Time-optimal attitude control scheme for a spinning missile

The problem of minimum-time attitude control of a spinning missile is addressed. The missile is modeled as a rigid body that is symmetric about its spin axis. A single reaction jet provides the necessary transverse moments. The missile is assumed to have some arbitrary initial transverse angular velocity, and it is desired to take it to some final attitude in minimum time while reducing the transverse angular velocity to zero. A scheme to generate thruster firing times as functions of the initial and desired states of a spinning missile is described. This scheme involves transforming the state variables and integrating the transformed state and costate equations backward in time and generating the control history using the properties of the optimal control. The control history, given in terms of the thruster firing times, is stored as a function of the boundary conditions. A feedback control law based on function generation is then proposed that uses only the first thruster turn-on and turn-off times. This proposed control scheme can be implemented in real time with good accuracy.