Design and Analysis of a Novel L1 Adaptive Control Architecture With Guaranteed Transient Performance

Conventional Model Reference Adaptive Controller (MRAC), while providing an architecture for control of systems in the presence of parametric uncertainties, offers no means for characterizing the system’s input/output performance during the transient phase. Application of adaptive controllers was therefore largely restricted due to the fact that the system uncertainties during the transient have led to unpredictable/undesirebale situations, involving control signals of high-frequency or large amplitudes, large transient errors or slow convergence rate of tracking errors, to name a few. In this paper, we develop a novel adaptive control architecture that ensures that the input and the output of an uncertain linear system track the input and output of a desired linear system during the transient phase, in addition to the asymptotic tracking. This new architecture has a low-pass filter in the feedback-loop that enables to enforce the desired transient performance by increasing the adaptation gain. For the proof of asymptotic stability, the L1 gain of a cascaded system, comprised of this filter and the closed-loop desired reference model, is required to be less than the inverse of the upper bound of the norm of unknown parameters used in projection based adaptation laws. The ideal (non-adaptive) version of this L1 adaptive controller is used along with the main system dynamics to define a closed-loop reference system, which gives an opportunity to estimate performance bounds in terms of L∞ norms for both system’s input and output signals as compared to the same signals of this reference system. Design guidelines for selection of the low-pass filter ensure that the closed-loop reference system approximates the desired system response, despite the fact that it depends upon the unknown parameters. The tools from this paper can be used to develop a theoretically justified verification and validation framework for adaptive systems. Simulation results illustrate the theoretical findings. Research is supported by AFOSR under Contract No. FA9550-05-1-0157. The authors are with Aerospace & Ocean Engineering, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061-0203, e-mail: chengyu, [email protected]