34,790 research outputs found
Minimally Constrained Stable Switched Systems and Application to Co-simulation
We propose an algorithm to restrict the switching signals of a constrained
switched system in order to guarantee its stability, while at the same time
attempting to keep the largest possible set of allowed switching signals. Our
work is motivated by applications to (co-)simulation, where numerical stability
is a hard constraint, but should be attained by restricting as little as
possible the allowed behaviours of the simulators. We apply our results to
certify the stability of an adaptive co-simulation orchestration algorithm,
which selects the optimal switching signal at run-time, as a function of
(varying) performance and accuracy requirements.Comment: Technical report complementing the following conference publication:
Gomes, Cl\'audio, Beno\^it Legat, Rapha\"el Jungers, and Hans Vangheluwe.
"Minimally Constrained Stable Switched Systems and Application to
Co-Simulation." In IEEE Conference on Decision and Control. Miami Beach, FL,
USA, 201
Data compression for estimation of the physical parameters of stable and unstable linear systems
A two-stage method for the identification of physical system parameters from experimental data is presented. The first stage compresses the data as an empirical model which encapsulates the data content at frequencies of interest. The second stage then uses data extracted from the empirical model of the first stage within a nonlinear estimation scheme to estimate the unknown physical parameters. Furthermore, the paper proposes use of exponential data weighting in the identification of partially unknown, unstable systems so that they can be treated in the same framework as stable systems. Experimental data are used to demonstrate the efficacy of the proposed approach
Adaptive control: Myths and realities
It was found that all currently existing globally stable adaptive algorithms have three basic properties in common: positive realness of the error equation, square-integrability of the parameter adjustment law and, need for sufficient excitation for asymptotic parameter convergence. Of the three, the first property is of primary importance since it satisfies a sufficient condition for stabillity of the overall system, which is a baseline design objective. The second property has been instrumental in the proof of asymptotic error convergence to zero, while the third addresses the issue of parameter convergence. Positive-real error dynamics can be generated only if the relative degree (excess of poles over zeroes) of the process to be controlled is known exactly; this, in turn, implies perfect modeling. This and other assumptions, such as absence of nonminimum phase plant zeros on which the mathematical arguments are based, do not necessarily reflect properties of real systems. As a result, it is natural to inquire what happens to the designs under less than ideal assumptions. The issues arising from violation of the exact modeling assumption which is extremely restrictive in practice and impacts the most important system property, stability, are discussed
Systems And Methods For Parameter Dependent Riccati Equation Approaches To Adaptive Control
Systems and methods for adaptive control are disclosed. The systems and methods can control uncertain dynamic systems. The control system can comprise a controller that employs a parameter dependent Riccati equation. The controller can produce a response that causes the state of the system to remain bounded. The control system can control both minimum phase and non-minimum phase systems. The control system can augment an existing, non-adaptive control design without modifying the gains employed in that design. The control system can also avoid the use of high gains in both the observer design and the adaptive control law.Georgia Tech Research Corporatio
Controlling Chaos Faster
Predictive Feedback Control is an easy-to-implement method to stabilize
unknown unstable periodic orbits in chaotic dynamical systems. Predictive
Feedback Control is severely limited because asymptotic convergence speed
decreases with stronger instabilities which in turn are typical for larger
target periods, rendering it harder to effectively stabilize periodic orbits of
large period. Here, we study stalled chaos control, where the application of
control is stalled to make use of the chaotic, uncontrolled dynamics, and
introduce an adaptation paradigm to overcome this limitation and speed up
convergence. This modified control scheme is not only capable of stabilizing
more periodic orbits than the original Predictive Feedback Control but also
speeds up convergence for typical chaotic maps, as illustrated in both theory
and application. The proposed adaptation scheme provides a way to tune
parameters online, yielding a broadly applicable, fast chaos control that
converges reliably, even for periodic orbits of large period
Adapting Predictive Feedback Chaos Control for Optimal Convergence Speed
Stabilizing unstable periodic orbits in a chaotic invariant set not only
reveals information about its structure but also leads to various interesting
applications. For the successful application of a chaos control scheme,
convergence speed is of crucial importance. Here we present a predictive
feedback chaos control method that adapts a control parameter online to yield
optimal asymptotic convergence speed. We study the adaptive control map both
analytically and numerically and prove that it converges at least linearly to a
value determined by the spectral radius of the control map at the periodic
orbit to be stabilized. The method is easy to implement algorithmically and may
find applications for adaptive online control of biological and engineering
systems.Comment: 21 pages, 6 figure
Chaotic Behaviour in Some Discrete āTime Adaptive Control Systems
It has been shown that nonlinear discrete maps can display extremely rich behaviour and under certain parameter conditions to show chaotic phenomenon. This work looks at adaptive control feedback systems which can be represented as nonlinear discrete maps and shows how model mismatch can lead to undesired complicated and chaotic behaviour. Moreover that a discrete-time adaptive control system which can display chaotic behaviour can be extended into higher order systems and the results show that under certain parameter conditions, the higher order systems also behave chaotically. A generalised equation form for the eigenvalues is also given
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