48 research outputs found
Decentralized control and periodic feedback
Cataloged from PDF version of article.The decentralized stabilization problem for linear, discretetime,
periodically timevarying plants using periodic controllers is considered.
The main tool used isl the technique of Uning a periodic system
to a timeinvariant 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 identieally zero inpnt-ontput map
is free of unstable input-output decoupling zeros. In the special case
of N = 1, this yields and clarifies all the mr exisling results on
decentralized stabilization of time-invariant plants by periodically time
varying controllers
Decentralized Blocking Zeros and Decentralized Strong Stabilization Problem
Cataloged from PDF version of article.This paper is concerned with a new system theoretic
concept, decentralized blocking zeros, and its applications in the
design of decentralized controllers for linear time-invariant finitedimensional
systems. The concept of decentralized blocking zeros
is a generalization of its centralized counterpart to multichannel
systems under decentralized control. Decentralized blocking zeros
are defined as the common blocking zeros of the main diagonal
transfer matrices and various complementary transfer matrices
of a given plant. As an application of this concept, we consider
the decentralized strong stabilization problem (DSSP) where the
objective is to stabilize a plant using a stable decentralized
controller. It is shown that a parity interlacing property should
be satisfied among the real unstable poles and real unstable
decentralized blocking zeros of the plant for the DSSP to be
solvable. That parity interlacing property is also suf6icient for the
solution of the DSSP for a large class of plants satisfying a certain
connectivity condition. The DSSP is exploited in the solution
of a special decentralized simultaneous stabilization problem,
called the decentralized concurrent stabilization problem (DCSP).
Various applications of the DCSP in the design of controllers for
large-scale systems are also discussed
Structural decomposition of general singular linear systems and its applications
Ph.DDOCTOR OF PHILOSOPH
Decentralized Control and Periodic Feedback
The decentralized stabilization problem for linear, discretetime, 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. © 1994 IEE
Algebraic theory of linear multivariable control systems
Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 125-132.The theory of linear multivariable systems stands out as tlie most developed
and sophisticated among the topics of system theory. In the literature,
many different solutions are presented to the linear midtivariable control problems
using three main approaches : geometric approacli, fractional approach
and polynomial model based approach. This thesis is a first draft for a textbook
on linear multivariable control which contains a description of solutions
to the most of the standard algebraic feedback control problems using simple
linear algebra and a minimal amount of polynomial algebra. These problems
are internal stabilization, disturbance decoupling by state feedback and measurement
feedback, output stabilization, tracking with regulation in a scalar
system, regulator problem with a single output channel and decentralized stabilization.Çetin, Sevgi BabacanM.S
Higher-Order Uncoupled Dynamics Do Not Lead to Nash Equilibrium \unicode{x2014} Except When They Do
The framework of multi-agent learning explores the dynamics of how individual
agent strategies evolve in response to the evolving strategies of other agents.
Of particular interest is whether or not agent strategies converge to well
known solution concepts such as Nash Equilibrium (NE). Most ``fixed order''
learning dynamics restrict an agent's underlying state to be its own strategy.
In ``higher order'' learning, agent dynamics can include auxiliary states that
can capture phenomena such as path dependencies. We introduce higher-order
gradient play dynamics that resemble projected gradient ascent with auxiliary
states. The dynamics are ``payoff based'' in that each agent's dynamics depend
on its own evolving payoff. While these payoffs depend on the strategies of
other agents in a game setting, agent dynamics do not depend explicitly on the
nature of the game or the strategies of other agents. In this sense, dynamics
are ``uncoupled'' since an agent's dynamics do not depend explicitly on the
utility functions of other agents. We first show that for any specific game
with an isolated completely mixed-strategy NE, there exist higher-order
gradient play dynamics that lead (locally) to that NE, both for the specific
game and nearby games with perturbed utility functions. Conversely, we show
that for any higher-order gradient play dynamics, there exists a game with a
unique isolated completely mixed-strategy NE for which the dynamics do not lead
to NE. These results build on prior work that showed that uncoupled fixed-order
learning cannot lead to NE in certain instances, whereas higher-order variants
can. Finally, we consider the mixed-strategy equilibrium associated with
coordination games. While higher-order gradient play can converge to such
equilibria, we show such dynamics must be inherently internally unstable
Robust Control of Linear Time-Invariant Plants Using Periodic Compensation
©1985 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones
Decentralized Blocking Zeros and the Decentralized Strong Stabilization Problem
This paper is concerned with a new system theoretic concept, decentralized blocking zeros, and its applications in the design of decentralized controllers for linear time-invariant finite-dimensional systems. The concept of decentralized blocking zeros is a generalization of its centralized counterpart to multichannel systems under decentralized control. Decentralized blocking zeros are defined as the common blocking zeros of the main diagonal transfer matrices and various complementary transfer matrices of a given plant. As an application of this concept, we consider the decentralized strong stabilization problem (DSSP) where the objective is to stabilize a plant using a stable decentralized controller. It is shown that a parity interlacing property should be satisfied among the real unstable poles and real unstable decentralized blocking zeros of the plant for the DSSP to be solvable. That parity interlacing property is also sufficient for the solution of the DSSP for a large class of plants satisfying a certain connectivity condition. The DSSP is exploited in the solution of a special decentralized simultaneous stabilization problem, called the decentralized concurrent stabilization problem (DCSP). Various applications of the DCSP in the design of controllers for large-scale systems are also discussed. © 1995 IEE
Non-Euclidian Metrics and the Robust Stabilization of Systems with Parameter Uncertainty
Abstract-This paper considers, from a complex function theoretic point of view, certain kinds of robust synthesis problems. In particular, we use a certain kind of metric on the disk (the "hyperbolic" metric) which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in nowEuclidian geometry. It is shown that several apparently different problems can be treated in a unified general framework. A new result on the gain margin problem for multivariable plants is also given. Finally, we apply our methods to systems with real zero or pole variations. f? and D are well known to be. conformally equivalent