Nonlinear CLOS guidance for missiles

The pitch and yaw dynamics for a Bank-To-Turn (BTT) missile couple in a nonlinear fashion through the missile´s lateral acceleration and bank angle. Due to these nonlinear dynamics, a solution for the optimal command to line-of-sight (CLOS) guidance problem can be found only by numerical methods for solving two point boundary value problems. For practical implementation, closed-form solutions for the control commands in terms of the current states are necessary. Because the dynamic response of the missile to the roll rate command is much faster than the dynamics of the rest of the system states, a solution to the optimal CLOS guidance problem is obtained using perturbation techniques. These techniques exploit the separation of the system into slow and fast states by finding solutions to the reduced-order problems. Then these reduced-order solutions are combined to obtain approximate solution to the full-order problem. The resultant solution is a combination of acceleration and roll-rate commands as functions of the current system states.