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With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....
In this paper, we investigate the geometric structures of the stable time-varying and the stable static output feedback systems. Firstly, we give a parametrization of stabilizing time-varying output feedback gains subject to certain constraints, that is, the subset of stabilizing time-varying output feedback gains is diffeomorphic to the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices satisfying certain algebraic conditions....
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...
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.
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 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...
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...
In this paper we show the existence of the solution for the
classical brachistochrone problem under the action of a
conservative field in presence of frictional forces. Assuming that
the frictional forces and the potential grow at most
linearly, we prove the existence of a minimizer on the travel
time between any two given points, whenever the initial velocity
is great enough. We also prove the uniqueness of the minimizer
whenever the given points are sufficiently close.
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