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Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: application to an anaerobic bioreactor

Francisco-Ronay López-Estrada, Jean-Christophe Ponsart, Didier Theilliol, Carlos-Manuel Astorga-Zaragoza, Jorge-Luis Camas-Anzueto (2015)

International Journal of Applied Mathematics and Computer Science

This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state...

Set membership estimation of parameters and variables in dynamic networks by recursive algorithms with a moving measurement window

Kazimierz Duzinkiewicz (2006)

International Journal of Applied Mathematics and Computer Science

The paper considers a set membership joint estimation of variables and parameters in complex dynamic networks based on parametric uncertain models and limited hard measurements. A recursive estimation algorithm with a moving measurement window is derived that is suitable for on-line network monitoring. The window allows stabilising the classic recursive estimation algorithm and significantly improves estimate tightness. The estimator is validated on a case study regarding a water distribution network....

Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

Marek T. Malinowski (2015)

Open Mathematics

We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...

Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties

Francesco Amato (2000)

Kybernetika

In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time....

Supervisory predictive control and on-line set-point optimization

Piotr Tatjewski (2010)

International Journal of Applied Mathematics and Computer Science

The subject of this paper is to discuss selected effective known and novel structures for advanced process control and optimization. The role and techniques of model-based predictive control (MPC) in a supervisory (advanced) control layer are first shortly discussed. The emphasis is put on algorithm efficiency for nonlinear processes and on treating uncertainty in process models, with two solutions presented: the structure of nonlinear prediction and successive linearizations for nonlinear control,...

Uncertain input data problems and the worst scenario method

Ivan Hlaváček (2007)

Applications of Mathematics

An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade.

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...

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...

What is not clear in fuzzy control systems

Andrzej Piegat (2006)

International Journal of Applied Mathematics and Computer Science

The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved.

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