Robust multiple model adaptive control: Modified using ν‐gap metric

Abstract

SUMMARYA new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the -gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open-loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the -synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on -gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case-study is a non-minimum-phase (NMP) system, which has an uncertain NMP zero; the second case-study is a mass-spring-dashpot system that has three uncertain real parameters. In the first case-study, five robust controller design methods (H 2 , H ∞ , QFT, H ∞ loop-shaping and -synthesis) are implemented and it is shown via extensive simulations that RMMAC/ /QFT method improves disturbance-rejection, when compared with the classic RMMAC. In the second case-study, two robust controller design methods (QFT and mixed -synthesis) are applied and it is shown that the RMMAC/ /QFT method improves disturbance-rejection, when compared with RMMAC/ /mixed-.

Robust adaptive LQR control of nonlinear system application to 3-Dof flight control system

“…Again the control voltages for the front motors and back motors are v f and v b , where they can be define by equation [5],…”

“…An adaptive controller was implemented to make the travel and elevation angles track the outputs of a reference model [4]. Input and state constraints were systematically accounted for within the control design procedure [5]. Form explanation of a robust control method for attitude regulation of the laboratory helicopter was considered [6].…”

Stability analysis of weighted multiple model adaptive control of a linear time-invariant discrete-time system

“…This kind of multiple model adaptive control is always produced as the probability-weighted average of elemental controller outputs. In recent years, a new type of weighted M-MAC, i.e., robust multiple model adaptive control (RMMAC) architecture was put forward with convictive experiment results [8][9][10], which arouses once again the enthusiasm of researchers in the field of adaptive control. Some useful convergence results on the probabilistic weighting have been obtained under suitable assumptions [11][12][13][14].…”

Observer‐based adaptive control using multiple‐models switching and tuning

“…Stability results for these schemes show that all closed‐loop signals are bounded and ‘robust performance is only recovered in steady state’ (see e.g. [13–15]).…”