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Feedback Stabilization of Continuous Systems by Adding an Integrator

100%

Outbib R. , Aggoune W.

tom Vol. 9, no 4

871-881

This note is devoted to the problem of global stabilization of continuous systems by adding an integrator. The goal is to prove that if a continuous non-linear system dot x =f(x,u) is globally asymptotically stable at the origin for u equiv 0, then the augmented system obtained by adding an integrator is stabilizable by means of a continuous feedback.

On Time-Optimal Vibration Control of One-Dimensional Distributed Parameter Systems

88%

Cupiał P.

tom Vol. 29, No. 2

5-22

The paper is concerned with the calculation of time-optimal, open-loop controls of one-dimensional vibrating systems (strings and beams). The problem consists in finding the forces or kinematic excitations which bring the initial displacements and velocities or the transient response of the system to zero in the shortest time. The solutions of the vibration problems are expressed in terms of Fourier series and the selection of the optimum solution is reduced to the l-problem of moments. Explicit time-optimal boundary controls are calculated for several cases including a string controlled by a force or displacement applied at one end and a beam with a control moment at the end. In the case of boundary control generalized Fourier solutions are used which are discussed at some length.

The role of parameter constraints in EE and OE methods for optimal identification of continuous LTI models

88%

Byrski W. , Byrski J.

nr 2

379-388

The paper presents two methods used for the identification of Continuous-time Linear Time Invariant (CLTI) systems. In both methods the idea of using modulating functions and a convolution filter is exploited. It enables the proper transformation of a differential equation to an algebraic equation with the same parameters. Possible different normalizations of the model are strictly connected with different parameter constraints which have to be assumed for the nontrivial solution of the optimal identification problem. Different parameter constraints result in different quality of identification. A thorough discussion on the role of parameter constraints in the optimality of system identification is included. For time continuous systems, the Equation Error Method (EEM) is compared with the continuous version of the Output Error Method (OEM), which appears as a special sub-case of the EEM.

On the control of the final speed for a class of finite-dimensional linear systems: controllability and regulation

88%

Rachik M. , Khaloufi I. , Benfatah Y. , Boutayeb H. , Laarabi H.

tom Vol. 33, No. 3

497--525

In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman’s theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring speed-controllability are not met, we adopt a regulation strategy that involves determining the control law to make the system’s final speed approach as closely as possible to the predefined final speed, and this at a lower cost. The theoretical results obtained are illustrated through three examples.

The fastest, simplified method of estimation of the largest Lyapunov exponent for continuous dynamical systems with time delay

63%

Balcerzak M. , Pikunov D.

tom Vol. 21, nr 4

985--994

This paper focuses on the applications of the new method of estimation of the Largest Lyapunov exponent. The method has been adapted to continuous dynamical systems with time delay. The paper presents efficiency of the new method in comparison with classical algorithms of LLE estimation. Computation times and convergence rates have been compared with the typically used method. It has been revealed in this paper that for the van der Pol oscillator, application of the new method increases the efficiency of calculations by 28% comparing to the classic one. Therefore, authors claim that the method presented in this paper is the fastest one in the assumed range of applications.