24,384 research outputs found
EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS
Time-dependent correlation functions of (unstable) particles undergoing
biased or unbiased diffusion, coagulation and annihilation are calculated. This
is achieved by similarity transformations between different stochastic models
and between stochastic and soluble {\em non-stochastic} models. The results
agree with experiments on one-dimensional annihilation-coagulation processes.Comment: 15 pages, Latex. Some corrections made and an appendix adde
SMC design for robust H∞ control of uncertain stochastic delay systems
Recently, sliding mode control method has been extended to accommodate stochastic systems. However, the existing results employ an assumption that may be too restrictive for many stochastic systems. This paper aims to remove this assumption and present in terms of LMIs a sliding mode control design method for stochastic systems with state delay. In some cases, the proposed method provides a control scheme for finite-time stabilization of stochastic delay systems
Predictive dynamical and stochastic systems
We study a system whose dynamics are governed by predictions of its future
states. A general formalism and concrete examples are presented. We find that
the dynamical characteristics depend on how to shape the predictions as well as
on how far ahead in time to make them. We also report that noise can induce
oscillatory behavior, which we call "predictive stochastic resonance".Comment: Presented and To appear in the Proc. of 9th Granada Seminar,
(Granada, Spain, September 11-15, 2006
Functional Methods in Stochastic Systems
Field-theoretic construction of functional representations of solutions of
stochastic differential equations and master equations is reviewed. A generic
expression for the generating function of Green functions of stochastic systems
is put forward. Relation of ambiguities in stochastic differential equations
and in the functional representations is discussed. Ordinary differential
equations for expectation values and correlation functions are inferred with
the aid of a variational approach.Comment: Plenary talk presented at Mathematical Modeling and Computational
Science. International Conference, MMCP 2011, Star\'a Lesn\'a, Slovakia, July
4-8, 201
Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey
The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out
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