A novel Q-modification term for adaptive control

Abstract

A novel modification term is suggested for use in adaptive control. The development is of use in any setting in which uncertainty is linearly parameterized. The modification uses state and control time histories. The effect is justified through stability analysis, and illustrated on a dynamic model for wing rock.

Direct Uncertainty Minimization Framework for System Performance Improvement in Model Reference Adaptive Control

“…To address this problem, the authors of [1][2][3][4][5][6][7][8] present modifications to adaptive update laws. In particular, the work in [1][2][3] uses filtered versions of the control input and state; [4][5][6] uses a moving time window of the system uncertainty; and [7,8] uses recorded and instantaneous data concurrently.…”

“…In particular, the work in [1][2][3] uses filtered versions of the control input and state; [4][5][6] uses a moving time window of the system uncertainty; and [7,8] uses recorded and instantaneous data concurrently. In contrast to these approaches, the authors of [9][10][11] present an approach called artificial basis functions that adds modification terms not only to the update law, but also to the adaptive controller and show that the system error can be suppressed during the transient system response.…”

“…In contrast to these approaches, the authors of [9][10][11] present an approach called artificial basis functions that adds modification terms not only to the update law, but also to the adaptive controller and show that the system error can be suppressed during the transient system response. The common denominator of the approaches in [1][2][3][4][5][6][7][8][9][10][11] is that they introduce additional mechanisms to model reference adaptive control laws that capture a form of the system uncertainty in order to suppress its effect.…”

“…Unlike the approaches in [1][2][3][4][5][6][7][8], the proposed framework consists of an architecture involving modification terms in both the adaptive controller and the update law, such that these terms are activated when the system error is nonzero and vanishes as the system reaches its steady state. In addition, this new framework directly allows one to suppress the effect of system uncertainty on the transient system response through a gradient minimization procedure and, hence, leads to improved system performance.…”

Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

“…It should be mentioned that there are other recently developed modifications to adaptive control such as the adaptive loop recovery method, 8 Kalman filter modification, 9 and Q-modification. 10 In the context of verifiable adaptive control, the optimal control modification exhibits an interesting property. Using a singular perturbation argument for fast adaptation, it can be shown that the asymptotic solution of the adaptive law for a linear uncertain system actually tends to a LTI model.…”