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Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...

Structural identifiability analysis of nonlinear time delayed systems with generalized frequency response functions

Gergely Szlobodnyik, Gábor Szederkényi (2021)

Kybernetika

In this paper a novel method is proposed for the structural identifiability analysis of nonlinear time delayed systems. It is assumed that all the nonlinearities are analytic functions and the time delays are constant. We consider the joint structural identifiability of models with respect to the ordinary system parameters and time delays by including delays into a unified parameter set. We employ the Volterra series representation of nonlinear dynamical systems and make use of the frequency domain...

Structurally stable design of output regulation for a class of nonlinear systems

Celia Villanueva-Novelo, Sergej Čelikovský, Bernardino Castillo-Toledo (2001)

Kybernetika

The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem...

Structured redundancy for fault tolerance in state-space models and Petri nets

Christoforos N. Hadjicostis, George C. Verghese (1999)

Kybernetika

The design and implementation of systems in state form has traditionally focused on minimal representations which require the least number of state variables. However, “structured redundancy” – redundancy that has been intentionally introduced in some systematic way – can be extremely important when fault tolerance is desired. The redundancy can be used to detect and correct errors or to guarantee desirable performance despite hardware or computational failures. Modular redundancy, the traditional...

Sturm-Liouville systems are Riesz-spectral systems

Cédric Delattre, Denis Dochain, Joseph Winkin (2003)

International Journal of Applied Mathematics and Computer Science

The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L^2(a,b) and the infinitesimal generator of a C_0-semigroup of bounded linear operators.

Suboptimal fault tolerant control design with the use of discrete optimization

Zdzisław Kowalczuk, Krzysztof E. Oliński (2008)

International Journal of Applied Mathematics and Computer Science

This paper presents a concept of designing fault tolerant control systems with the use of suboptimal methods. We assume that a given (nonlinear) dynamical process is described in a state space. The method consists in searching (at the off-line stage) for a trajectory of operational points of the system state space. The sought trajectory can be constrained by certain conditions, which can express faults or failures already detected. Within this approach, we are able to use the autonomous dynamics...

Sufficient optimality conditions for multivariable control problems

Andrzej Nowakowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.

Currently displaying 341 – 360 of 422