Trajectory Desensitization In Optimal Control Problems

The efficacy of the so-called sensitivity function in developing desensitized optimal control schemes is studied. A sensitivity function provides information about the first order variation of the state under parameter variations at a given time instant along a trajectory. It is demonstrated that the sensitivity function can be employed to effectively desensitize either an optimal trajectory or the state at a particular time instant ( for example, the final state) along the optimal trajectory. Zermelo's path optimization problem is chosen to test the theory. MonteCarlo simulations are carried out, validating the key idea. The limitations of the proposed approach are identified and the possibilities for future work are discussed.