Positive μ-modification for stable adaptation in dynamic inversion based adaptive control with input saturation

For a class of uncertain nonlinear dynamical systems in Brunovsky form a dynamic inversion (DI) based 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 bounded tracking for initial conditions within the domain of attraction. An estimate of the latter is derived based on the input saturation magnitude and system parameters. Simulation of a benchmark example verifies the theoretical statements.