Nonlinear Optimal Control for Guidance and 3D Trajectory Tracking of Missiles

The paper proposes a nonlinear optimal control method for guidance and three-dimensional trajectory tracking of missiles. It is proven that the kinematic-dynamic model of the missile is differentially flat, which confirms the controllability of this system. Next, to apply the nonlinear optimal control scheme the dynamic model of the missile undergoes approximate linearization with the use of first-order Taylor-series expansion and through the computation of the associated Jacobian matrices. The linearization takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the missile an H-infinity optimal feedback controller is designed. To compute the controller's stabilizing feedback gains an algebraic Riccati equation has to be solved repetitively at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control scheme are proven through Lyapunov analysis. This control method exhibits specific advantages: (i) unlike global linearization-based control schemes it avoids complicated changes of state variables and state-space model transformations, (ii) unlike Nonlinear model-predictive control approaches its convergence to the optimum does not depend on ad-hoc initialization and empirical selection of the controller's parameters, (iii) unlike multi-model feedback control schemes with linearization around multiple operating points, it avoids the solution of an exponentially large number or Riccati equations or the solution of LMIs of large dimensionality.