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Unifying approach to observer-filter design

Václav Černý (2009)

Kybernetika

The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory,...

Unique continuation principle for systems of parabolic equations

Otared Kavian, Luz de Teresa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we prove a unique continuation result for a cascade system of parabolic equations, in which the solution of the first equation is (partially) used as a forcing term for the second equation. As a consequence we prove the existence of ε-insensitizing controls for some parabolic equations when the control region and the observability region do not intersect.

Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems

Caroline Fabre (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this article is the study of the approximate controllability for two approximations of Navier Stokes equations with distributed controls. The method of proof combines a suitable linearization of the system with a fixed point argument. We then are led to study the approximate controllability of linear Stokes systems with potentials. We study both the case where there is no constraint on the control and the case where we search a control having one null component. In both cases,...

Variable measurement step in 2-sliding control

Arie Levant (2000)

Kybernetika

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties, improve its precision with discrete measurements and remove the chattering...

Variable structure observer design for a class of uncertain systems with a time-varying delay

Wen-Jeng Liu (2012)

International Journal of Applied Mathematics and Computer Science

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for...

Variance-Constrained H ∞ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols

Ming Lyu, Jie Zhang, YuMing Bo (2020)

Kybernetika

In this paper, the variance-constrained H ∞ finite-horizon filtering problem is investigated for a class of time-varying nonlinear system under muti-rate communication network and stochastic protocol (SP). The stochastic protocol is employed to determine which sensor obtains access to the muti-rate communication network in order to relieve communication burden. A novel mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization...

Vector and operator valued measures as controls for infinite dimensional systems: optimal control

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a general class of systems determined by operator valued measures which are assumed to be countably additive in the strong operator topology. This replaces our previous assumption of countable additivity in the uniform operator topology by the weaker assumption. Under the relaxed assumption plus an additional assumption requiring the existence of a dominating measure, we prove some results on existence of solutions and their regularity properties both for linear and semilinear...

Verified solution method for population epidemiology models with uncertainty

Joshua A. Enszer, Mark A. Stadtherr (2009)

International Journal of Applied Mathematics and Computer Science

Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters...

Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Rezounenko, Alexander V. (2017)

Proceedings of Equadiff 14

We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...

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