Showing papers in "Control and Cybernetics in 2007"

Application of a quantitative multiple criteria decision making (MCDM-1) approach to the analysis of investments in construction

Abstract: The paper considers major principles of methods based on quantitative measurements. The problem of construction investments is of paramount importance because they determine the potential of construction and the structure of expenses. The cal- culation of investments is an expensive tool of enterprise manage- ment used in planning the investments. It can be perceived as the harmonization and evaluation of the models for investment decision- making. Methods based on a single criterion can hardly be used in solving the problems associated with sophisticated technological or marketing systems. It is a multiple attribute decision method, taking into consideration major efficiency criteria, that enables the effective methods of solving complicated problems. When the quantitative criteria are precisely defined, the developed quantitative multiple criteria decision making (MCDM-1) method can be successfully ap- plied. The present paper is devoted to the analysis of the algorithm and methods of application of the suggested technique.

Variational principles for set-valued mappings with applications to multiobjective optimization

Abstract: This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (includ- ing those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational princi- ples for set-valued mappings, which—being certainly of independent interest—are mainly motivated by applications to multiobjective op- timization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued ex- tension of the subdifferential principle by Mordukhovich and Wang, formulated via an appropriate subdifferential notion for set-valued mappings with values in partially ordered spaces. Based on these variational principles and corresponding tools of generalized differen- tiation, we derive new conditions of the coercivity and Palais-Smale types ensuring the existence of optimal solutions to set-valued opti- mization problems with noncompact feasible sets in infinite dimen- sions and then obtain necessary optimality and suboptimality con- ditions for nonsmooth multiobjective optimization problems with general constraints, which are new in both finite-dimensional and infinite-dimensional settings.

Interactive multi-objective optimization for simulated moving bed processes

Abstract: In this paper, efficient optimization techniques are used to solve multi-objective optimization problems arising from Simulated Moving Bed (SMB) processes. SMBs are widely used in many industrial separations of chemical products and they are very challenging from the optimization point of view. With the help of interactive multi-objective optimization, several conflicting objec- tives can be considered simultaneously without making unnecessary simplifications, as it has been done in previous studies. The op- timization techniques used are the interactive NIMBUS R method and the IPOPT optimizer. To demonstrate the usefulness of these techniques, the results of solving an SMB optimization problem with four objectives are reported.

Equivalence of second order optimality conditions for bang-bang control problems. Part 2 : Proofs, variational derivatives and representations

Abstract: In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit rela- tions between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and ini- tial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms. Keywords: bang-bang control, second order necessary and sufficient conditions, critical cones, equivalence of quadratic forms, representation of the Hessian of the Lagrangian.

An existence theorem for set differential inclusions in a semilinear metric space

Abstract: Using the notion of continuous approximate selec- tions, we establish an existence theorem for set differential inclusions in a semi-linear metric space.

Weak sharp minima in multiobjective optimization

Abstract: We extend some necessary and sufficient conditions for strict local Pareto minima of orderm obtained by Jimenez (2002) to the case of weak -sharp local Pareto minima, i.e., to the case when the local solution is not necessarily unique.

Optimal control for a class of mechanical thermoviscoelastic frictional contact problems

Abstract: We study the optimal control of systems governed by a coupled system of hemivariational inequalities modeling a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt viscoelastic law, include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. We consider optimal control problem for boundary and distributed parameter control systems, time optimal control problem and maximum stay control problem. We deliver conditions that guarantee the existence of optimal solutions.

Existence conditions in symmetric multivalued vector quasiequilibrium problems

Abstract: We consider symmetric multivalued vector quasiequi- librium problems in topological vector spaces. Sufficient conditions for the solution existence are established under relaxed assumptions, which are shown by examples to be essential, easy to check and more advantageous than recent known results. Applications to lower and upper bounded quasiequilibrium problems and to coincidence point problems are given.

Emotional learning based intelligent speed and position control applied to neurofuzzy model of switched reluctance motor

Abstract: Control and Intelligent Processing Center of ExcellenceElectrical and Computer Engineering Department, University of Tehran, Irane-mail: horouhani@ut.ac.ir, a.sadeghzadeh@ece.ut.ac.ir, lucas@ipm.ir,araabi@ut.ac.irAbstract: In this paper, rotor speed and position of a SwitchedReluctance Motor (SRM) are controlled using an intelligent controlalgorithm. The controller is working based on a PID signal whileits gain is permanently tuned by means of an Emotional LearningAlgorithm to achieve a better control performance. Here, nonlinearcharacteristic of SRM is identified using an efficient training algo-rithm (LoLiMoT) for Locally Linear Neurofuzzy Model as an un-specified nonlinear plant model. Then, the Brain Emotional Learn-ing Based Intelligent Controller (BELBIC) is applied to the obtainedmodel. While the intelligent controller works based on a computa-tional model of a limbic system in the mammalian brain, its contri-bution is to improve the performance of a classic controller like PIDwithout much more control effort. The results demonstrate excellentimprovements of control action in different working situations.Keywords: intelligent control, emotion based learning, neuro-fuzzy models, switched reluctance motor.

