Direct adaptive-Q control for online performance enhancement of switching linear systems

Friedrich, Stefan; Buss, Martin

doi:10.1109/cdc.2016.7799250

Cited by 1 publication

(6 citation statements)

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“…In this section, we provide a concise summary of the plant/controller factorization 10 approach central to this article. The resulting Q-parameterization is ubiquitously used in control theory, eg, in robust control, 15,16 computer-aided design, 17 gain scheduling, 18,19 model predictive, 20 hybrid, 21 and adaptive [22][23][24] control. For a general introductory exposition, the reader is referred to the work of Anderson.…”

Section: Controller Parameterization By Factorizationmentioning

confidence: 99%

“…Second, an outer-loop PD controller is commonly 1-4 applied to stabilize (6) prior to the robustness analysis. Therefore, in all subsequent developments, one has to work with an error system (24) where the gains K P , K D of the controller occur in the dynamic matrix A. These aspects entail unfavorable consequences.…”

Section: Drawbacks Of Established Approachesmentioning

confidence: 99%

“…It is unfortunately not obvious to find in the literature [1][2][3][4]26,48 a suitable generalized plant 15,49 description for AID, as most methods work with error dynamics (21) or (24). Therefore, the first problem we tackle is how the standard robotic bounds (9)-(10) translate into a generalized setup ( Figure 3A) without lumping the effects of (7)-(8) into a single additive term.…”

Section: Problem Statementmentioning

confidence: 99%

“…There is a multitude of design methods for the parameter Q, and the reader is referred to the literature. [15][16][17]19,21,22,24 Controller design in Q is beyond the scope of this article, yet in general, the less restricted ||Q|| ∞ needs to be, the more design freedom there is for any such method. Let us briefly illustrate this trade-off.…”

Section: Illustrative Example: P560 With Varying Payloadmentioning

confidence: 99%

“…By the revised robust control design, Bascetta and Rocco 5 essentially undo the step in the Lyapunov-based designs (Section 2.5.2) of lumping the closed-loop uncertainty into a single term in (24). Their method consists of two steps: First, the nominal PD controller is designed to ensure global asymptotic stability of the error system under perturbation with any admissible matrix || M || ≤ .…”

Section: Comparison To Lyapunov-based Designsmentioning

confidence: 99%

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Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

Friedrich

Buss

2019

Intl J Robust & Nonlinear

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We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid-body manipulators under approximate inverse dynamics control. Outer-loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well-known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer-loop feedback controller by means of an uncertain dual-Youla operator. Therefore, using the dual-Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid-body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double-Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six-degree-of-freedom robot scenario with varying payload. KEYWORDS approximate inverse dynamics, dual-Youla parameterization, robust robot manipulator control, robust/adaptive control, uncertainty quantification INTRODUCTIONOperating conditions of robot manipulators change over time, impairing the control performance, for example, by wear, varying load, etc. To adapt the controller to such situations, a variety of data-driven methods have been proposed in the literature, including adaptive and learning control. [1][2][3][4] In practice, however, very simple feedback controllers and model-based architectures are prevalent.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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