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We propose a new dynamic extension of the thrust variable in the quadcopter dynamics that preserves the positive sign of the thrust. This extension not only eliminates the positive sign constraint on the thrust variable, but also leads to global chartwise feedback linearization of the quadcopter dynamics. For the latter, an atlas is first constructed on the entire state space of the quadcopter and then the dynamically extended quadcopter system is transformed to a 14-dimensional linear controllable system on each chart in the atlas. Based on the chartwise dynamic feedback linearization, a global tracking strategy is proposed for the quadcopter and its excellent performance is demonstrated with a simulation. [ABSTRACT FROM AUTHOR]

We present necessary and sufficient optimality conditions for finite-time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush–Kuhn–Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine (PWA) system can be written as the optimizer of a mathematical program, which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with PWA dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation. [ABSTRACT FROM AUTHOR]