Let $\left(A,B\right)$ be a linear time dependent control process, defined on an open interval $J=]a,\omega [$ with $a\ge -\mathrm{\infty }$ and $\omega \le \mathrm{\infty }$; in this paper we give a description of the function $\tau :I\to J$, $\tau \left(t\right)=inf\mathit{\{}t{}^{\prime }>t:(A,B)$ is $\left[t,t^{\prime }\right]$-globally controllable from $0\mathit{\}}$ where $I=\mathit{\{}t\in J:\mathrm{\exists }t{}^{\prime }\in J$ with $\left(A,B\right)\left[t,t^{\prime }\right]$-globally controllable from $0\mathit{\}}$.

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that...

Let $\mathrm{\Sigma }$ be a constrained mechanical system locally referred to state coordinates $(q^1,\mathrm{\dots },q^N,{\gamma }^1,\mathrm{\dots },{\gamma }^M)$. Let $({\tilde{\gamma }}^1\mathrm{\dots }{\tilde{\gamma }}^M)(\cdot )$ be an assigned trajectory for the coordinates ${\gamma }^{\alpha }$ and let $u(\cdot )$ be a scalar function of the time, to be thought as a control. In [4] one considers the control system ${\mathrm{\Sigma }}_{\widehat{\gamma }}$, which is parametrized by the coordinates $(q^1,\mathrm{\dots },q^N)$ and is obtained from $\mathrm{\Sigma }$ by adding the time-dependent, holonomic constraints ${\gamma }^{\alpha }={\widehat{\gamma }}^{\alpha }(t):={\tilde{\gamma }}^{\alpha }(u(t))$. More generally, one can consider a vector-valued control $u(\cdot )=(u^1,\mathrm{\dots },u^M)(\cdot )$ which is directly identified with $\widehat{\gamma }(\cdot )=({\widehat{\gamma }}^1,\mathrm{\dots },{\widehat{\gamma }}^M)(\cdot )$. If one denotes the momenta conjugate...

An observer design based on backstepping approach for a class of state affine systems is proposed. This class of nonlinear systems is determined via a constructive algorithm applied to a general nonlinear Multi Input–Multi Output systems. Some examples are given in order to illustrate the proposed methodology.

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations...

This paper describes the problem of designing control laws for path following robots, including two types of nonholonomic mobile manipulators. Due to a cascade structure of the motion equation, a backstepping procedure is used to achieve motion along a desired path. The control algorithm consists of two simultaneously working controllers: the kinematic controller, solving motion constraints, and the dynamic controller, preserving an appropriate coordination between both subsystems of a mobile manipulator,...