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Switching control

Enrique Zuazua (2011)

Journal of the European Mathematical Society

We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to the other in a systematic way so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, switching control strategies exist and can be built in a systematic way. To do this we introduce a new variational principle building...

Symmetries of control systems

Alexey Samokhin (1996)

Banach Center Publications

Symmetries of the control systems of the form u t = f ( t , u , v ) , u ∈ ℝ n , v ∈ ℝ m are studied. Some general results concerning point symmetries are obtained. Examples are provided.

The anti-disturbance property of a closed-loop system of 1-d wave equation with boundary control matched disturbance

Xiao-Rui Wang, Gen-Qi Xu (2019)

Applications of Mathematics

We study the anti-disturbance problem of a 1-d wave equation with boundary control matched disturbance. In earlier literature, the authors always designed the controller such as the sliding mode control and the active disturbance rejection control to stabilize the system. However, most of the corresponding closed-loop systems are boundedly stable. In this paper we show that the linear feedback control also has a property of anti-disturbance, even if the disturbance includes some information of the...

The asymptotical stability of a dynamic system uppercasewith structural damping

Xuezhang Hou (2003)

International Journal of Applied Mathematics and Computer Science

A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.

The balayage method: boundary control of a thermo-elastic plate

Walter Littman, Stephen Taylor (2008)

Applicationes Mathematicae

We discuss the null boundary controllability of a linear thermo-elastic plate. The method employs a smoothing property of the system of PDEs which allows the boundary controls to be calculated directly by solving two Cauchy problems.

The Differentiable Functions from R into R n

Keiko Narita, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.

The dynamical Lame system : regularity of solutions, boundary controllability and boundary data continuation

M. I. Belishev, I. Lasiecka (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input → state” map in L 2 -norms is established. A structure of the reachable sets for arbitrary T > 0 is studied. In general case, only the first component u ( · , T ) of the complete state { u ( · , T ) , u t ( · , T ) } may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....

The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation

M. I. Belishev, I. Lasiecka (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The boundary control problem for the dynamical Lame system (isotropic elasticity model) is considered. The continuity of the “input → state" map in L2-norms is established. A structure of the reachable sets for arbitrary T>0 is studied. In general case, only the first component u ( · , T ) of the complete state { u ( · , T ) , u t ( · , T ) } may be controlled, an approximate controllability occurring in the subdomain filled with the shear (slow) waves. The controllability results are applied to the problem of the boundary data continuation....

The equivalence of controlled lagrangian and controlled hamiltonian systems

Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, Craig A. Woolsey (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...

The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems

Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, Craig A. Woolsey (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...

Towards a framework for continuous and discrete multidimensional systems

Rudolf Rabenstein, Lutz Trautmann (2003)

International Journal of Applied Mathematics and Computer Science

Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations...

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