On regularity estimates for mappings between embedded manifolds

Abstract: We describe a class of metric spaces such that for set-valued mappings into such spaces it is possible to give a pre- cise expression of regularity moduli in terms of slopes of DeGiorgi- Marino-Tosques. We also show that smooth manifolds in Banach spaces endowed with the induced metric belong to this class.

Condition numbers and Ritz type methods in unconstrained optimization

Abstract: Condition numbers for infinite-dimensional optimiza- tion, as defined in Zolezzi (2002, 2003), are shown to exhibit a stable behavior when employing finite-dimensional solution methods of the Ritz type, in particular finite elements. The same behavior is shown to hold in connection with the so called extended Ritz method.

Towards historical roots of necessary conditions of optimality. Regula of Peano

Abstract: At the end of 19th century Peano discerned vector spaces, differentiability, convex sets, limits of families of sets, tangent cones, and many other concepts, in a modern perfect form. He applied these notions to solve numerous problems. The theorem on necessary conditions of optimality (Regula) is one of these. The formal language of logic that he developed, enabled him to perceive mathematics with great precision and depth. Actually he built mathematics axiomatically based exclusively on logical and set-theoretic primitive terms and properties, which was a revolutionary turning point in the development of mathematics.

An inflationary inventory model with time dependent demand with Weibull distribution deterioration and partial backlogging under permissible delay in payments

Abstract: This paper proposes to present a general inventory model with due consideration to the factors of time dependent par- tial backlogging and time dependent deterioration. It also takes into account the impact of inflation, time-dependent demand and per- missible delay in payments.

On possibilities of the practical implementation of balance-based adaptive control methodology

Abstract: This paper deals with two approaches to the practical implementation of the Balance-Based Adaptive Controller(B-BAC): the low-level PLC-based approach of the explicit form of the B-BAC and the high-level PC-based one in the form of the general "virtual controller". In both cases, we discuss the details of meeting the general requirements of a particular practical implementation. We also consider the implementation aspects that are independent of the implementation, such as development of the front panel, saturation of a manipulated variable, on-line measurement and data acquisi- tion, implementation of the on-line estimation procedure, bumpless switching between the automatic and manual mode, etc. Addition- ally, we present how to derive both the general form and the final explicit form of the B-BAC on the example of a biotechnological process and how to apply these forms in the particular practical implementation.

Composite semi-infinite optimization

Abstract: We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the con- straint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality con- ditions for these problems. Finally, we apply these results to non- convex stochastic optimization problems with stochastic dominance constraints, generalizing earlier results.

On weak sharp minima in vector optimization with applications to parametric problems

Abstract: In the paper we discuss the concepts of weak sharp solutions to vector optimization problems. As an application we provide sufficient conditions for stability of solutions in perturbed vector optimization problems.

New formula for the failure/repair frequency of multi-state monotone systems and its applications

Abstract: Abstract: The paper deals with calculation methods for failure and repair frequencies of multi-state monotone systems, both for the instantaneous and steady state cases. First, the fixed demand is considered. Based on the binary representation of multi-state structure, we have obtained a new formula for the failure/repair frequency. This formula is used to derive simple rules for the calculation of failure/repair frequency. These rules show how to convert an expression for the system availability into appropriate expression for the system failure/repair frequency. The applicability of the rules is illustrated by some examples. Finally, expressions for the failure/repair frequency for systems operating under random demand are obtained. Since both input and output data have similar format, the rules can be used in a recursive manner, allowing easy analysis of complex systems with hierarchical structure.

A generalization of the Opial's theorem

Abstract: Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1 = Uxk for a nonexpansive and asymptotically regular operator U with nonempty FixU. Several iterative schemes have, however, the form xk+1 = Ukxk, where (Uk) is a sequence of operators with a common fixed point. We show that under some conditions on the sequence (Uk) the sequence (xk) converges weakly to a common fixed point of operators Uk. We show also that the Opial's theorem and the Krasnoselskii-Mann theorem are the corollaries descending from the obtained results. Finally, we present some applications of the results to the convex feasibility problems.

