Browsing by Subject "Theorem proving"

Now showing 1 - 20 of 21

Open Access
Approximations in compensator design: a duality
(The Institution of Engineering and Technology (IET), 2002) Özgüler, A. B.; Gündeş, A. N.
In classical controller design, poles fat to the left of dominant poles are sometimes ignored. Similarly, in some proportional-integral compensation techniques, the controller zero is placed close to the origin and design proceeds after cancelling this zero with a pole at the origin. A rigorous basis for these methods is provided, it being shown that there is a duality between the two.
Open Access
Constructing convex directions for stable polynomials
(IEEE, 2000) Özgüler, A. B.
The constructions of convex directions based on phase-derivative interpretations were obtained for Hurwitz-stable polynomials. The phase-derivative conditions were based on the sensitivity of root-locus associated with the even and odd parts of a polynomial. The phase-growth condition directly established anti-Hurwitz polynomials, polynomials of degree one, even polynomials and odd polynomials for the entire set of Hurwitz polynomials.
Open Access
A critical look at quantum diffusion and some of its interesting aspects
(Springer, 2007) Mukhopadhyay, S.; Saglam, M.; Chatterjee, A.
A fresh and critical look has been given to the long-time behaviour of the quantum diffusion problem and a marginally more accurate solution has been obtained as compared to the one reported in the recent literature. Attempt has also been made to bring out a few interesting generic features of this problem which may have important bearing on real systems in the quantum domain.
Open Access
An efficient algorithm for the single machine total tardiness problem
(Taylor & Francis, 2001) Tansel, B. Ç.; Kara, B. Y.; Sabuncuoğlu İ.
This paper presents an exact algorithm for the single machine total tardiness problem (1// L T;). We present a new synthesis of various results from the literature which leads to a compact and concise representation of job precedences, a simple optimality check, new decomposition theory, a new lower bound, and a check for presolved subproblems. These are integrated through the use of an equivalenceconcept that permits a continuous reformation of the data to permit early detection of optimality at the nodes of an enumeration tree. The overall effect is a significant reduction in the size of the search tree, CPU times, and storage requirements. The algorithm is capable of handling much larger problems (e.g., 500 jobs) than its predecessors in the literature (:s; 150). In addition, a simple modification of the algorithm gives a new heuristic which significantly outperforms the best known heuristics in the literature.
Open Access
Fixed zeros of decentralized control systems
(IEEE, 2000) ÜÜnyelioglu, K. A.; Özgüner, Ü.; Özgüler, A. B.
This paper considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an N-channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of Channel i (1 ≤ i ≤ N) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of N - 1 controllers around the other channels, which make the resulting single-channel system stabilizable and detectable. This paper gives a complete characterization of unstable decentralized fixed zeros in terms of system-invariant zeros.
Open Access
A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes
(Elsevier, 2001) Fadıloğlu, M. M.; Yeralan, S.
In this paper a spectral theory pertaining to Quasi-Birth–Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth–death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method is based on finding the eigenvalue–eigenvector pairs that solve a matrix polynomial equation. Since the computational effort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove different properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal unified theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.
Open Access
Language evolution and information theory
(IEEE, 2004-06-07) Ahlswede, R.; Arıkan, Erdal; Bäumer, L.; Deppe, C.
The use of Nowak's model to study the language evolution and to settle a conjecture by Nowak was discussed. These models explained the ways by which natural selection can lead to the gradual emergence of human language. It was shown that the Nowak's conjecture is true for a class of spaces defined by a certain condition on the distance function. A connection between Nowak's model and standard information-theoretic models was indicated.
Open Access
LinGraph: a graph-based automated planner for concurrent task planning based on linear logic
(Springer New York LLC, 2017) Kortik S.; Saranli, U.
In this paper, we introduce an automated planner for deterministic, concurrent domains, formulated as a graph-based theorem prover for a propositional fragment of intuitionistic linear logic, relying on the previously established connection between intuitionistic linear logic and planning problems. The new graph-based theorem prover we introduce improves planning performance by reducing proof permutations that are irrelevant to planning problems particularly in the presence of large numbers of objects and agents with identical properties (e.g. robots within a swarm, or parts in a large factory). We first present our graph-based automated planner, the Linear Logic Graph Planner (LinGraph). Subsequently we illustrate its application for planning within a concurrent manufacturing domain and provide comparisons with four existing automated planners, BlackBox, Symba-2, Metis and the Temporal Fast Downward (TFD), covering a wide range of state-of-the-art automated planning techniques and implementations. We show that even though LinGraph does not rely on any heuristics, it still outperforms these systems for concurrent domains with large numbers of identical objects and agents. These gains persist even when existing methods on symmetry reduction and numerical fluents are used, with LinGraph capable of handling problems with thousands of objects. Following these results, we also show that plan construction with LinGraph is equivalent to multiset rewriting systems, formally relating LinGraph to intuitionistic linear logic. © 2017, Springer Science+Business Media New York.
Open Access
Local convex directions for Hurwitz stable polynomials
(IEEE, 2002) Özgüler, A. B.; Saadaoui, K.
