An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Synthesis of PID controllers for a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results on the design of proportional plus integral plus derivative (PID) controllers for a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. As far as we know, previous results on the synthesis of PID controllers rely on the solution of transcendental equations. This paper also extends previous results on the synthesis of proportional controllers for a class of delay systems Of retarded type to a larger class of delay systems. (C) 2009 Elsevier Ltd. All rights reserved.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Scaling of structures subject to impact loads when using a power law constitutive equation

It is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads. (C) 2009 Elsevier Ltd. All rights reserved.

Investigation of a method for predicting AUV derivatives

The paper addresses the problem of autonomous underwater vehicle (AUV) modelling and parameter estimation as a means to predict the dynamic performance of underwater vehicles and thus provide solid guidelines during their design phase. The use of analytical and semi-empirical (ASE) methods to estimate the hydrodynamic derivatives of a popular class of AUVs is discussed. A comparison is done with the results obtained by using computational fluid dynamics to evaluate the bare hull lift force distribution around a fully submerged body. An application is made to the estimation of the hydrodynamic derivatives of the MAYA AUV, an autonomous underwater vehicle developed under a joint Indian-Portuguese project. The estimates obtained were used to predict the turning diameter of the vehicle during sea trials. (C) 2008 Elsevier Ltd. All rights reserved.

Stable Model Predictive Control for Integrating Systems with Optimizing Targets

This paper concern the development of a stable model predictive controller (MPC) to be integrated with real time optimization (RTO) in the control structure of a process system with stable and integrating outputs. The real time process optimizer produces Optimal targets for the system inputs and for Outputs that Should be dynamically implemented by the MPC controller. This paper is based oil a previous work (Comput. Chem. Eng. 2005, 29, 1089) where a nominally stable MPC was proposed for systems with the conventional control approach where only the outputs have set points. This work is also based oil the work of Gonzalez et at. (J. Process Control 2009, 19, 110) where the zone control of stable systems is studied. The new control for is obtained by defining ail extended control objective that includes input targets and zone controller the outputs. Additional decision variables are also defined to increase the set of feasible solutions to the control problem. The hard constraints resulting from the cancellation of the integrating modes Lit the end of the control horizon are softened,, and the resulting control problem is made feasible to a large class of unknown disturbances and changes of the optimizing targets. The methods are illustrated with the simulated application of the proposed,approaches to a distillation column of the oil refining industry.

Minimizing total tardiness in a stochastic single machine scheduling problem using approximate dynamic programming

This paper addresses the non-preemptive single machine scheduling problem to minimize total tardiness. We are interested in the online version of this problem, where orders arrive at the system at random times. Jobs have to be scheduled without knowledge of what jobs will come afterwards. The processing times and the due dates become known when the order is placed. The order release date occurs only at the beginning of periodic intervals. A customized approximate dynamic programming method is introduced for this problem. The authors also present numerical experiments that assess the reliability of the new approach and show that it performs better than a myopic policy.

Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure. (C) 2008 Published by Elsevier B.V.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

A Class of Channels Resulting in Ill-Convergence for CMA in Decision Feedback Equalizers

This paper analyzes the convergence of the constant modulus algorithm (CMA) in a decision feedback equalizer using only a feedback filter. Several works had already observed that the CMA presented a better performance than decision directed algorithm in the adaptation of the decision feedback equalizer, but theoretical analysis always showed to be difficult specially due to the analytical difficulties presented by the constant modulus criterion. In this paper, we surmount such obstacle by using a recent result concerning the CM analysis, first obtained in a linear finite impulse response context with the objective of comparing its solutions to the ones obtained through the Wiener criterion. The theoretical analysis presented here confirms the robustness of the CMA when applied to the adaptation of the decision feedback equalizer and also defines a class of channels for which the algorithm will suffer from ill-convergence when initialized at the origin.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

New simple and efficient heuristics for the uncapacitated single allocation hub location problem

Hub-and-spoke networks are widely studied in the area of location theory. They arise in several contexts, including passenger airlines, postal and parcel delivery, and computer and telecommunication networks. Hub location problems usually involve three simultaneous decisions to be made: the optimal number of hub nodes, their locations and the allocation of the non-hub nodes to the hubs. In the uncapacitated single allocation hub location problem (USAHLP) hub nodes have no capacity constraints and non-hub nodes must be assigned to only one hub. In this paper, we propose three variants of a simple and efficient multi-start tabu search heuristic as well as a two-stage integrated tabu search heuristic to solve this problem. With multi-start heuristics, several different initial solutions are constructed and then improved by tabu search, while in the two-stage integrated heuristic tabu search is applied to improve both the locational and allocational part of the problem. Computational experiments using typical benchmark problems (Civil Aeronautics Board (CAB) and Australian Post (AP) data sets) as well as new and modified instances show that our approaches consistently return the optimal or best-known results in very short CPU times, thus allowing the possibility of efficiently solving larger instances of the USAHLP than those found in the literature. We also report the integer optimal solutions for all 80 CAB data set instances and the 12 AP instances up to 100 nodes, as well as for the corresponding new generated AP instances with reduced fixed costs. Published by Elsevier Ltd.