  This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.
