R.E. Kalman: A great human being

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. © 2006 IEEE

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. © 2016 Elsevier Lt

A new method for the computation of all stabilizing controllers of a given order

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. © 2005 Taylor & Francis Ltd

Local convex directions for Hurwitz stable polynomials

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

Robust controller design based on reduced order plants

Two dual controller design methods are proposed for linear, time-invariant, multi-input multi-output systems, where designs based on a reduced order plant robustly stabilizer higher order plants with additional poles or zeros in the stable region. The additional poles (or zeros) are considered as multiplicative perturbations of the reduced plant. The methods are tailored towards closed-loop stability and performance and they yield estimates for the stability robustness and performance of the final design. They can be considered as formalizations of two classical heuristic model reduction techniques. One method neglects a plant-pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant-zero with a pole at the origin

Plant Order Reduction for Controller Design

Two dual methods of plant order reduction for controller design are proposed for linear, time-invariant, multi-input multi-output systems. The model reduction methods are tailored towards closed-loop stability and performance and they yield estimates for the stability robustness and performance of the final design. They can be considered as formalizations of two classical heuristic model reduction techniques: One method neglects a plant-pole sufficiently far to the left of dominant poles and the other cancels a sufficiently small stable plant-zero with a pole at the origin

Stabilizing first-order controllers with desired stability region

In this paper, we determine the set of all stabilizing first-order controllers that place the poles of the closed-loop system in a desired stability region. The solution is based on a generalization of the Hermite-Biehler theorem applicable to polynomials with complex coefficients and the application of a modified stabilizing gain algorithm to three subsidiary plants. The method given is also applicable to PID controllers

PI and low-order controllers for two-channel decentralized systems

A systematic design method is proposed for simple loworder decentralized controllers in the cascaded form of proportional-integral and first-order blocks. The plant is linear, time-invariant and has two channels, each with a single-input and single-output; there may be any number of poles in the region of stability, but the unstable poles can only occur at the origin

Local convex directions

A proof of a strengthened version of the phase growth condition for Hurwitz stable polynomials is given. Based on this result, a necessary and sufficient condition for a polynomial p(s) to be a local convex direction for a Hurwitz stable polynomial q(s) is obtained. The condition is in terms of polynomials associated with the even and odd parts of p(s) and q(s). © 2001 EUCA

Tracking and regulation control of a 2-DOF robot arm with unbalance

Servomechanism synthesis for a two degree-of-freedom robot arm assembled on a vessel and affected from sea disturbances is considered. Dynamic equations of the robot arm with unbalance and of an approximate base disturbance model are derived. Direct linear controller synthesis based on a linearized model is then studied. It is shown that, although the plant model is nonlinear, linear controller that is synthesized based on the "internal model principle" provide good performance and perform better than the commonly used PID controllers. © 2012 IEEE