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2 Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

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Flying between obstacles - formulation and solution to the problem

Bunakov A., Grevtsov N., Efimov O., Melts I., Sazonov D., Tegin A.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

2001

nr 11

29-39

The paper presents a short description of two approaches to solving of the fly-around-obstacles problem. This problem consists in finding of a global optimal flying object trajectory or route for a flight over an area with obstacles of natural or artificial type. The trajectory length or fuel consumption is limited. The paper contains two parts corresponding to the combinatory and variational approaches, respectively.

Lagrange multipliers determination for optimum control problem solution

Grevtsov N., Efimov O., Melts I.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

1998

nr 8

209-214

This paper considers the problem of Lagrange multipliers initial proximity determination for iterative procedure of second order method of optimum control problem solution. The control problem corresponds to the optimum control of dynamic system described by finite - difference equations with account of terminal conditions, control and phase variables or mixed inequality constraints. The time of control process is free or fixed. The problem of Lagrange multipliers determination is formulated as the problem of finding the minimum of the norm square of the relations describing optimality conditions at initial proximity of control. This problem is reduced to the special two point boundary value problem (TPBVP). The method of this TPBVP solution for initial proximity of Lagrange multipliers determination is proposed.