The successive backward sweep method for optimal control of nonlinear systems with constraints

This paper presents variations of the Successive Backward Sweep (SBS) method for solving nonlinear problems involving terminal and control constraints. The proposed SBS method is based on the linear quadratic control methodology and is relatively insensitive to the initial guesses of the state and control histories. The overall procedure of this method is similar to the existing neighboring extremals or differential dynamic programming algorithms. Several methods of Hessian modification are utilized, when required, to enable the backward integration of the gain equations. An "aiming point" variant of the sweep method is developed to satisfy the terminal constraints accurately. However, this method does not require consistency of the starting states and controls with respect to the system dynamics. Four numerical examples are considered to demonstrate the performance of SBS method and the results are compared to their respective open-loop counterparts.

The successive backward sweep method for optimal control of nonlinear systems with constraints Conference Paper