| This dissertation, based on practical background of design of 3D-trajectory of horizontal wells, studies nonlinear multistage optimal control systems, including the existence of solutions of state equations and optimal solutions of the optimal control system?optimality conditions?global optimization algorithms for solving the optimal control system and applying these algorithms to practical design of 3D-trajectory of horizontal wells. The main results, obtained in this dissertation, may be summarized as follows:1. For a class of nonlinear multistage optimal control systems, the existence of solutions of the state equations and the existence of optimal solutions of the optimal control system and optimality conditions for the optimal control system are discussed.2. In order to obtain the global optimal solution of the nonlinear multistage optimal control system, the optimal control system is translated into a nonlinear programming problem. Since the objective function and constraint function can be implicit functions or nondifferentiable in this nonlinear programming problem, three global optimization algorithms, based on stochastic search techniques, are proposed.(1) Based on a combination of the uniform design?clustering idea and genetic algorithms, an improved hybrid genetic algorithm is proposed for solving the nonlinear multiage optimal control system without terminal constraints. The convergence of the algorithm is analyzed.(2) An improved evolutionary programming algorithm is developed for solving nonlinear multiage optimal control system with terminal constraints. In this algorithm, each individual can be regarded as a charged particle. According to two cases, two kinds of charge are defined on each individual for objective function and each constraint function, respectively. After calculating these charges, like the electromagnetic force a combination force exerted on each individual is calculated. The direction of this force is taken as a search direction of mutation operator. In order to discard infeasible individual with higher probability, a new fitness function is defined. The convergence of this algorithm is proved.(3) A global optimization algorithm for solving nonlinear multiage optimal control system with equality terminal constraints is proposed. In this algorithm, firstly, based on aggregate function, a new set that can substitute for the feasible region in which the value of objective function is lower than the current value of objective function is defined, then, in this new set, a feasible point is found by stochastic search and local search. The process stops until the new feasible point cannot be found. The convergence proof of this algorithm is given. According to the idea of the proposed algorithm, a global optimization algorithm is constructed for solving the optimal control system of design of 3D trajectory of horizontal wells with terminal constraints.3. According to the features of 3D-trajectory formed in horizontal wells, we construct a nonlinear multistage dynamical system (i.e. state equations) in which state variables are inclination?azimuth?north coordinate?east coordinate and vertical depth coordinate. The dynamical system describes the 3D-trajectory of horizontal wells. Based on this dynamical system, four optimal control systems of design of 3D-trajectory of horizontal wells are proposed from different points of view. There are two aims for designing 3D-trajectory of horizontal wells. Firstly, the terminal output of this dynamical system will approximate the corresponding values of the target point as close as possible. Secondly, the total length of 3D-trajectory of horizontal wells is as short as possible. Based on the two aims, one optimal control system is developed for designing 3D-trajectory of horizontal wells; if the total length of 3D-trajectory of horizontal wells is only considered under satisfying condition of the given terminal output of this dynamical system, then the other optimal control system with terminal constraints is propo...
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