A new condition for a polynomial p(s) to be a local convex direction for a Hurwitz stable polynomial q(s) is derived. The condition is in terms of polynomials associated with the even and odd parts of p(s) and q(s), and constitutes a generalization of Rantzer's phase-growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials.
Open Access
A model-based scheme for anticontrol of some discrete-time chaotic systems
(World Scientific, 2004) Morgül, Ö.
We consider a model-based approach for the anticontrol of some discrete-time systems. We first assume the existence of a chaotic model in an appropriate form. Then by using an appropriate control input we try to match the controlled system with the chaotic system model. We also give a procedure to generate the model chaotic systems in arbitrary dimensions. We show that with this approach, controllable systems can always be chaotified. Moreover, if the system to be controlled is stable, control input can be chosen arbitrarily small.
Open Access
A new method for the computation of all stabilizing controllers of a given order
(Taylor & Francis, 2005) Saadaoui, K.; Özgüler, A. B.
A new method is given for computing the set of all stabilizing controllers of a given order for linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem and the successive application of a modified constant gain stabilizing algorithm to subsidiary plants. It is applicable to both continuous and discrete time systems.
Open Access
Newton's method for linear inequality systems
(Elsevier, 1998) Pınar, M. Ç.
We describe a modified Newton type algorithm for the solution of linear inequality systems in the sense of minimizing the ℓ2 norm of infeasibilities. Finite termination is proved, and numerical results are given. © 1998 Elsevier Science B.V.
Open Access
A note on "continuous review perishable inventory systems: models and heuristics"
(2003) Gürler, Ü.; Özkaya, B. Y.
In a recent paper, Lian and Liu (2001) consider a continuous review perishable inventory model with renewal arrivals, batch demands and zero lead times. However, the main analytical result they provide holds only for some special cases such as Poisson arrivals with exponential interarrival times. In this note we generalize Theorem 1 of Lian and Liu (2001) for the case where the arrivals follow an arbitrary renewal process.
Open Access
On Roth, Korth, and Silberschatz's extended algebra and calculus for nested relational databases
(1992) Tansel, A. U.; Garnett, Lucy
We discuss the issues encountered in the extended algebra and calculus languages for nested relations defined by Roth, Korth, and Silberschatz. Their equivalence proof between algebra and calculus fails because of the keying problems and the use of extended set operations. Extended set operations also have unintended side effects. Furthermore, their calculus seems to allow the generation of power sets, thus making it more powerful than their algebra.
Open Access
On the boundary control of a flexible robot arm
(IEEE, 2001) Morgül, Ömer
We consider a flexible robot arm modeled as a single flexible link clamped to a rigid body. We assume that the system performs only planar motion. For this system, we pose two control problems; namely, the orientation and stabilization of the system. We propose a class of controllers to solve these problems.
Open Access
On the set of all stabilizing first-order controllers
(IEEE, 2003) Saadaoui, Karim; Özgüler, Arif Bülent
A computational method is given for determining the set of all stabilizing proper first-order controllers for finite dimensional, linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem.
Open Access
On the stabilization of a cable with a tip mass
(IEEE, 1994) Morgül, Ö.; Rao, B. P.; Conrad, F.
In this note, we consider a vertical cable which is pinched at the upper end. A mass is attached at the lower end where a control force is also applied. We show that this hybrid system is uniformly stabilized by choosing a suitable control law for the control force depending on the velocity and angular velocity at the free end. Moreover for specific values of the feedback coefficients, we obtain the rate of decay of the energy of the system.
Open Access
Optimal short-time Fourier transform for monocomponent signals
(IEEE, 2004) Güven, Hüseyin Emre
New methods of improving the short-time Fourier transform representation of signals have recently emerged. These methods use linear canonical transforms to bring the signal into a minimal time-bandwidth product form. Here we show that linear canonical transforms are not sufficient to achieve the minimum time-bandwidth product for high-order modulated mono-component signals. Therefore we propose a novel short-time Fourier transform method which requires an adaptive window, making use of an initial instantaneous frequency estimator. The new approach is able to achieve the highest possible resolution for monocomponent signals. Finally, we discuss the benefits of the proposed method.
Open Access
Quasi-particle properties in a quasi-two-dimensional electron liquid
(Indian Academy of Sciences, 2008) Asgari, R.; Tanatar, Bilal
We consider the quasi-particle properties such as the effective mass and spin susceptibility of quasi-two-dimensional electron systems. The finite quantum well width effects are incorporated into the local-field factors that describe the charge and spin correlations. We employ the Fermi-hypernetted chain formalism in conjunction with fluctuation-dissipation theorem to obtain the local-field factors. Our results are in good agreement with recent experiments.
Open Access
Sampling and series expansion theorems for fractional Fourier and other transforms
(Elsevier, 2003) Candan, Ç.; Özaktaş, Haldun M.
The sampling and series expansion theorems for fractional Fourier transforms were analyzed. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley and scale transforms. The technique could also be useful as a generic tool which can produce key relations systematically in a few steps.