Search results for "Limit Cycle"
showing 9 items of 29 documents
Multiple Canard Cycles in Generalized Liénard Equations
2001
AbstractThe paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in “Canard Cycles and Center Manifolds” (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc., 121). The presentation is limited to generalized Liénard equations εx+α(x, c)x+β(x, c)=0.
Cyclicity of common slow–fast cycles
2011
Abstract We study the limit cycles of planar slow–fast vector fields, appearing near a given slow–fast cycle, formed by an arbitrary sequence of slow parts and fast parts, and where the slow parts can meet the fast parts in a nilpotent contact point of arbitrary order. Using the notion slow divergence integral, we delimit a large subclass of these slow–fast cycles out of which at most one limit cycle can perturb, and a smaller subclass out of which exactly one limit cycle will perturb. Though the focus lies on common slow–fast cycles, i.e. cycles with only attracting or only repelling slow parts, we present results that are valid for more general slow–fast cycles. We also provide examples o…
A novel digital control for DC/DC converters to improve steady-state performances
2006
This paper describes an innovative digital PWM control implementation for low voltage, high current DC-DC converters. The proposed technique, based on the use of a low resolution DAC, improves steady-state performances, minimizing limit cycle effects. The novel technique is tested on a FPGA-based single phase buck converter operating at 250 kHz. A detailed description of the proposed architecture is given and test results, simulation and experimental ones, are shown
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…
On the coupling between agent internal and agent/ environmental dynamics: Development of spatial representations in evolving autonomous robots
2008
In this article we describe how a population of evolving robots can autonomously develop forms of spatial representation which allow them to self-localize and to discriminate different locations of their environment by integrating sensory-motor information over time. The evolving robots also display a remarkable ability to generalize their skill in new environmental conditions that they have never experienced before. The analysis of the obtained results indicates that the evolved robots come up with simple and robust solutions that exploit quasi-periodic limit cycle dynamics emerging from the coupling between the robot/environmental dynamics and a robot's internal dynamics. More specifical…
Darboux systems with a cusp point and pseudo-abelian integrals
2018
International audience; We study pseudo-abelian integrals associated with polynomial deformations of Darboux systems having a cuspidal singularity. Under some genericity hypothesis we provide locally uniform boundedness of on the number of their zeros.
Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization
2011
Iterative Learning Applied to Hydraulic Pressure Control
2018
This paper addresses a performance limiting phenomenon that may occur in the pressure control of hydraulic actuators subjected to external velocity disturbances. It is demonstrated that under certain conditions a severe peaking of the control error may be observed that significantly degrades the performance of the system due to the presence of nonlinearities. The phenomenon is investigated numerically and experimentally using a system that requires pressure control of two hydraulic cylinders. It is demonstrated that the common solution of feed forwarding the velocity disturbance is not effective in reducing the peaking that occurs as a result of this phenomenon. To improve the system perfor…