control with limited communication and message losses

We propose an H^∞ approach to a remote control problem where the communication is constrained due to the use of a shared channel. The controller employs a periodic time sequencing scheme for message transmissions from multiple sensors and to multiple actuators of the system. It further takes into account the information on the random message losses that occur in the channel. An exact characterization for controller synthesis is obtained and is stated in terms of linear matrix inequalities. Furthermore, an analysis on the loss probabilities of the messages to accomplish stabilization is carried out. The results are illustrated through a numerical example.     

Challenges of 22 nm and beyond CMOS technology

It is predicted that CMOS technology will probably enter into 22 nm node around 2012. Scaling of CMOS logic technology from 32 to 22 nm node meets more critical issues and needs some significant changes of the technology, as well as integration of the advanced processes. This paper will review the key processing technologies which can be potentially integrated into 22 nm and beyond technology nodes, including double patterning technology with high NA water immersion lithography and EUV lithography, new devi...     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.     

Controller certification

A modern problem from aerospace control involves the certification of a large set of potential controllers with either a single plant or a fleet of potential plant systems, with both plants and controllers being MIMO and, for the moment, linear. Experiments on a limited number of controller/plant pairs should establish the stability and a certain level of margin of the complete set. We consider this certification problem for a set of controllers and provide algorithms for selecting an efficient subset for testing. This is done for a finite set of candidate controllers and, at least for SISO plants, for compact infinite set. In doing this, the ν-gap metric will be the main tool. Computational examples are given, including one of certification of an aircraft engine controller. The overarching aim is to introduce truly MIMO margin calculations and to understand their efficacy in certifying stability over a set of controllers and in replacing legacy single-loop gain and phase margin calculations.     

Maximally equidistributed pseudorandom number generators via linear output transformations

This article discusses construction of maximally equidistributed (ME) linear feedback shift register generators by using linear output transformations. We introduce a new strategy to find linear output transformations attaining the ME property, and apply it to the WELL generators and the Mersenne Twister. As a result, we found a modified version of the WELL generators with the ME property, having fewer operations than the original ME WELL generators. We also found a ME Mersenne Twister which is faster than the WELL generators with a period of 2¹⁹⁹³⁷−1$2^{19937}-1$ on some platforms. The C codes of the obtained generators are available at http://www3.ocn.ne.jp/∼harase/megenerators.html.     

On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

In this paper, to obtain an efficient parallel algorithm to solve sparse block-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism. Moreover, some theoretical results concerning these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block tridiagonal H-matrices is also described. In addition, the validity of these preconditioners is illustrated with some numerical experiments arising from the second order elliptic partial differential equations and oil reservoir simulations.     

General linear methods for ordinary differential equations

General linear methods were introduced as the natural generalizations of the classical Runge–Kutta and linear multistep methods. They have potential applications, especially for stiff problems. This paper discusses stiffness and emphasises the need for efficient implicit methods for the solution of stiff problems. In this context, a survey of general linear methods is presented, including recent results on methods with the inherent RK stability property.     

Patterns for multigrid equidistributed functions: Application to general parabolas and length estimation

We show that for some special functions (called k-multigrid equidistributed functions), we can compute the limit of the frequency of patterns in the discretization of their graph, when the resolution tends to zero. This result is applied to parabolas. We deduce also that local length estimators almost never converge to the length for the parabolas.     

On Constructing Unit Triangular Matrices with Prescribed Singular Values

We propose an efficient algorithm for computing a unit lower triangular n×n matrix with prescribed singular values of O(n ²) cost. This is a solution of the question raised by N. J. Higham in [4, Problem 26.3, p. 528]. Received July 21, 1999; revised November 4, 1999     

A Cascadic Multigrid Algorithm for Semilinear Indefinite Elliptic Problems

We propose a cascadic multigrid algorithm for a semilinear indefinite elliptic problem. We use a standard finite element discretization with piecewise linear finite elements. The arising nonlinear equations are solved by a cascadic organization of Newton's method with frozen derivative on a sequence of nested grids. This gives a simple version of a multigrid method without projections on coarser grids. The cascadic multigrid algorithm starts on a comparatively coarse grid where the number of unknowns is small enough to obtain an approximate solution within sufficiently high precision without substantial computational effort. On each finer grid we perform exactly one Newton step taking the approximate solution from the coarsest grid as initial guess. The linear Newton systems are solved iteratively by a Jacobi-type iteration with special parameters using the approximate solution from the previous grid as initial guess. We prove that for a sufficiently fine initial grid and for a sufficiently good start approximation the algorithm yields an approximate solution within the discretization error on the finest grid and that the method has multigrid complexity with logarithmic multiplier. Received February 1999, revised July 13, 1999