An adaptive neural network backstepping control for a class of uncertain nonlinear systems is presented in this paper. Three main issues will be treated: (1) unknown nonlinearities; (2) unknown system parameters; (3) external or internal disturbances. The proposed technique is applied to a simple pendulum. This latter is an unstable system which is perfectly described by a nonlinear model obtai...

In this paper we investigate a biological framework to generate and adapt a motion pattern so that can be energy efficient. In fact, the motion pattern in legged animals and human emerges among interaction between a central pattern generator neural network called CPG and the musculoskeletal system. Here, we model this neuro - musculoskeletal system by means of a leg - like mechanical system cal...

We consider the positive solution of the perturbed simple pendulum problem u′′(r) + N − 1 r u′(r)− g(u(t)) + λ sinu(r) = 0, with 0 < r < R, u′(0) = u(R) = 0. To understand well the shape of the solution uλ when λ 1, we establish the leading and second terms of ‖uλ‖q (1 ≤ q < ∞) with the estimate of third term as λ → ∞. We also obtain the asymptotic formula for uλ(R) as λ→∞.

We compare the performance of several discretizations of simple pendulum equation in a series of numerical experiments. The stress is put on the long-time behaviour. We choose for the comparison numerical schemes which preserve the qualitative features of solutions (like periodicity). All these schemes are either symplectic maps or integrable (preserving the energy integral) maps, or both. We d...

This paper presents the validation of a computational tool that serves to obtain continuous measurements of moving objects. The software uses techniques of computer vision, pattern recognition and optical flow, to enable tracking of objects in videos, generating data trajectory, velocity, acceleration and angular movement. The program was applied to track a ball around a simple pendulum. The me...