Lyapunov-based Nonlinear Control
The research is focused on the development and application of a Lyapunov-based control methodology, which incorporates the full nonlinear system dynamics in the design and analysis without requiring the solution of the nonlinear equations of motion. Research efforts are specifically focused on adaptive, robust, and learning control designs for nonlinear systems to address issues related to uncertain nonlinear dynamics with limited or uncalibrated/corrupt sensor information.
Robust Integral of the Sign of the Error (RISE) is a recently developed new differentiable high gain feedback control strategy that contains a unique integral signum term which can accommodate for sufficiently smooth bounded disturbances. This technique can be used to develop a tracking controller for nonlinear systems in the presence of additive disturbances and parametric uncertainties under the assumption that the disturbances are C2 with bounded time derivatives. A significant outcome of this new control structure is that:
- asymptotic stability is obtained despite a fairly general uncertain disturbance. (The typical adaptive control methods cannot be applied for the systems with additive non-LP disturbances.)
- the RISE controller is continuous which is especially useful from the implementation point of view. (Other robust discontinuous feedback strategies are disadvantageous in that they require infinite bandwidth and cause chattering that may cause undesirable oscillations in the mechanical systems.)
In addition, the RISE technique has been used for fault detection and identification, as well as an implicit learning tool to identify unknown nonlinear dynamics in the system.
N. Fischer, Z. Kan, R. Kamalapurkar, and W. E. Dixon, “Saturated RISE Feedback Control for Second-Order Nonlinear Euler-Lagrange-like Systems,” IEEE Transactions on Automatic
Control, Vol. 59, No. 4., pp. 1094-1099 (2013). [pdf]
- N. Fischer, Z. Kan, and W. E. Dixon, “Saturated RISE Feedback Control for Euler-Lagrange Systems,” American Control Conference, Montréal, Canada, 2012, pp. 244-249. [pdf]
S. Bhasin, P. Patre, Z. Kan, and W. E. Dixon, “Control of a Robot Interacting with an Uncertain Viscoelastic Environment with Adjustable Force Bounds,” American Control Conference,
Baltimore, MD, 2010, pp. 5242-5247. [pdf]