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Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria

Hassan Saberi Nik, Ping He, Sayyed Taha Talebian (2014)

Kybernetika

In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...

Optimal control of variational inequality with applications to axisymmetric shells

Ján Lovíšek (1987)

Aplikace matematiky

The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.

Optimal control problems on parallelizable riemannian manifolds : theory and applications

Ram V. Iyer, Raymond Holsapple, David Doman (2006)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group S E ( 3 ) , which is also a parallelizable riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions employing calculus...

Optimal control problems on parallelizable Riemannian manifolds: theory and applications

Ram V. Iyer, Raymond Holsapple, David Doman (2005)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation for this work is the real-time solution of a standard optimal control problem arising in robotics and aerospace applications. For example, the trajectory planning problem for air vehicles is naturally cast as an optimal control problem on the tangent bundle of the Lie Group SE(3), which is also a parallelizable Riemannian manifold. For an optimal control problem on the tangent bundle of such a manifold, we use frame co-ordinates and obtain first-order necessary conditions...

Optimal heat kernel bounds under logarithmic Sobolev inequalities

Dominique Bakry, Daniel Concordet, Michel Ledoux (2010)

ESAIM: Probability and Statistics

We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators of the type Laplacian minus the gradient of a smooth potential with a given growth at infinity....

Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2016)

Journal of the European Mathematical Society

We consider the wave and Schrödinger equations on a bounded open connected subset Ω of a Riemannian manifold, with Dirichlet, Neumann or Robin boundary conditions whenever its boundary is nonempty. We observe the restriction of the solutions to a measurable subset ω of Ω during a time interval [ 0 , T ] with T > 0 . It is well known that, if the pair ( ω , T ) satisfies the Geometric Control Condition ( ω being an open set), then an observability inequality holds guaranteeing that the total energy of solutions can be...

Orbits of families of vector fields on subcartesian spaces

Jedrzej Śniatycki (2003)

Annales de l'Institut Fourier

Orbits of complete families of vector fields on a subcartesian space are shown to be smooth manifolds. This allows a description of the structure of the reduced phase space of a Hamiltonian system in terms of the reduced Poisson algebra. Moreover, one can give a global description of smooth geometric structures on a family of manifolds, which form a singular foliation of a subcartesian space, in terms of objects defined on the corresponding family of vector fields. Stratified...

Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Ján Brajerčík (2011)

Czechoslovak Mathematical Journal

Let μ : F X → X be a principal bundle of frames with the structure group Gl n ( ℝ ) . It is shown that the variational problem, defined by Gl n ( ℝ ) -invariant Lagrangian on J r F X , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

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