Input shaping design using sequential linear programming (SLP) for non-linear systems

This paper presents a sequential optimization technique for the design of optimal controllers. Linearizing the system model about nominal trajectories results in a linear programming problem which is used to select a perturbation to the nominal control to satisfy the boundary conditions and the state and control constraints. Sequential solution of linear programming problem where the linearized system and control influence matrices are time varying results in the optimal control. Two approaches wherein the perturbation control is constant and linearly varying within a sampling interval are tested on benchmark problems and the results are compared to illustrate the performance of the proposed technique.