Unified control parameterization approach for finite-horizon feedback control with trajectory shaping

This study presents control parametrisation as a unifying framework for designing a linear feedback control law that achieves finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains which is appropriate for practical use. The unified control parametrisation approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasise expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parametrisation viewpoint and shows how the notion of specifying input basis functions not only generalises various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of design process in handling the shaping requirements more directly through construction of appropriate basis.