The relationship between terminal state constraints and penalties for the discrete-time LQP problem associated with the adjustment of accelerometer data (Q1116659)

This paper is concerned with the problem of adjusting and integrating accelerometer data by including them in the discrete-time optimal control framework of minimizing the sum of squares of adjustments, regarded as controls, subject to the linear dynamics of double integration. A terminal penalty weighting the deviations in terminal velocity and displacement can be added to the quadratic cost. A procedure using terminal state constraints is developed as an alternative to terminal penalties to prevent drift in the terminal states. The explicit relationships S between the control laws for these two alternatives are determined. This procedure of terminal constraints is most appropriate for the adjustment of accelerometer data of phenomena, such as shock wave induced motion, which lack a regular structure or an a priori equilibrium, but where the values (known or assumed) of the state variables at the end points could be used as terminal constraints.