1,082 research outputs found
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers
Relaxing the conditions of ISS for multistable periodic systems
The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a sign-indefinite function, which explicitly takes the systemsâ periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov (2013, 2015). The new result is established based on the framework of cell structure introduced in Leonov (1974) and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input
A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics
In multiagent dynamical systems, privacy protection corresponds to avoid
disclosing the initial states of the agents while accomplishing a distributed
task. The system-theoretic framework described in this paper for this scope,
denoted dynamical privacy, relies on introducing output maps which act as
masks, rendering the internal states of an agent indiscernible by the other
agents as well as by external agents monitoring all communications. Our output
masks are local (i.e., decided independently by each agent), time-varying
functions asymptotically converging to the true states. The resulting masked
system is also time-varying, and has the original unmasked system as its limit
system. When the unmasked system has a globally exponentially stable
equilibrium point, it is shown in the paper that the masked system has the same
point as a global attractor. It is also shown that existence of equilibrium
points in the masked system is not compatible with dynamical privacy.
Application of dynamical privacy to popular examples of multiagent dynamics,
such as models of social opinions, average consensus and synchronization, is
investigated in detail.Comment: 38 pages, 4 figures, extended version of arXiv preprint
arXiv:1808.0808
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
Chaos and Asymptotical Stability in Discrete-time Neural Networks
This paper aims to theoretically prove by applying Marotto's Theorem that
both transiently chaotic neural networks (TCNN) and discrete-time recurrent
neural networks (DRNN) have chaotic structure. A significant property of TCNN
and DRNN is that they have only one fixed point, when absolute values of the
self-feedback connection weights in TCNN and the difference time in DRNN are
sufficiently large. We show that this unique fixed point can actually evolve
into a snap-back repeller which generates chaotic structure, if several
conditions are satisfied. On the other hand, by using the Lyapunov functions,
we also derive sufficient conditions on asymptotical stability for symmetrical
versions of both TCNN and DRNN, under which TCNN and DRNN asymptotically
converge to a fixed point. Furthermore, generic bifurcations are also
considered in this paper. Since both of TCNN and DRNN are not special but
simple and general, the obtained theoretical results hold for a wide class of
discrete-time neural networks. To demonstrate the theoretical results of this
paper better, several numerical simulations are provided as illustrating
examples.Comment: This paper will be published in Physica D. Figures should be
requested to the first autho
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