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Adaptive interpolating control for constrained systems with parametric uncertainty and disturbances
Author(s) -
Zhang Sixing,
Dai Li,
Gao Yulong,
Xia Yuanqing
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5140
Subject(s) - parametric statistics , control theory (sociology) , mathematical optimization , adaptive control , convergence (economics) , controller (irrigation) , constraint (computer aided design) , robust control , stability (learning theory) , constraint satisfaction , mathematics , set (abstract data type) , computer science , control system , control (management) , artificial intelligence , engineering , machine learning , statistics , geometry , electrical engineering , probabilistic logic , agronomy , economics , biology , programming language , economic growth
Summary An adaptive interpolating control (AIC) algorithm is proposed for constrained linear systems with parametric uncertainty and additive disturbance. This adaptive algorithm consists of an iterative set membership identification algorithm, which updates the uncertain parameter set at each time step, and an interpolating controller, which robustly stabilizes the uncertain system with state and input constraints. We prove that the AIC algorithm is recursively feasible and guarantees robust constraint satisfaction and robust asymptotic stability of the closed‐loop system in the presence of uncertainties. Moreover, we detail two possible extensions of the AIC algorithm: (a) persistent excitation conditions can be embedded into the AIC algorithm to accelerate the convergence of system parameters and (b) the combination of the AIC algorithm and aggressive learning is able to enlarge the size of the feasible region with every iteration by exploiting information from previous iterations. We illustrate the effectiveness of the proposed algorithms through comparisons with adaptive model predictive control and one example of mobile carrier robot.