Structured adaptive model inversion (SAMI): Theory and applications to trajectory tracking for non-linear dynamical systems

The objective of the proposed research is to evolve efficient control strategies, thereby demonstrating the application of Structured Adaptive Model Inversion as a theory that can be applied to tracking bounded reference trajectories for a wide range of uncertain nonlinear dynamical systems with applications drawn from the Aerospace and Robotics literature. Control law designs employing this methodology recognize the underlying truth, with respect to modelling a class of dynamical systems, that a subset of the governing differential equations are exact or perfectly known (e.g. the description of the kinematic relations). It is further recognized that these equations are free of any uncertainties arising from forces/torques or modelling errors. Hence all the adaptation is restricted to the subset of the state space corresponding to the acceleration level differential equations governing the system dynamics. Robust adaptive feedback control laws are derived that guarantee stability and bounded tracking errors in the presence of un-modelled dynamics, unknown disturbances, and actuator saturation limits. A methodology to derive stable control laws is demonstrated for a constrained dynamical system and all the theoretical results are demonstrated through numerical simulation of several example problems.