This paper introduces a solution to the problem of steering an aerodynamical system, with non-holonomic constraints superimposed on dynamic equations of motion. The proposed approach is a dimensionality reduction of the Optimal Control Problem (OCP) with heavy path constraints to be solved by Rapidly-Exploring Random Tree (RRT) algorithm. In this research, we formulated and solved the OCP with Euler–Lagrange formula in order to find the optimal-time trajectory. The RRT constructs a non-collision path in static, high-dense obstacle environment (i.e. heavy path constraint). Based on a real-world aircraft model, our simulation results found the collision-free path and gave improvements of time and fuel consumption of the optimized Hamiltonian-based model over the original non-optimized model.

In this paper we present a selective segmentation model using a dual level set variational formulation. Our variational model aims to segment all objects with one level set function (global) and the selected object, which is the closest to the geometric constraints (markers), with another level set (local). It is a combination of edge detection, markers distance function and active contour without edges. Experimental results show that our model is more robust than previous work.

We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question here. In particular, we demonstrate that the determinant of the gradient of any admissible deformation with finite energy is strictly positive on the closure of the domain. With this in hand, Gâteaux differentiability of the potential energy at a minimizer is automatic, yielding the existence of a weak solution. We indicate how our results hold for a general class of boundary value problems, including “mixed” boundary conditions. For each of the two possible pure displacement formulations (in second-gradient problems), we show that the resulting deformation is an injective mapping, whenever the imposed placement on the boundary is itself the trace of an injective map.

The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: ${\displaystyle\inf_{{\displaystyle(u,v)\in {\cal U}_{ad}}}\int_{0}^{1} f\left(t, u(\theta_v(t)),u^{\prime}(t),v(t)\right){\rm d}t}$ , (1)where ${\cal U}_{ad} $ is a set of admissible controls and $\theta_v$ is the solution of the following equation: $\{ \frac{{\rm d}\theta(t)}{{\rm d}t}=g(t,\theta(t),v(t)), t\in [0,1]$ ; $\displaystyle\theta(0)=\theta_0, \theta(t)\in [0,1]\forall t$ . (2).The results are nonlocal and new.