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A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

Lan Zhou, Jinhua She, Shaowu Zhou (2014)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic outputfeedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value...

A backstepping approach to ship course control

Anna Witkowska, Mirosław Tomera, Roman Smierzchalski (2007)

International Journal of Applied Mathematics and Computer Science

As an object of course control, the ship is characterised by a nonlinear function describing static manoeuvring characteristics that reflect the steady-state relation between the rudder deflection and the rate of turn of the hull. One of the methods which can be used for designing a nonlinear ship course controller is the backstepping method. It is used here for designing two configurations of nonlinear controllers, which are then applied to ship course control. The parameters of the obtained nonlinear...

A belief revision approach for argumentation-based negotiation agents

Pablo Pilotti, Ana Casali, Carlos Chesñevar (2015)

International Journal of Applied Mathematics and Computer Science

Negotiation is an interaction that happens in multi-agent systems when agents have conflicting objectives and must look for an acceptable agreement. A typical negotiating situation involves two agents that cannot reach their goals by themselves because they do not have some resources they need or they do not know how to use them to reach their goals. Therefore, they must start a negotiation dialogue, taking also into account that they might have incomplete or wrong beliefs about the other agent's...

A biochemical multi-species quality model of a drinking water distribution system for simulation and design

Krzysztof Arminski, Tomasz Zubowicz, Mietek A. Brdys (2013)

International Journal of Applied Mathematics and Computer Science

Drinking Water Distribution Systems (DWDSs) play a key role in sustainable development of modern society. They are classified as critical infrastructure systems. This imposes a large set of highly demanding requirements on the DWDS operation and requires dedicated algorithms for on-line monitoring and control to tackle related problems. Requirements on DWDS availability restrict the usability of the real plant in the design phase. Thus, a proper model is crucial. Within this paper a DWDS multi-species...

A biologically inspired approach to feasible gait learning for a hexapod robot

Dominik Belter, Piotr Skrzypczyński (2010)

International Journal of Applied Mathematics and Computer Science

The objective of this paper is to develop feasible gait patterns that could be used to control a real hexapod walking robot. These gaits should enable the fastest movement that is possible with the given robot's mechanics and drives on a flat terrain. Biological inspirations are commonly used in the design of walking robots and their control algorithms. However, legged robots differ significantly from their biological counterparts. Hence we believe that gait patterns should be learned using the...

A boundary-value problem for linear PDAEs

Wiesław Marszałek, Zdzisław Trzaska (2002)

International Journal of Applied Mathematics and Computer Science

We analyze a boundary-value problem for linear partial differential algebraic equations, or PDAEs, by using the method of the separation of variables. The analysis is based on the Kronecker-Weierstrass form of the matrix pencil[A,-λ_n B]. A new theorem is proved and two illustrative examples are given.

A Brauer’s theorem and related results

Rafael Bru, Rafael Cantó, Ricardo Soto, Ana Urbano (2012)

Open Mathematics

Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices, Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including the case when the system...

A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations

Louis Tebou (2008)

ESAIM: Control, Optimisation and Calculus of Variations

First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt. 46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...

A Carleman estimates based approach for the stabilization of some locally damped semilinear hyperbolic equations

Louis Tebou (2007)

ESAIM: Control, Optimisation and Calculus of Variations

First, we consider a semilinear hyperbolic equation with a locally distributed damping in a bounded domain. The damping is located on a neighborhood of a suitable portion of the boundary. Using a Carleman estimate [Duyckaerts, Zhang and Zuazua, Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); Fu, Yong and Zhang, SIAM J. Contr. Opt.46 (2007) 1578–1614], we prove that the energy of this system decays exponentially to zero as the time variable goes to infinity. Second, relying on another Carleman...

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher, Martin A. Grepl (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we employ the reduced basis method as a surrogate model for the solution of linear-quadratic optimal control problems governed by parametrized elliptic partial differential equations. We present a posteriori error estimation and dual procedures that provide rigorous bounds for the error in several quantities of interest: the optimal control, the cost functional, and general linear output functionals of the control, state, and adjoint variables. We show that, based on the assumption...

A class of stationary stochastic processes

Victor D. Didenko, Natalia A. Rozhenko (2014)

Studia Mathematica

Regular stationary stochastic vector processes whose spectral densities are the boundary values of matrix functions with bounded Nevanlinna characteristic are considered. A criterion for the representability of such processes as output data of linear time invariant dynamical systems is established.

A collector for information without probability in a fuzzy setting

Doretta Vivona, Maria Divari (2005)

Kybernetika

In the fuzzy setting, we define a collector of fuzzy information without probability, which allows us to consider the reliability of the observers. This problem is transformed in a system of functional equations. We give the general solution of that system for collectors which are compatible with composition law of the kind “inf”.

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