Trustable autonomous systems using adaptive control

A long standing problem in adaptive control is the derivation of robustness properties in the presence of unmodeled dynamics, a necessary and highly desirable property for designing adaptive flight control for systems with trustable autonomy. We provide a solution to this problem in this paper for linear time-invariant plants whose states are accessible for measurement. This is accomplished by using a Lipschitz continuous projection algorithm that allows the utilization of properties of a linear system when the adaptive parameter lies on the projection boundary. This in turn helps remove the restriction on plant initial conditions, as opposed to the currently existing proofs of semi-global stability. A direct implication of this result is the robustness of adaptive control systems to time-delays, and the guarantee that the underlying adaptive system will have a delay margin.

[1]  Sanjeev M. Naik,et al.  Robust continuous time adaptive control by parameter projection , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[2]  T Labarta,et al.  Aspects of operational radiation protection during dismantling of nuclear facilities relevant for the estimation of internal doses. , 2007, Radiation protection dosimetry.

[3]  K. Narendra,et al.  Robust adaptive control in the presence of bounded disturbances , 1986 .

[4]  Kumpati S. Narendra,et al.  Stable Adaptive Schemes for System Identification and Control - Part II , 1974, IEEE Trans. Syst. Man Cybern..

[5]  K. Narendra,et al.  Stable model reference adaptive control in the presence of bounded disturbances , 1982 .

[7]  Hassan K. Khalil,et al.  Output feedback control of nonlinear systems using RBF neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[8]  L. Praly,et al.  Adaptive nonlinear regulation: estimation from the Lyapunov equation , 1992 .

[9]  J. Hale,et al.  Ordinary Differential Equations , 2019, Fundamentals of Numerical Mathematics for Physicists and Engineers.

[10]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[11]  K. Narendra,et al.  Stable adaptive controller design, part II: Proof of stability , 1980 .

[12]  R. Bellman.  The stability of solutions of linear differential equations , 1943 .

[13]  Kumpati S. Narendra,et al.  Stable Adaptive Schemes for System Identification and Control-Part I , 1974, IEEE Trans. Syst. Man Cybern..

[14]  P. Hartman.  Ordinary Differential Equations , 1965 .