotating machinery industry due to their advantages over traditional bearings such as fluid film and rolling element bearings. The AMB control system must provide robust performance over a wide range of machine operating conditions and over the machine lifetime in order to make this technology commercially viable. An accurate plant model for AMB systems is essential for the aggressive design of control systems. In this paper, we propose two approaches to obtain accurate AMB plant models for the purpose of control design: physical modelling and system identification. The former derives a model based upon the underlying physical principles. The latter uses input – output data without explicitly resorting to physical principles. For each problem, a brief summary of the theoretical derivation and assumptions is given. Experimental results based on data collected from an AMB test facility at the United Technologies Research Center provide a vehicle for a comparison of the two approaches.     

Quasi hyperrigidity and weak peak points for non-commutative operator systems

In this article, we introduce the notions of weak boundary representation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in \(C^*\)-algebras. An analogue of Saskin’s theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of \(C^*\)-algebras is proved. We also show that, if an irreducible representation is a weak boundary representation and weak peak then it is a boundary representation. Several examples are provided to illustrate these notions.     

Optimization models for assessing the peak capacity utilization of intelligent transportation systems

With limited economic and physical resources, it is not feasible to continually expand transportation infrastructure to adequately support the rapid growth in its usage. This is especially true for traffic coordination systems where the expansion of road infrastructure has not been able to keep pace with the increasing number of vehicles, thereby resulting in congestion and delays. Hence, in addition to striving for the construction of new roads, it is imperative to develop new intelligent transportation management and coordination systems. The effectiveness of a new technique can be evaluated by comparing it with the optimal capacity utilization. If this comparison indicates that substantial improvements are possible, then the cost of developing and deploying an intelligent traffic system can be justified. Moreover, developing an optimization model can also help in capacity planning. For instance, at a given level of demand, if the optimal solution worsens significantly, this implies that no amount of intelligent strategies can handle this demand, and expanding the infrastructure would be the only alternative. In this paper, we demonstrate these concepts through a case study of scheduling vehicles on a grid of intersecting roads. We develop two optimization models namely, the mixed integer programming model and the space-time network flow model, and show that the latter model is substantially more effective. Moreover, we prove that the problem is strongly NP-hard and develop two polynomial-time heuristics. The heuristic solutions are then compared with the optimal capacity utilization obtained using the space-time network model. We also present important managerial implications.     

Interior peak solutions for an elliptic system of FitzHugh-Nagumo type

We consider the Dirichlet problem for an elliptic system of FitzHugh-Nagumo type. We prove that the problem has a solution with a sharp peak inside the domain.     

A Hyland-Bernstein approach to the digital control of Pritchard-Salamon systems

In this paper we consider the fixed finite-order digital linear-quadraticcontrol of Pritchard-Salamon infinite-dimensional systems withunbounded input and output operators under gaussian disturbances.A set of necessary conditions is given in terms of the solvabilityof a discrete-time Hyland-Bernstein system of equations (twomodified Riccati equations and two modified Lyapunov equationscoupled by an projection operator).     

A Popov-theory-based survey on digital control of infinite-dimensional systems with unboundedness

This paper represents a Popov-theory-based assessment of thecurrent status of the digital control of infinite–dimensionalsystems with certain unboundedness in control and/or observation,summarizing some results and indicating which, in the authors'opinion, would be the promising directions for future research.     

An optimal linear-quadratic digital tracker for analog neutral time-delay systems

^** Email: shtsai{at}mail.ncku.edu.tw In this paper, an optimal hybrid tracking control problem forcontinuous neutral time-delay systems is formulated and studied.An optimal linear integral quadratic cost function that hasa high-gain property is used for tracking control specification.Two interpolation methods are applied to directly convert theoriginal analog neutral time-delay system into an equivalentdigital retarded time-delay system, and meanwhile convert thecontinuous-time quadratic cost function into a discretized form.Then, an extended state vector is constructed for an associateextended discrete-time optimal control problem without timedelay. Using the standard discrete-time linear-quadratic optimalcontrol theory and an indirect digital redesign technique witha predictive feature, an effective digital tracker is designedfor the original analog neutral time-delay system. An exampleis finally given for illustrating the effectiveness of the newtracker design method.     

Simple digital quantum algorithm for symmetric first-order linear hyperbolic systems

Numerical Algorithms - This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first-order linear hyperbolic systems, thanks to the reservoir...     

A Popov-theory-based approach to digital H{infty} control with measurement feedback for Pritchard-Salamon systems

In this paper, we deal with the digital output-measurement-feedbackH control problem for Pritchard-Salamon infinite-dimensionalsystems with unbounded input and output operators. A discretePopov-theory-based solution is given in terms of the solvabilityof Kalman-Szegö-Popov-Yakubovitch systems associated withthe equivalent discrete-time time-invariant system obtainedby lifting the T-periodic continuous-time system.     

A new method of digital simulation for an aircraft gas turbine engine control system

An LD-9 aircraft gas turbine engine with its control system is simulated digitally by a new method, called the ‘method of spare parts’. The computer program of simulation possesses the main capabilities of a real engine altitude test facility and is called a ‘digital engine altitude simulator’. The results of simulation show that the capabilities of this new method are much better than that of the ordinary ‘method of block diagram’. The method can be used for modelling and simulating any type of gas turbine engines or industrial process control systems.     

A model for peak formation in the two-phase equations

We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.

     

A regularity criterion for the 2D MHD system with zero magnetic diffusivity

This note proves a regularity criterion ∇b∈L¹(0,T;BMO(R²)) for the 2D MHD system with zero magnetic diffusivity.     

Basis difference method for orthogonal systems on a surface

The basis operator method intended for constructing systems of difference approximations to differential operators in vector and tensor analysis is extended to orthogonal systems on a surface. A class of completely conservative differential-difference schemes for continuum mechanics in Lagrangian variables is constructed. Basis operators are constructed using the finite volume equation, consistency conditions for discrete operators of the first derivative, and consistent projection operators for grid functions. A system of differential-difference continuum mechanics equations on a surface is obtained, which implies all conservation laws typical of the continuum case, including additional ones. A stability estimate is derived for discrete equations of an incompressible viscous fluid.     

Scatteing for hydrogen-like systems in a constant magnetic field ∗∗

We prove asymptotic completeness for a system of two particles with opposite charges interacting via a long-range potential decaying faster than |r|^-1/2 at infinity in a homogeneous magnetic field. In particular, our result implies asymptotic completeness for the hydrogen atom with finite nuclear mass in a uniform magnetic field, which has not been proven previously.