Positive μ-modification for stable adaptation in the presence of input constraints

For a class of linear dynamical systems with unknown parameters a direct model reference adaptive control framework is developed that provides stable adaptation in the presence of input constraints. The proposed design methodology, termed "positive μ-modification", protects the control law from actuator position saturation. Moreover, the design is Lyapunov based and ensures global asymptotic tracking for open-loop stable systems. For unstable systems an estimate for the domain of attraction is derived based on the input saturation magnitude and system parameters. Simulation of a benchmark example verifies the theoretical statements.