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Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm

Haylim Chha (Tongji University, Shanghai, China)
Yongbo Peng (Tongji University, Shanghai, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 9 June 2023

Issue publication date: 15 June 2023




In real life, excitations are highly non-stationary in frequency and amplitude, which easily induces resonant vibration to structural responses. Conventional control algorithms in this case cannot guarantee cost-effective control effort and efficient structural response alleviation. To this end, this paper proposes a novel adaptive linear quadratic regulator (LQR) by integrating wavelet transform and genetic algorithm (GA).


In each time interval, multiresolution analysis of real-time structural responses returns filtered time signals dominated by different frequency bands. Minimization of cost function in each frequency band obtains control law and gain matrix that depend on temporal-frequency band, so suppressing resonance-induced filtered response signal can be directly achieved by regulating gain matrix in the temporal-frequency band, leading to emphasizing cost-function weights on control and state. To efficiently subdivide gain matrices in resonant and normal frequency bands, the cost-function weights are optimized by a developed procedure associated to genetic algorithm. Single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structures subjected to near- and far-fault ground motions are studied.


Resonant band requires a larger control force than non-resonant band to decay resonance-induced peak responses. The time-varying cost-function weights generate control force more cost-effective than time-invariant ones. The scheme outperforms existing control algorithms and attains the trade-off between response suppression and control force under non-stationary excitations.


Proposed control law allocates control force amounts depending upon resonant or non-resonant band in each time interval. Cost-function weights and wavelet decomposition level are formulated in an elegant manner. Genetic algorithm-based optimization cost-efficiently results in minimizing structural responses.



Chha, H. and Peng, Y. (2023), "Adaptive linear quadratic regulator for optimal structural control based on wavelet transform and genetic algorithm", Engineering Computations, Vol. 40 No. 4, pp. 1016-1039.



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