Chaos synchronization criteria and costs of sinusoidally coupled horizontal platform systems.
Composite control of the -link chained mechanical systems
In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of -link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization...
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
Construction of algebraic and difference equations with a prescribed solution space
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...
Control geométrico de sistemas mecánicos.
Control of nonholonomic systems via dynamic compensation
Control of the underactuated mechanical systems using natural motion
The paper deals with the control of underactuated mechanical systems between equilibrium positions across the singular positions. The considered mechanical systems are in the gravity field. The goal is to find feasible trajectory connecting the equilibrium positions that can be the basis of the system control. Such trajectory can be stabilized around both equilibrium positions and due to the gravity forces the mechanical system overcomes the singular positions. This altogether constitutes the control...
Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension
We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L2(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem...
Controllability properties of a class of systems modeling swimming microscopic organisms
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable...
Controlling a non-homogeneous Timoshenko beam with the aid of the torque
Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally...
Cooperative attitude control of multiple rigid bodies with multiple time-varying delays and dynamically changing topologies.
Coplanar control of a satellite around the earth
We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.
Coplanar control of a satellite around the Earth
We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.