Abstract:
We establish the existence and uniqueness of a local solution for the system of differential equations $$displaylines{ frac{partial }{partial t}u(x,t) = uBig(vBig(int_0^t u(x,s)ds, tBig), tBig) cr frac{partial }{partial t}v(x,t) = vBig(uBig(int_0^t v(x,s)ds, tBig), tBig). }$$ with given initial conditions $u(x,0)=u_0(x)$ and $v(x,0)=v_0(x)$.

Abstract:
The topic of this paper is the utilisation of a strategy with a dual control system for the prevention of damage on laboratory equipment used in a remote laboratory. One control system is implemented before the laboratory is deployed and is responsible for damage control and can override the second control system that is programmed by the user of the remote laboratory and is fully configurable. The laboratory is used for verification of control algorithms for quad rotor helicopters through practical experiments. The damage control strategy should not limit or impede the natural movement of the equipment as long as the behaviour is kept within predefined limits. The nature of the system to be controlled, exclude the use of physical constraints that are normally used for damage control, as these in some way or another will impede or limit the movement of the helicopter.

Abstract:
We present a method for determining the motion of an electron in a hydrogen atom, which starts from a field Lagrangean foundation for non-conservative systems that can exhibit chaotic behavior. As a consequence, the problem of the formation of the atom becomes the problem of finding the possible stable orbital attractors and the associated transition paths through which the electron mechanical energy varies continuously until a stable energy state is reached.

Abstract:
this paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. the subject has being analyzed by a number of authors such as karagiannis and pfeiffer (1991), for the ideal excitation case. an interesting model of the same problem by moon (1992) has been recently used by souza and caldas (1999) to detect chaotic behavior. we consider two spur gears with different diameters and gaps between the teeth. suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. in the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. in this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. thus an extra degree of freedom is introduced in the problem. the equations of motion are obtained via a lagrangian approach with some assumed characteristic torque curves. next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Abstract:
This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Abstract:
The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach.

Abstract:
this paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. the behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. a control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. the state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. general polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. this methodology is applied to systems with quadratic and cubic non-linearities. strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Abstract:
a motion control strategy for robot manipulators, with inverse dynamics and non-linear proportional-derivative gains is presented. on account of a possible interaction of the robot with the environment, impedance is incorporated to modify the robot's motion references according to the interaction force. the gains, that are non-linear state functions, allow to improve robot performance and to prevent actuator saturation. it is proved that an asymptotically stable closed-loop system is obtained with the proposed controller. simulation results on a 3-dof robot show a good performance of the controller with variable gains, as opposed to that of a constant gain pd controller.

Abstract:
in this work, a model to optimize the planning of gas and oil production in several wells is proposed. the planning horizon is divided in several periods for which the demand is known, and a cost coefficient is associated to each well in the objective function. the formulation includes the pressure decrease effect at the wellbore when the well is producing and the pressure increase when the well is not producing. in addition, constrains to the flow and the wells interconnectivity are also incorporated in the model. the results show that the proposed model can be used in planning oil and gas production without using mixed integer non-linear programming

Abstract:
oscillatory and resonant phenomena are usually explored in many experimental physics courses. these experiments are generaly interpreted in the regime of small angle oscillation and uniform fields. in this paper we describe a low cost resonance experiment to explore physics phenomena out of this regime. in such case, non-linear terms in the differential equation are responsible for interesting physics behavior of the oscillatory system.