Decentralized structural control approach for Petri nets

Abstract: The structural controller, described by adding the control places to the Petri nets, is introduced in this work to lead the Petri net to the desired marking vectors. An algorithm (Algo- rithm I) is developed to determine the control places for the given Petri net. The connections and the initial marking of each control place are determined in this algorithm. Moreover, a decentralized structural control approach, based on overlapping decompositions, is introduced in this work. In this decentralized approach, all disjoint Petri subnets, which are obtained by using overlapping decomposi- tions, are determined. The control places for each Petri subnet are determined by using the given algorithm. Then, the control places for the orginal Petri net are obtained by the control places of each PSN by another algorithm (Algorithm II) and these places are added to the orginal Petri net. Therefore, a decentralized structural con- troller which guarantees to lead the Petri net to the desired marking vectors is obtained.

A weak* approximation of subgradient of convex function

Abstract: Let f be a limit of Mosco converging convex functions {fn}. The aim of the talk is to present results ensuring that for every subgradient x∗ of f at x there are sequences {xn} and {xn} such that xn −→ x, fn(xn) −→ f(x) and the sequence of subgradients {xn} converges in weak∗ topology to x∗.

An approach to finding trade-off solutions by a linear transformation of objective functions

Abstract: Abstract: We address the problem of deriving Pareto optimal solutions of multiple objective optimization problems with predetermined upper bounds on trade-offs. As shown, this can be achieved by a linear transformation of objective functions. Each non-diagonal element of the transformation matrix is related to a bound on the trade-off between a pair of the objective functions.

Radiality and semismoothness

Abstract: We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Dini-radiality as well as Dini-convexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarke-radiality and semismoothness of order m and show that each subanalytic set satisfies these properties. Similar proper- ties are obtained for locally Lipschitzian subanalytic functions.

Stability of higher-level energy norms of strong solutions to a wave equation with localized nonlinear damping and a nonlinear source term

Abstract: We derive global in time a priori bounds on higher- level energy norms of strong solutions to a semilinear wave equa- tion: in particular, we prove that despite the influence of a nonlinear source, the evolution of a smooth initial state is globally bounded in the strong topology ∼ H 2 × H 1 . And the bound is uniform with respect to the corresponding norm of the initial data. It is known that an m-accretive semigroup generator monotoni- cally propagates smoothness of the initial condition; however, this re- sult does not hold in general for Lipschitz perturbations of monotone systems where higher order Sobolev norms of the solution may blow- up asymptotically as t → ∞. Due to nonlinearity of the system, the only a priori global-in-time bound that follows from classical meth- ods is that on finite energy: ∼ H 1 × L 2 . We show that under some correlation between growth rates of the damping and the source, the norms of topological order above the finite energy level remain globally bounded. Moreover, we also establish this result when damping exhibits sublinear or superlinear growth at the origin, or at infinity, which has immediate applications to asymptotic estimates on the decay rates of the finite energy. The approach presented in the paper is not specific to the wave equation, and can be extended to other hyperbolic systems: e.g. plate, Maxwell, and Schrodinger equations.

On stability of some lexicographic multicriteria Boolean problem

Abstract: We consider a multicriteria lexicographic Boolean problem of minimizing absolute deviations of linear functions from zero. We investigate the stability radius which can be understood as a limit level of independent perturbations of the parameters, for which new lexicographic optima do not appear. Lower and upper accessible bounds of the stability radius are obtained.

Continuous characters and joint topological spectrum

Abstract: It is well known that there is a one-to-one correspondence between the characters of a finitely generated commutative Banach algebra and the joint spectrum of its generators. In this paper we show that this fact is also true for an arbitrary semitopological algebra and its continuous characters, provided we replace the concept of a joint spectrum by concept of a topological joint spectrum. In particular, we show that a finitely generated semitopological algebra has a continuous character if and only if the topological joint spectrum of its generators is non-void.

Fixed points of mappings in Klee admissible spaces

Abstract: In this paper we generalize the Lefschetz fixed point theorem from the case of metric ANR-s to the case of acceptable subsets of Klee admissible spaces. The results presented in this paper were announced in an earlier publication of the authors.

Estimation of tolerance relation on the basis of multiple pairwise comparisons with random errors

Abstract: The methods of tolerance relation estimation on the basis of pairwise comparisons with random errors, in the case of multiple comparisons for each pair, are proposed in the paper. Each comparison expresses the number of common features of both el- ements or the number of their missing features. The assumptions made about distributions of comparison errors are very weak, in particular they may be unknown. Two approaches are discussed: the first one, based on averaging of comparisons for each pair and the second, based on the median from comparisons. The estimated form of the relation is determined (in both cases) on the basis of the appropriate discrete programming task. The properties of esti- mators are based on some probabilistic inequalities. An example of application of the estimators proposed is presented.