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A general transfer function representation for a class of hyperbolic distributed parameter systems

Krzysztof Bartecki (2013)

International Journal of Applied Mathematics and Computer Science

Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer...

A generalised proportional-derivative force/vision controller for torque-driven planar robotic manipulators

Carlos Vidrios-Serrano, Marco Mendoza, Isela Bonilla, Berenice Maldonado-Fregoso (2020)

Kybernetika

In this paper, a family of hybrid control algorithms is presented; where it is merged a free camera-calibration image-based control scheme and a direct force controller, both with the same priority level. The aim of this generalised hybrid controller is to regulate the robot-environment interaction into a two-dimensional task-space. The design of the proposed control structure takes into account most of the dynamic effects present in robot manipulators whose inputs are torque signals. As examples...

A generalization of Ueno's inequality for n-step transition probabilities

Andrzej Nowak (1998)

Applicationes Mathematicae

We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.

A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms

Paolo Mercorelli (2012)

Kybernetika

In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...

A geometric procedure for robust decoupling control of contact forces in robotic manipulation

Paolo Mercorelli, Domenico Prattichizzo (2003)

Kybernetika

This paper deals with the problem of controlling contact forces in robotic manipulators with general kinematics. The main focus is on control of grasping contact forces exerted on the manipulated object. A visco-elastic model for contacts is adopted. The robustness of the decoupling controller with respect to the uncertainties affecting system parameters is investigated. Sufficient conditions for the invariance of decoupling action under perturbations on the contact stiffness and damping parameters...

A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems

Eduardo Aranda-Bricaire, Ülle Kotta (2004)

Kybernetika

The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.

A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model

Luis H. Rodriguez-Alfaro, Efrain Alcorta-Garcia, David Lara, Gerardo Romero (2015)

International Journal of Applied Mathematics and Computer Science

The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The...

A hierarchical decomposition of decision process Petri nets for modeling complex systems

Julio Clempner (2010)

International Journal of Applied Mathematics and Computer Science

We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic...

A learning paradigm for motion control of mobile manipulators

Foudil Abdessemed, Eric Monacelli, Khier Benmahammed (2006)

International Journal of Applied Mathematics and Computer Science

Motion control of a mobile manipulator is discussed. The objective is to allow the end-effector to track a given trajectory in a fixed world frame. The motion of the platform and that of the manipulator are coordinated by a neural network which is a kind of graph designed from the kinematic model of the system. A learning paradigm is used to produce the required reference variables for each of the mobile platform and the robot manipulator for an overall coordinate behavior. Simulation results are...

A level set method in shape and topology optimization for variational inequalities

Piotr Fulmański, Antoine Laurain, Jean-Francois Scheid, Jan Sokołowski (2007)

International Journal of Applied Mathematics and Computer Science

The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology...

A Lyapunov functional for a system with a time-varying delay

Józef Duda (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

A Lyapunov-based design tool of impedance controllers for robot manipulators

Marco Mendoza, Isela Bonilla, Fernando Reyes, Emilio González-Galván (2012)

Kybernetika

This paper presents a design tool of impedance controllers for robot manipulators, based on the formulation of Lyapunov functions. The proposed control approach addresses two challenges: the regulation of the interaction forces, ensured by the impedance error converging to zero, while preserving a suitable path tracking despite constraints imposed by the environment. The asymptotic stability of an equilibrium point of the system, composed by full nonlinear robot dynamics and the impedance control,...

A mathematical framework for learning and adaption: (generalized) random systems with complete connections.

Ulrich Herkenrath, Radu Theodorescu (1981)

Trabajos de Estadística e Investigación Operativa

The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski (2014)

International Journal of Applied Mathematics and Computer Science

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations...

A method for sensor placement taking into account diagnosability criteria

Abed Alrahim Yassine, Stéphane Ploix, Jean-Marie Flaus (2008)

International Journal of Applied Mathematics and Computer Science

This paper presents a new approach to sensor placement based on diagnosability criteria. It is based on the study of structural matrices. Properties of structural matrices regarding detectability, discriminability and diagnosability are established in order to be used by sensor placement methods. The proposed approach manages any number of constraints modelled by linear or nonlinear equations and it does not require the design of analytical redundancy relations. Assuming that a constraint models...

A model-based fault detection and diagnosis scheme for distributed parameter systems : a learning systems approach

Michael A. Demetriou (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system’s dynamics for unanticipated failures, and its well...

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