Adaptive dynamic inversion of nonlinear systems subjected to control saturation constraints

Abstract

The adaptive dynamic inversion control methodology uses dynamic inversion to calculate the control, and adaptation to compensate for the errors in the inversion due to model uncertainties. Traditionally, adaptive control assumes full authority control and lacks an adequate theoretical treatment for control in the presence of actuator saturation limits. The objective of this research is to investigate the problems introduced in the adaptive dynamic inversion control scheme due to bounds on the control, and design control strategies to overcome these problems. The unique contribution of this research is that it identifies the maximum possible domain of attraction considering the control position limit, and uses a switching control strategy to contain the plant within the maximum possible domain of attraction. Another novel idea is that of a direction consistent control constraint mechanism which maintains the resultant direction of the rate of change of state the same as that of the desired, even in the presence of control saturation. This research uses a modified adaptation mechanism to prevent incorrect adaptation arising from trajectory errors due to control saturation. Mathematical development of the control laws and the adaptation mechanisms is presented along with rigorous proofs for convergence of the tracking error and stability of the overall control scheme. Finally, numerical simulation results are presented to validate the control methodology.