Improving transient performance of discrete‐time model reference adaptive control architectures. (27th April 2020) - Dogan, K. Merve; Yucelen, Tansel; Haddad, Wassim M.; Muse, Jonathan A.
Summary: Discrete‐time adaptive control algorithms can be executed directly in embedded code unlike their continuous‐time counterparts, which require discretization. However, their designs predicated on quadratic Lyapunov‐based frameworks are quite intricate due to the resulting complexity in the Lyapunov difference expressions. Therefore, a wide array of available continuous‐time results addressing transient performance issues using adaptive control algorithms cannot be applied or readily extended to the discrete‐time case. In this article, we present a new model reference adaptive control architecture for discrete‐time uncertain dynamical systems. Specifically, the proposed architecture consists of a command governor mechanism that adjusts the trajectory of a given command during the closed‐loop transient response. It is shown that this mechanism is effective in improving transient performance of discrete‐time model reference adaptive control architectures. Using a logarithmic Lyapunov function, we prove Lyapunov stability of the closed‐loop system as well as asymptotic convergence of the system error states involving the difference between the states of the uncertain dynamical system and the states of the reference model, as well as driving the command governor signal to zero.