Transient performance, estimator resetting and filtering in nonlinear multiple model adaptive backstepping control

Abstract

Multiple model adaptive control (MMAC) is a well established approach for implementing adaptive systems with fast transient response. This paper considers a recently developed MMAC method based on adaptive nonlinear backstepping control where the parameter estimate may be instantaneously reset based on a criterion that requires a negative jump in the associated control Lyapunov function. Particular attention is paid to transient effects due to data filtering, which must be introduced in any practical implementation of the MMAC algorithm in order to reduce the sensitivity to noise, disturbances and model uncertainty. The main contribution of this paper is insight into the robust behavior of the adaptive system resulting from the filtering, and an investigation into the trade-offs between high transient performance and robustness to uncertainty.We also suggest data filter tuning guidelines and illustrate the results using a simulation example.

Lyapunov-Based Integrator Resetting With Application to Marine Thruster Control

“…These issues are discussed in greater detail in [17]. Also note that the reset strategy above may lead to chattering effects, since the steady state position is not exactly known.…”

“…holds, then the originx = 0 is a globally exponentially stable (GES) equilibrium point of (17). Proof: The time derivative of (23) along the trajectories of the nonlinear system (17) iṡ…”

“…The linear part aω is subtracted from the nonlinearity in (16), leaving F (x, h R , ω * ) as the remaining nonlinear part in (17). This is done in order to incorporate a linear approximation of the nonlinear part of the system as accurately as possible.…”

“…Proposition 2: Given the closed-loop system with PIcontroller (17). Assume that V in (23) is a Lyapunov function that proves the equilibrium point of the nonlinear system in (17) to be GES.…”

“…[14] presents an MMAC in an adaptive backstepping control algorithm. [17] is an extension of [14], discussing the effect of estimating the steady state, and gives tuning guidelines for the controller. In [18], MMAC is developed for adaptive control of feedback linearizable systems.…”