6,795 research outputs found
Invariance principles for switched systems with restrictions
In this paper we consider switched nonlinear systems under average dwell time
switching signals, with an otherwise arbitrary compact index set and with
additional constraints in the switchings. We present invariance principles for
these systems and derive by using observability-like notions some convergence
and asymptotic stability criteria. These results enable us to analyze the
stability of solutions of switched systems with both state-dependent
constrained switching and switching whose logic has memory, i.e., the active
subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm
This paper provides a geometrical derivation of the Hybrid Minimum Principle
(HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups
which are left invariant under the controlled dynamics of the
system, and whose switching manifolds are defined as smooth embedded time
invariant submanifolds of . The analysis is expressed in terms of extremal
(i.e. optimal) trajectories on the cotangent bundle of the state manifold .
The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is
extended to the so-called Exponential Gradient algorithm. The convergence
analysis for the algorithm is based upon the LaSalle Invariance Principle and
simulation results illustrate their efficacy
Invariance Principles and Observability in Switched Systems with an Application in Consensus
Using any nonnegative function with a nonpositive derivative along
trajectories to define a virtual output, the classic LaSalle invariance
principle can be extended to switched nonlinear time-varying (NLTV) systems, by
considering the weak observability (WO) associated with this output. WO is what
the output informs about the limiting behavior of state trajectories (hidden in
the zero locus of the output). In the context of switched NLTV systems, WO can
be explored using the recently established framework of limiting zeroing-output
solutions. Adding to this, an extension of the integral invariance principle
for switched NLTV systems with a new method to guarantee uniform global
attractivity of a closed set (without assuming uniform Lyapunov stability or
dwell-time conditions) is proposed. By way of illustrating the proposed method,
a leaderless consensus problem for nonholonomic mobile robots with a switching
communication topology is addressed, yielding a new control strategy and a new
convergence result
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
Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference
The problem of modulation classification for a multiple-antenna (MIMO) system
employing orthogonal frequency division multiplexing (OFDM) is investigated
under the assumption of unknown frequency-selective fading channels and
signal-to-noise ratio (SNR). The classification problem is formulated as a
Bayesian inference task, and solutions are proposed based on Gibbs sampling and
mean field variational inference. The proposed methods rely on a selection of
the prior distributions that adopts a latent Dirichlet model for the modulation
type and on the Bayesian network formalism. The Gibbs sampling method converges
to the optimal Bayesian solution and, using numerical results, its accuracy is
seen to improve for small sample sizes when switching to the mean field
variational inference technique after a number of iterations. The speed of
convergence is shown to improve via annealing and random restarts. While most
of the literature on modulation classification assume that the channels are
flat fading, that the number of receive antennas is no less than that of
transmit antennas, and that a large number of observed data symbols are
available, the proposed methods perform well under more general conditions.
Finally, the proposed Bayesian methods are demonstrated to improve over
existing non-Bayesian approaches based on independent component analysis and on
prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog
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