The norm optimal approach, both in its basic form and the extension to predictive action, where the predicted errors on a number of future trials are explicitly included in the cost function for controller design, is ...
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The norm optimal approach, both in its basic form and the extension to predictive action, where the predicted errors on a number of future trials are explicitly included in the cost function for controller design, is now a well established area in iterative learning control in terms of the underlying theory. By the fact that it includes the predicted errors on future trials in the cost function, predictive iterative learning control is clearly a higher order law. Hence it is now appropriate to ask if, in practical situations, predictive norm optimal iterative learning control can deliver significantly improved performance over its norm optimal alternative to merit the extra computational and hardware costs associated with its application. This is the area addressed in this paper using a somewhat new application area in the form of chain conveyor systems.
We study the complexity of approximating stochastic integrals with error epsilon for various classes of functions. For Ito integration, we show that the complexity is of order epsilon (-1), even for classes of very sm...
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We study the complexity of approximating stochastic integrals with error epsilon for various classes of functions. For Ito integration, we show that the complexity is of order epsilon (-1), even for classes of very smooth functions. The lower bound is obtained by showing that Ito integration is not easier than Lebesgue integration in the average case setting with the Wiener measure. The upper bound is obtained by the Milstein algorithm, which is almost optimal in the considered classes of functions. The Milstein algorithm uses the values of the Brownian motion and the integrand. It is bilinear in these values and is very easy to implement. For Stratonovich integration, we show that the complexity depends on the smoothness of the integrand and may be much smaller than the complexity of Ito integration.
Recent years has seen much progress in the theory and application of iterative learning control schemes for both linear and (classes of) nonlinear dynamics. In the case of the former, many algorithms based on minimizi...
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Recent years has seen much progress in the theory and application of iterative learning control schemes for both linear and (classes of) nonlinear dynamics. In the case of the former, many algorithms based on minimizing a suitable cost function have been reported. Here the interest is in the so-called norm optimal approach where the basic philosophy is to compute the control input on the current trial such that the tracking error is reduced in an optimal way without too much deviation from the control input used on the previous trial. This paper compares the performance of a range of controllers arising from use of the norm optimal approach - both stand alone and against alternatives.
Norm optimal iterative learning control is an optimization-based approach where, in contrast to other such approaches, a term in the cost function is a measure of the difference between the control vectors used on suc...
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Norm optimal iterative learning control is an optimization-based approach where, in contrast to other such approaches, a term in the cost function is a measure of the difference between the control vectors used on successive trials. This approach has very well defined theoretical properties and is predicted to give superior performance relative to alternatives when applied to physical processes. In this paper, we describe on-going work towards the implementation of controllers designed using this approach to chain conveyor systems with the eventual aim of examining/verifying performance in 'real world' applications.
The problem of finding a sublogarithmic time optimal parallel algorithm for 3-colouring rooted forests has been open for long. We settle this problem by obtaining an O ((log log n) log*(log* n)) time optimal parallel ...
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The problem of finding a sublogarithmic time optimal parallel algorithm for 3-colouring rooted forests has been open for long. We settle this problem by obtaining an O ((log log n) log*(log* n)) time optimal parallel algorithm on a TOLERANT Concurrent Read Concurrent Write (CRCW) Parallel Random Access Machine (PRAM). Furthermore, we show that if f(n) is the running time of the best known algorithm for 3-colouring a rooted forest on a COMMON or TOLERANT CRCW PRAM, a fractional independent set of the rooted forest can be found in O(f(n)) time with the same number of processors, on the same model. Using these results, it is shown that decomposable top-down algebraic computation a,nd, hence, depth computation (ranking), 2-colouring and prefix summation on rooted forests can be done in O (log n) optimal time on a TOLERANT CRCW PRAM. These algorithms have been obtained by proving a result of independent interest, one concerning the self-simulation property of TOLERANT: an N-processor TOLERANT CRCW PRAM that uses an address space of size O (N) only, can be simulated on an n-processor TOLERANT PRAM in O (N/n) time, with no asymptotic increase in space or cost, when n = O (N/log log N).
The complexities of weighted approximation and weighted integration problems for univariate functions defined over R have recently been found in [7]. Complexity (almost) optimal algorithms have also been provided ther...
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The complexities of weighted approximation and weighted integration problems for univariate functions defined over R have recently been found in [7]. Complexity (almost) optimal algorithms have also been provided therein. In this paper, we propose another class of (almost) optimal algorithms that, for a number of instances, are easier to implement. More importantly, these new algorithms have a cost smaller than the original algorithms from [7]. Since both classes of algorithms are (almost) optimal, their costs differ by a multiplicative constant that depends on the specific weight functions and the error demand. In one of our tests we observed this constant to be as large as four, which means a cost reduction by a factor of four.
An optimal algorithm is presented for tracking the phase of a slowly modulating signal by means of digital sampling of its sign. Error bounds and a numerical illustration are given.
An optimal algorithm is presented for tracking the phase of a slowly modulating signal by means of digital sampling of its sign. Error bounds and a numerical illustration are given.
A distributed computing system consists of a set of individual processors that communicate through some medium. Coordinating the actions of such processors is essential in distributed computing. Researchers have long ...
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A distributed computing system consists of a set of individual processors that communicate through some medium. Coordinating the actions of such processors is essential in distributed computing. Researchers have long endeavored to find efficient solutions to a variety of coordination problems. Recently, processor knowledge has been used to characterize such solutions and to derive more efficient ones. Most of this work has concentrated on the relationship between common knowledge and simultaneous coordination. This paper considers non-simultaneous coordination problems. The results of this paper add to our understanding of the relationship between knowledge and the different requirements of coordination problems. This paper considers the ideas of optimal and optimum solutions to a coordination problem and precisely characterizes the problems for which optimum solutions exist. This characterization is based on combinations of eventual common knowledge and continual common knowledge. The paper then considers more general problems, for which optimal, but no optimum, solutions exist. It defines a new form of knowledge, called extended knowledge, which combines eventual and continual knowledge, and shows how extended knowledge can be used to both characterize and construct optimal protocols for coordination. (C) 1999 Elsevier Science B.V. All rights reserved.
Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total worklo...
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Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
The channel-assignment problem is central to the integrated circuit fabrication process. Given a two-sided printed circuit board, the problem is to make n pairs of components electrically equivalent. The connections a...
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The channel-assignment problem is central to the integrated circuit fabrication process. Given a two-sided printed circuit board, the problem is to make n pairs of components electrically equivalent. The connections are made using two vertical runs along with a horizontal one. Each horizontal run lies in a channel. The problem is to minimize the total number of channels used. Our main contribution is to propose a time- and cost-optimal parallel algorithm to solve this problem. Specifically, with an instance of size n of the channel assignment problem as input, our algorithm runs in O(log n)time and uses O(n) processors in the EREW-PRAM model of computation.
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