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Regional detection and reconstruction of unknown internal or boundary sources

Larbi Afifi, Abdelhaq El Jai, Malika Merry (2001)

International Journal of Applied Mathematics and Computer Science

The purpose of this paper is to study the problem of regional detection, to characterize internal or boundary regionally detectable sources and regionally spy sensors, and to establish a relationship between these sensors and regionally strategic sensors. It is shown how to reconstruct a regionally detectable internal or a boundary source from a given output, with an extension to the case when the output is affected by an observation error. Numerical results are given in the case of a diffusion...

Regional observation and sensors

Abdelhaq El Jai, Houria Hamzaoui (2009)

International Journal of Applied Mathematics and Computer Science

The purpose of this short paper is to provide original results related to the choice of the number of sensors and their supports for general distributed parameter systems. We introduce the notion of extended sensors and we show that the observation error decreases when the support of a sensor is widened. We also show that the observation error decreases when the number of sensors increases.

Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo, Benedetto Piccoli (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo, Benedetto Piccoli (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

Rejection of nonharmonic disturbances in nonlinear systems

Shutang Liu, Yuan Jiang, Ping Liu (2010)

Kybernetika

This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm...

Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Rajagopal Joice Nirmala, Krishnan Balachandran (2017)

Kybernetika

This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

Reliable robust path planning with application to mobile robots

Romain Pepy, Michel Kieffer, Eric Walter (2009)

International Journal of Applied Mathematics and Computer Science

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic...

Remark on stabilization of tree-shaped networks of strings

Kaïs Ammari, Mohamed Jellouli (2007)

Applications of Mathematics

We consider a tree-shaped network of vibrating elastic strings, with feedback acting on the root of the tree. Using the d’Alembert representation formula, we show that the input-output map is bounded, i.e. this system is a well-posed system in the sense of G. Weiss (Trans. Am. Math. Soc. 342 (1994), 827–854). As a consequence we prove that the strings networks are not exponentially stable in the energy space. Moreover, we give explicit polynomial decay estimates valid for regular initial data.

Remarks on exact controllability for the Navier-Stokes equations

Oleg Yu. Imanuvilov (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain ω Ω n , n { 2 , 3 } . The result that we obtained in this paper is as follows. Suppose that v ^ ( t , x ) is a given solution of the Navier-Stokes equations. Let v 0 ( x ) be a given initial condition and v ^ ( 0 , · ) - v 0 < ε where ε is small enough. Then there exists a locally distributed control u , supp u ( 0 , T ) × ω such that the solution v ( t , x ) of the Navier-Stokes equations: t v - Δ v + ( v , ) v = p + u + f , div v = 0 , v | Ω = 0 , v | t = 0 = v 0 coincides with...

Remarks on exact controllability for the Navier-Stokes equations

Oleg Yu. Imanuvilov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain Ω with control distributed in a subdomain ω Ω n , n { 2 , 3 } . The result that we obtained in this paper is as follows. Suppose that v ^ ( t , x ) is a given solution of the Navier-Stokes equations. Let v 0 ( x ) be a given initial condition and v ^ ( 0 , · ) - v 0 < ε where ε is small enough. Then there exists a locally distributed control u , supp u ( 0 , T ) × ω such that the solution v(t,x) of the Navier-Stokes equations: t v - Δ v + ( v , ) v = p + u + f , div v = 0 , v | Ω = 0 , v | t = 0 = v 0 coincides...

Remarks on non controllability of the heat equation with memory

Sergio Guerrero, Oleg Yurievich Imanuvilov (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

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