23,710 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
Robust output stabilization: improving performance via supervisory control
We analyze robust stability, in an input-output sense, of switched stable
systems. The primary goal (and contribution) of this paper is to design
switching strategies to guarantee that input-output stable systems remain so
under switching. We propose two types of {\em supervisors}: dwell-time and
hysteresis based. While our results are stated as tools of analysis they serve
a clear purpose in design: to improve performance. In that respect, we
illustrate the utility of our findings by concisely addressing a problem of
observer design for Lur'e-type systems; in particular, we design a hybrid
observer that ensures ``fast'' convergence with ``low'' overshoots. As a second
application of our main results we use hybrid control in the context of
synchronization of chaotic oscillators with the goal of reducing control
effort; an originality of the hybrid control in this context with respect to
other contributions in the area is that it exploits the structure and chaotic
behavior (boundedness of solutions) of Lorenz oscillators.Comment: Short version submitted to IEEE TA
Koopman operator-based model reduction for switched-system control of PDEs
We present a new framework for optimal and feedback control of PDEs using
Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a
linear but infinite-dimensional operator which describes the dynamics of
observables. A numerical approximation of the Koopman operator therefore yields
a linear system for the observation of an autonomous dynamical system. In our
approach, by introducing a finite number of constant controls, the dynamic
control system is transformed into a set of autonomous systems and the
corresponding optimal control problem into a switching time optimization
problem. This allows us to replace each of these systems by a K-ROM which can
be solved orders of magnitude faster. By this approach, a nonlinear
infinite-dimensional control problem is transformed into a low-dimensional
linear problem. In situations where the Koopman operator can be computed
exactly using Extended Dynamic Mode Decomposition (EDMD), the proposed approach
yields optimal control inputs. Furthermore, a recent convergence result for
EDMD suggests that the approach can be applied to more complex dynamics as
well. To illustrate the results, we consider the 1D Burgers equation and the 2D
Navier--Stokes equations. The numerical experiments show remarkable performance
concerning both solution times and accuracy.Comment: arXiv admin note: text overlap with arXiv:1801.0641
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