1,721,018 research outputs found
Optimal decay for a wave-heat system with Coleman-Gurtin thermal law
Get PDFWe study the long-term behaviour of solutions to a one-dimensional coupled
wave-heat system with Coleman-Gurtin thermal law. Our approach is based on the
asymptotic theory of -semigroups and recent results developed for coupled
control systems. As our main results, we represent the system as a feedback
interconnection between the wave part and the Coleman-Gurtin part and we show
that the associated semigroup in the history framework of Dafermos is
polynomially stable with optimal decay rate as . In
particular, we obtain a sharp estimate for the rate of energy decay of
classical solutions to the problem.Comment: Accepted for publication in Journal of Mathematical Analysis and
Application
Output Regulation Theory for Linear Systems with Infinite-Dimensional and Periodic Exosystems
Get PDFIn this thesis we consider the output regulation problem consisting of choosing a controller to asymptotically steer the output of a linear infinite-dimensional system to a given reference signal despite external disturbances. In particular we are interested in a situation where the considered reference and disturbance signals are nonsmooth polynomially bounded functions. The existing theory on this problem can only be used in the case where the signals to be tracked and rejected are smooth and polynomially bounded, or nonsmooth but uniformly bounded functions. The availability of more general reference and disturbance signals is useful in many applications such as the control of robot arms and disk drive systems.
For generating our reference and disturbance signals we consider two separate methods, namely, a time-invariant infinite-dimensional exosystem and a periodically time-dependent finite-dimensional exosystem. We will see that the chosen method has a considerable effect on the properties of the resulting control law as well as on the behavior of the controlled closed-loop system. One of the main differences in these respective theories of output regulation is that the control law designed based on the infinite-dimensional exosystem is guaranteed to be robust with respect to a class of perturbations preserving the stability of the closed-loop system.
The first main result of this thesis is the generalization of the well-known internal model principle of finite-dimensional control theory for distributed parameter systems with infinite-dimensional exosystems. On a general level this result states that in order for a controller to solve the robust output regulation problem related to a given signal generator, the controller must be able to reproduce the dynamics of this exosystem. In addition to its theoretical significance the internal model principle can also be applied in the construction of controllers solving the robust output regulation problem. Our proof of this result is based on a close connection between the behavior of the state of the closed-loop system and an associated Sylvester operator equation. In particular, the controllers achieving asymptotic tracking of the reference signals can be characterized using the solvability of certain constrained Sylvester equations, and the robustness of this property can be expressed as a condition involving equations of this type.
The second main contribution of this thesis consists of the development of the theory of output regulation for infinite-dimensional systems with periodically time-dependent exosystems. In particular this also includes designing nonautonomous controllers achieving asymptotic output tracking and disturbance rejection. Our treatment shows that it is possible to study the output regulation problem for a distributed parameter system together with a nonautonomous exosystem using methods similar to the ones familiar from case of a time-invariant signal generator. In particular, the solvability of the problem related to a given periodic exosystem can be characterized using a periodically time-dependent version of the well-known regulator equations if the associated Sylvester operator equation is replaced with an infinite-dimensional Sylvester differential equation
Stability and Robust Regulation of Passive Linear Systems
Get PDFWe study the stability of coupled impedance passive regular linear systems
under power-preserving interconnections. We present new conditions for strong,
exponential, and non-uniform stability of the closed-loop system. We apply the
stability results to the construction of passive error feedback controllers for
robust output tracking and disturbance rejection for strongly stabilizable
passive systems. In the case of nonsmooth reference and disturbance signals we
present conditions for non-uniform rational and logarithmic rates of
convergence of the output. The results are illustrated with examples on
designing controllers for linear wave and heat equations, and on studying the
stability of a system of coupled partial differential equations.Comment: 33 pages, 2 figures, to appear in SIAM Journal on Control and
Optimizatio
Robust Output Regulation for Continuous-Time Periodic Systems
Get PDFWe consider controller design for robust output tracking and disturbance
rejection for continuous-time periodic linear systems with periodic reference
and disturbance signals. As our main results we present four different
controllers: A feedforward control law and a discrete-time dynamic error
feedback controller for output tracking and disturbance rejection, a robust
discrete-time feedback controller, and finally a discrete-time feedback
controller that achieves approximate robust output tracking and disturbance
rejection. The presented constructions are also new for time-invariant finite
and infinite-dimensional systems. The results are illustrated with two
examples: A periodically time-dependent system of harmonic oscillators and a
nonautonomous two-dimensional heat equation with boundary disturbance.Comment: 26 pages, 8 figures, accepted for publication in IEEE Transactions on
Automatic Contro
Robustness of strongly and polynomially stable semigroups
No full textAbstractIn this paper we study the robustness properties of strong and polynomial stability of semigroups of operators. We show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator. The presented results apply to general polynomially stable semigroups and bounded perturbations. The conditions on the perturbations generalize well-known criteria for the preservation of exponential stability of semigroups. We also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a Riesz-spectral operator. The theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one-dimensional wave equation
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Asymptotic Behaviour of Platoon Systems
No full textIn this paper we study the asymptotic behaviour of various platoon-type systems using the general theory developed by the authors in a recent article. The aim is to steer an infinite number of vehicles towards a target configuration in which each vehicle has a prescribed separation from its neighbour and all vehicles are moving at a given velocity. More specifically, we study systems in which state feedback is possible, systems in which observer-based dynamic output feedback is required, and also a situation in which the control objective is modified to allow the target separations to depend on the vehicles’ velocities. We show that in the first and third cases the objective can be achieved, but that in the second case the system is unstable in the sense that the associated semigroup is not uniformly bounded. We also present some quantified results concerning the rate of convergence of the platoon to its limit state when the limit exists.Peer reviewe
Polynomial stability of a coupled wave-heat network
Get PDFWe study the long-time asymptotic behaviour of a topologically non-trivial
network of wave and heat equations. By analysing the simpler wave and the heat
networks separately, and then applying recent results for abstract coupled
systems, we establish energy decay at the rate as for all
classical solutions
Robust output regulation of counter-flow heat exchangers
No full text<p>We consider a partial differential equation model widely used for counter-flow heat exchangers and the related robust output regulation problem with boundary control and boundary observation. We show that the control system is an exponentially stable regular linear system, which enables us to use a specific known controller design to robustly regulate the system. The results are illustrated with numerical simulations.</p>Peer reviewe
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