Adaptive dynamic inversion control of a linear scalar plant with constrained control inputs

This paper develops a methodology for stable adaptation in the presence of control position limits, for a class of linear time invariant systems with uncertain parameters. The central idea is to modify the desired reference by the best estimated deficiency in the state derivative, because of the saturation. The modified reference is used in determining the modified tracking error which is further used in the parameter update laws. A notion of ´points of no return´ is presented for unstable systems with bounded control, and a switching control strategy is devised to address this problem of containing the state within the points of no return. The paper presents stability proofs for the control scheme and numerical simulations to demonstrate the performance of the controller.