A. Bülent Özgüler

A common solution to a pair of linear matrix equations over a principal ideal domain

Abstract A necessary and sufficient condition for the existence of a common solution to a pair of linear matrix equations over a principal ideal domain is obtained. The equations are of the type A i = B i XC i for i = 1,2. The solvability condition is that the equations each have a solution and a bilateral linear matrix equation made up of the matrices A i , B i , and C i has a solution.

Decentralized stabilization: characterization of all solutions and genericity aspects

Electrical and The decentralized stabilization problem of multivariable finite-dimensional systems is considered in a fractional set-up. A new synthesis procedure for decentralized stabilizing compensators is proposed. The class of all admissible local compensators that can be applied to a specified channel as an element of a decentralized compensator is identified. The conditions under which the class of admissible local compensators is generic are investigated. The problem of making a multi-channel system stabilizable and detectable from a single channel applying decentralized feedback around the other channels has been shown to be generically solvable for a given set of dynamic compensators if and only if the plant is strongly connected.

Diagonal stabilization of linear multivariable systems

A new procedure is presented for the synthesis of diagonal compensators for N × N linear multivariable systems that are free of fixed modes with respect to constant diagonal output feedbacks. The synthesis procedure employs simple polynomial algebra and it is in the form of an N-step algorithm. The geometric configurations 2N- and 2N-cells in N-space are shown to be especially suitable for visualizing diagonal feedback and aiding the application of the synthesis algorithm.

Decentralized simultaneous stabilization and reliable control using periodic feedback

In this note we consider the simultaneous decentralized stabilization problem for linear, periodically time-varying, discrete time systems. We show that a finite number of periodically time-varying systems can be simultaneously stabilized by a periodically time-varying decentralized compensator if and only if each system admits a decentralized stabilizing compensator, The result is applicable in the design of reliable decentralized stabilizing compensators for interconnected systems.

Watermarking via zero assigned filter banks

In order to identify the owner and distributor of digital data, a watermarking scheme in frequency domain for multimedia files is proposed. The scheme satisfies the imperceptibility and persistence requirements and it is robust against additive noise. It consists of a few stages of wavelet decomposition of several subblocks of the original signal using special zero assigned filter banks. By assigning zeros to filters on the high frequency portion of the spectrum, filter banks with frequency selective response are obtained. The information is then inserted in the wavelet-decomposed and compressed signal. Several robustness tests are performed on male voice, female voice, and music files, color and gray level images. The algorithm is tested under white Gaussian noise and against JPEG compression and it is observed to be robust even when exposed to high levels of corruption.

Completeness and single channel stabilizability

Abstract A matrix equational characterization of completeness is given which provides a simple interpretation for the concept in terms of a dynamic partial state-feedback problem. As an initial application of this characterization to local output feedback, the problem of making a two-input channel system stabilizable by dynamic output feedback around one channel is solved.

Swarming Behavior as Nash Equilibrium

Abstract The question of whether swarms can form as a result of a non-cooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in one-dimensional motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The game is shown to have a Nash equilibrium that has all the features of a swarm behavior.

Automated discrimination of psychotropic drugs in mice via computer vision-based analysis

We developed an inexpensive computer vision-based method utilizing an algorithm which differentiates drug-induced behavioral alterations. The mice were observed in an open-field arena and their activity was recorded for 100 min. For each animal the first 50 min of observation were regarded as the drug-free period. Each animal was exposed to only one drug and they were injected (i.p.) with either amphetamine or cocaine as the stimulant drugs or morphine or diazepam as the inhibitory agents. The software divided the arena into virtual grids and calculated the number of visits (sojourn counts) to the grids and instantaneous speeds within these grids by analyzing video data. These spatial distributions of sojourn counts and instantaneous speeds were used to construct feature vectors which were fed to the classifier algorithms for the final step of matching the animals and the drugs. The software decided which of the animals were drug-treated at a rate of 96%. The algorithm achieved 92% accuracy in sorting the data according to the increased or decreased activity and then determined which drug was delivered. The method differentiated the type of psychostimulant or inhibitory drugs with a success ratio of 70% and 80%, respectively. This method provides a new way to automatically evaluate and classify drug-induced behaviors in mice.

Foraging motion of swarms with leaders as Nash equilibria

The consequences of having a leader in a swarm are investigated using differential game theory. We model foraging swarms with leader and followers as a non-cooperative, multi-agent differential game. The agents in the game start from a set of initial positions and migrate towards a target. The agents are assumed to have no desire, partial desire or full desire to reach the target. We consider two types of leadership structures, namely hierarchical leadership and a single leader. In both games, the type of leadership is assumed to be passive. We identify the realistic assumptions under which a unique Nash equilibrium exists in each game and derive the properties of the Nash solutions in detail. It is shown that having a passive leader economizes in the total information exchange at the expense of aggregation stability in a swarm. It turns out that, the leader is able to organize the non-identical followers into harmony under missing information.

R.E. Kalman: A Great Human Being [Historical Perspectives]

I came to know about Prof. Kalman through a Turkish post-doc of his during my M.Sc. studies at Middle East Technical University. When I learned that I was accepted to carry on my doctoral studies under his supervision, I was excited, happy, and very scared.