87 research outputs found
Partial Stabilization of Stochastic Systems with Application to Rotating Rigid Bodies
This paper addresses the problem of stabilizing a part of variables for
control systems described by stochastic differential equations of the Ito type.
The considered problem is related to the asymptotic stability property of
invariant sets and has important applications in mechanics and engineering.
Sufficient conditions for the asymptotic stability of an invariant set are
proposed by using a stochastic version of LaSalle's invariance principle. These
conditions are applied for constructing the state feedback controllers in the
problem of single-axis stabilization of a rigid body. The cases of control
torques generated by jet engines and rotors are considered as illustrations of
the proposed control design methodology.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019
Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays
published_or_final_versio
Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances
This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 IOP Publishing LtdThis paper is concerned with the synchronization problem for a new class of continuous time delayed complex networks with stochastic nonlinearities (randomly occurring nonlinearities), interval time-varying delays, unbounded distributed delays as well as multiple stochastic disturbances. The stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment. By utilizing a new matrix functional with the idea of partitioning the lower bound h1 of the time-varying delay, we employ the stochastic analysis techniques and the properties of the Kronecker product to establish delay-dependent synchronization criteria that ensure the globally asymptotically mean-square synchronization of the addressed stochastic delayed complex networks. The sufficient conditions obtained are in the form of linear matrix inequalities (LMIs) whose solutions can be readily solved by using the standard numerical software. A numerical example is exploited to show the applicability of the proposed results.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60804028, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers under Grant 200802861044, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, and the Alexander von Humboldt Foundation of Germany
Optimal switching problems with an infinite set of modes: An approach by randomization and constrained backward SDEs
We address a general optimal switching problem over finite horizon for a stochastic system described
by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for
infinitely many modes (or regimes, i.e. the possible values of the piecewise-constant control process).
We allow all the given coefficients in the model to be path-dependent, that is, their value at any time
depends on the past trajectory of the controlled system. The main aim is to introduce a suitable (scalar)
backward stochastic differential equation (BSDE), with a constraint on the martingale part, that allows
to give a probabilistic representation of the value function of the given problem. This is achieved by
randomization of control, i.e. by introducing an auxiliary optimization problem which has the same value
as the starting optimal switching problem and for which the desired BSDE representation is obtained.
In comparison with the existing literature we do not rely on a system of reflected BSDE nor can we
use the associated Hamilton\u2013Jacobi\u2013Bellman equation in our non-Markovian framework
Optimal switching problems with an infinite set of modes: an approach by randomization and constrained backward SDEs
International audienceWe address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes, i.e. the possible values of the piecewise-constant control process). We allow all the given coefficients in the model to be path-dependent, that is, their value at any time depends on the past trajectory of the controlled system. The main aim is to introduce a suitable (scalar) backward stochastic differential equation (BSDE), with a constraint on the martingale part, that allows to give a probabilistic representation of the value function of the given problem. This is achieved by randomization of control, i.e. by introducing an auxiliary optimization problem which has the same value as the starting optimal switching problem and for which the desired BSDE representation is obtained. In comparison with the existing literature we do not rely on a system of reflected BSDE nor can we use the associated Hamilton-Jacobi-Bellman equation in our non-Markovian framework
Estimates of exponential convergence for solutions of stochastic nonlinear systems
This paper aims to analyze the behavior of the solutions of a stochastic perturbed system
with respect to the solutions of the stochastic unperturbed system. To prove our stability
results, we have derived a new Gronwall–type inequality instead of the Lyapunov techniques,
which makes it easy to apply in practice and it can be considered as a more general tool
in some situations. On the one hand, we present sufficient conditions ensuring the global
practical uniform exponential stability of SDEs based on Gronwall’s inequalities. On the
other hand, we investigate the global practical uniform exponential stability with respect to
a part of the variables of the stochastic perturbed system by using generalized Gronwall’s
inequalities. It turns out that, the proposed approach gives a better result comparing
with the use of a Lyapunov function. A numerical example is presented to illustrate the
applicability of our results
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