National Aeronautics and Space Administration


Date of this Version



Systems & Control Letters 61 (2012) 485–494; doi:10.1016/j.sysconle.2012.01.009


In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain so as to reduce the tracking error rapidly. However, a large adaptive gain can lead to highfrequency oscillations which can adversely affect robustness. A new adaptive law, called optimal control modification, is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations. The modification is based on a minimization of the L2 norm of the tracking error bounded away from some lower bound, formulated as an optimal control problem. The optimality condition is used to derive the modification based on the Pontryagin’s Minimum Principle. The optimal control modification is shown to improve robustness of the standard MRAC without significantly compromising the tracking performance. Flight control simulations demonstrate the effectiveness of the new adaptive law. A series of recent, successful flight tests of this adaptive law on a NASA F/A-18A aircraft at NASA Dryden Flight Research Center further demonstrate the effectiveness of the optimal control modification adaptive law.