746 research outputs found
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
Interval Prediction for Continuous-Time Systems with Parametric Uncertainties
The problem of behaviour prediction for linear parameter-varying systems is
considered in the interval framework. It is assumed that the system is subject
to uncertain inputs and the vector of scheduling parameters is unmeasurable,
but all uncertainties take values in a given admissible set. Then an interval
predictor is designed and its stability is guaranteed applying Lyapunov
function with a novel structure. The conditions of stability are formulated in
the form of linear matrix inequalities. Efficiency of the theoretical results
is demonstrated in the application to safe motion planning for autonomous
vehicles.Comment: 6 pages, CDC 2019. Website:
https://eleurent.github.io/interval-prediction
Learning linear dynamical systems under convex constraints
We consider the problem of identification of linear dynamical systems from a
single trajectory. Recent results have predominantly focused on the setup where
no structural assumption is made on the system matrix , and have consequently analyzed the ordinary least squares (OLS)
estimator in detail. We assume prior structural information on is
available, which can be captured in the form of a convex set
containing . For the solution of the ensuing constrained least squares
estimator, we derive non-asymptotic error bounds in the Frobenius norm which
depend on the local size of the tangent cone of at . To
illustrate the usefulness of this result, we instantiate it for the settings
where, (i) is a dimensional subspace of , or (ii) is -sparse and is a suitably scaled
ball. In the regimes where , our bounds improve upon
those obtained from the OLS estimator.Comment: 17 page
Homological mirror symmetry for punctured spheres
We prove that the wrapped Fukaya category of a punctured sphere ( with
an arbitrary number of points removed) is equivalent to the triangulated
category of singularities of a mirror Landau-Ginzburg model, proving one side
of the homological mirror symmetry conjecture in this case. By investigating
fractional gradings on these categories, we conclude that cyclic covers on the
symplectic side are mirror to orbifold quotients of the Landau-Ginzburg model.Comment: 38 pages, 5 figures; v2: minor revisions (similar to published
version
Moment Matching Based Model Reduction for LPV State-Space Models
We present a novel algorithm for reducing the state dimension, i.e. order, of
linear parameter varying (LPV) discrete-time state-space (SS) models with
affine dependence on the scheduling variable. The input-output behavior of the
reduced order model approximates that of the original model. In fact, for input
and scheduling sequences of a certain length, the input-output behaviors of the
reduced and original model coincide. The proposed method can also be
interpreted as a reachability and observability reduction (minimization)
procedure for LPV-SS representations with affine dependence
Enhancement of adaptive observer robustness applying sliding mode techniques
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The problem studied in this paper is one of improving the performance of a class of adaptive observer in the presence of exogenous disturbances. The H1 gains of both, a conventional and the newly proposed sliding-mode adaptive observer, are evaluated to assess the effect of disturbances on the estimation errors. It is shown that if the disturbance is \matched" in the plant equations, then including an additional sliding-mode feedback injection term, dependent on the plant output, improves the accuracy of observation
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