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We present structure preserving integrators for solving linear quadraticoptimal control problems. This problem requires the numerical integration ofmatrix Riccati differential equations whose exact solution is a symmetricpositive definite time-dependent matrix which controls the stability of theequation for the state. This property is not preserved, in general, by thenumerical methods. We propose second order exponential methods based on theMagnus series expansion which unconditionally preserve positivity for thisproblem and analyze higher order Magnus integrators. This method can also beused for the integration of nonlinear problems if they are previouslylinearized. The performance of the algorithms is illustrated with thestabilization of a quadrotor which is an unmanned aerial vehicle.

Structure preserving integrators for solving linear quadratic optimal control problems with applications to describe the flight of a quadrotor