In this thesis, we consider two challenging problems in optimal control theory: mixed-integer optimal control problems and bilevel optimal control problems and their applications to flight path optimization and task scheduling. In the first part of the thesis, we focus on mixed-integer optimal control problems, in which constraints, depending on the discrete valued control are present. This introduces additional complexity to the problem, since the only constraints to be considered are those depending on the current value of the discrete control. We show that after time transformation techniques and discretization, a mathematical program with block of vanishing constraints is obtained. Exploiting the special structure of the problem, we formulate first order necessary optimality conditions and derive constraint qualification, which guarantee the existence of nontrivial Lagrange multipliers. Additionally, we illustrate a relaxation method suitable for numerical purposes and prove the converge of the solutions the relaxed problem to the solution of the original one, as the relaxation parameter goes to zero. Finally, we consider a simplified dynamical model of an aircraft, whose flaps configuration is treated as discrete control and in which constraints on speed are imposed, based on the current flaps configuration. In the second part of the thesis, we focus our attention on bilevel optimal control problems. We show that in special cases, the value function of the lower level problem can be exploited, in order to transform the initial problem into an equivalent nonsmoot optimal control problem, for which first order necessary optimality conditions are derived, under the partially calmness constraint qualification. Additionally, we investigate the application of bilevel optimal control theory to scheduling problems, in which the scheduling of several tasks has to be optimized and in which each task represents an optimal control problem itself. We show that the problem can be treated as mixed-integer optimal control problem, after applying the local minimum principle on the lower level problem (in the presence of pure-state, additional virtual controls have to be introduced). In the last part of the thesis, we consider the applications of the developed theory to a variety of optimization problems, including robot interactions, quadcopter flight path optimization and optimal scheduling of take-off and landing aircrafts in proximity of an airport.    «

In this thesis, we consider two challenging problems in optimal control theory: mixed-integer optimal control problems and bilevel optimal control problems and their applications to flight path optimization and task scheduling. In the first part of the thesis, we focus on mixed-integer optimal control problems, in which constraints, depending on the discrete valued control are present. This introduces additional complexity to the problem, since the only constraints to be considered are those dep...    »