Adaptive Control of Discrete-Time Systems with Unknown, Unstable Zero Dynamics

Adaptive control of systems with poorly known or unmodeled unstable zero dynamics remains a challenging problem. This paper presents an extension of retrospective cost adaptive control (RCAC) called data-driven RCAC (DDRCAC), which does not require that the zero dynamics be known a priori. Instead, the method uses online identification to obtain an approximate model of the plant numerator dynamics for use in the target model of RCAC. DDRCAC is demonstrated numerically on systems with linear and nonlinear unstable zero dynamics that are a priori unknown.