A.B. Ozguler

Decentralized control and periodic feedback

The decentralized stabilization problem for linear, discrete-time, periodically time-varying plants using periodic controllers is considered. The main tool used is the technique of lifting a periodic system to a time-invariant one via extensions of the input and output spaces. It is shown that a periodically time-varying system of fundamental period N can be stabilized by a decentralized periodic controller if and only if: 1) the system is stabilizable and detectable, and 2) the N-lifting of each complementary subsystem of identically zero input-output map is free of unstable input-output decoupling zeros. In the special case of N=1, this yields and clarifies all the major existing results on decentralized stabilization of time-invariant plants by periodically time-varying controllers. >

Decentralized control: a stable proper fractional approach

Three decentralized control problems are considered in a fractional setup for two-channel multivariable systems. All three problems are instances of decentralized control or local output feedback problems. The problems are: (i) making the system stabilizable and detectable through the first channel via dynamic output feedback around the second channel, (ii) the first problem with the constraint of internal stability, and (iii) the decentralized stabilization problem. All three problems are equivalent as far as the solvability conditions are concerned. A characterization of all solutions in each case is given. The results apply to a class of systems having fractional representations over an arbitrary principal ideal domain. >

Disturbance decoupling problems via dynamic output feedback

This paper considers the disturbance decoupling problems, with or without internal stability and pole placement, via dynamic output feedback using polynomial and rational matrix techniques. We show that in all three problems considered, the central solvability condition can be expressed as a two-sided matching problem A = BXC , where A, B , and C are the polynomial system matrices of certain natural subsystems of the system model and X is to be determined over various subrings of the rational functions. This matching problem can in turn be reduced to certain appropriate zero-cancellation conditions on the polynomial system matrices A, B , and C .

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.

Regulator problem with internal stability: A frequency domain solution

This paper considers the general regulator problem with internal stability where the measured outputs are not necessarily the same as the regulated outputs. Using polynomial matrix techniques, necessary and sufficient conditions are obtained in terms of skew-primeness of two polynomial matrices; one of these polynomial matrices represents the disturbance modes, whereas the other is the polynomial system matrix representing the system zeros. Various special cases considered in the literature are also analyzed in terms of these necessary and sufficient conditions.

A solution to the diagonalization problem by constant precompensator and dynamic output feedback

A solution is presented for the problem of diagonalization (row-by-row decoupling). The problem is solved using a constant precompensator and a dynamic output feedback compensator of a p*m linear time-invariant system. The solvability condition is compact and concerns the dimension of a single subspace defined via the concepts of essential rows and static kernels associated with the transfer matrix. A characterization of the set of all solutions to the problem is also given. In solving this dynamic feedback problem, a complete solution to its state-feedback counterpart, namely, the restricted state-feedback problem of diagonalization, is also presented. >

Foraging Swarms as Nash Equilibria of Dynamic Games

The question of whether foraging swarms can form as a result of a noncooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in 1-D 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 unique Nash equilibrium under two different foraging location specifications, and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging.

PID CONTROLLER SYNTHESIS FOR A CLASS OF UNSTABLE MIMO PLANTS WITH I/O DELAYS

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional + Integral + Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability. 2006 Elsevier Ltd. All rights reserved.

Implications of a characterization result on strong and reliable decentralized control

A number of special purpose decentralized control problems are defined and examined for a two-by-two plant. Using a characterization of the set of all diagonal stabilizing compensators it is shown that reliable diagonal stabilization can equivalently be viewed either as a strong diagonal stabilization problem or simultaneous stabilization problems for suitably defined plants. Various solvability conditions are determined for strong and reliable stabilization and robust reliable stabilization of a scalar plant is shown to be equivalent to diagonal reliable stabilization problem of special two-by-two plant.

Global stabilization via local stabilizing actions

Stabilization of a linear, time-invariant system via stabilization of its main diagonal subsystems is the underlying problem in all diagonal dominance techniques for decentralized control. In these techniques as well as all Nyquist-based techniques, sufficient conditions are obtained under the assumption that the collection of the unstable poles of all diagonal subsystems is the same as the unstable poles of the overall system. We show that this assumption is by itself enough to construct a solution to the problem at least in cases where the diagonal subsystems have disjoint poles.Stabilization of a linear, time-invariant system via stabilization of its main diagonal subsystems is the underlying problem in all diagonal dominance techniques for decentralized control. In these techniques as well as all Nyquist-based techniques, sufficient conditions are obtained under the assumption that the collection of the unstable poles of all diagonal subsystems is the same as the unstable poles of the overall system. We show that this assumption is by itself enough to construct a solution to the problem at least in cases where the diagonal subsystems have disjoint poles.