Nowadays, the importance of the vehicles and its dramatic effects on human life is no secret. The use of trailers with multiple axels for transporting bulky and heavy equipment is essential. Increase in trailers axles which results increment of wheels, needs considerations in order to increase in transporting speed, maneuverability, safety, better control and path following accurately.  Therefo...

Adaptive Intelligent Tutoring Systems (ITS) aim at helping students going through the resolution of a given problem in a principled way according to the desired outcomes, the intrinsic capabilities of the student, and the particular context in which the exercise takes place. These systems should be capable of acting according to mistakes, boredness, distractions, etc. Several works propose diff...

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

In this paper, the path following controller of an omnidirectional mobile robot (OMR) has been extended in such a way that the forward velocity has been optimized and the actuator velocity constraints have been taken into account. Both have been attained through the proposed model predictive control (MPC) framework. The forward velocity has been included into the objective function, while the a...

The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

We present a new algorithm obtained by changing the search directions in the algorithm given in [8]. This algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only the full Nesterov-Todd (NT)step. Moreover, we obtain the currently best known iteration bound for the infeasible interior-point algorithms with full NT...

In this paper, we propose a path-following method for computing a curve of equilibria of a dynamical system, based upon the smooth Singular Value Decomposition (SVD) of the Jacobian matrix. Our method is capable of detecting fold points, and continuing past folds. It is also able to detect branch points and to switch branches at such points. Algorithmic details and examples are given.