Ricardo Luiz Utsch de Freitas Pinto

An exact penalty function based on the projection matrix

This paper proposes an exact penalty function based on the projection matrix concept. The proposed penalty function finds solutions which satisfy the necessary optimality conditions of the original problem. Some theoretical results are presented showing that every regular point provides an absolute minimum to the proposed penalty function if and only if it satisfies the necessary conditions of the original constrained problem. As a general rule, penalty functions may have spurious local minima. An advantage of the proposed penalty function is its ability to identify if an obtained minimum is spurious. The proposed penalty function was applied to solve equality constrained problems from the Hock-Schittkowski Collection. Some solutions were obtained more efficiently using the new penalty function than by using a conventional constrained optimization method.

Aircraft Configuration Improvement Study from Aerodynamic and Structure Standpoints

In this work improvements on the geometry of a high aspect ratio aircraft wing are studied, in order to reduce the wing in-flight deformation, without changing the drag of the aircraft and without increasing the structural weight. For this, from a reference rectangular wing, one new wing with elliptical planform has been defined; and comparative analyses of loads and structural deformation have been made for the wings considered: the original rectangular wing and the new corresponding elliptical wing. The aerodynamic analysis is based on the lifting line approach. A computer routine is made by the authors based on this approach, to obtain both induced drag values and the load distribution of the two wings, the original one and the corresponding elliptical. Based on the loads, spars for the two wings have been defined, and in order to evaluate the vertical displacements in flight, a finite element routine have been used. The main result of this study is the comparison of the deformation of wings considered, subjected to the same load factor, and for the same aircraft mass. The results obtained are encouraging for further developments using the present methodology.

Flight Path Optimization for Competition Sailplanes through State Variables Parameterization

This paper presents a numerical process for determining optimal flight paths for competition soaring. The goal is reduction of flight time required to fly towards an ascending thermal and climb to a given altitude. The optimization procedure applies a direct method to obtain sub-optimal solutions through parameterization of state variables, unlike a previous study by the same authors which was based on control parameterization. A mathematical programming procedure is used to determine the sub-optimal values for the parameterized state variables. The optimal control law, which is necessary for the generation of the sub-optimal state, is obtained through a step-by-step penalty technique. The results demonstrate that the optimization of transitory phases is important for the minimization of total flight time.