Abstract
One of the main components of a robust control theory is a quantifiable description of system uncertainty. A good uncertainty description should have three desirable properties. First, it is required to capture and perturbations. Second, it needs to be mathematically tractable, preferably by using elementary tools. Third, it should lead to a self-contained robust control theory, encompassing analysis and synthesis techniques that are accessible to both researchers and practitioners. While the additive uncertainty and multiplicative uncertainty are two of the most commonly employed uncertainty descriptions in systems modeling and control, they come up short of fulfilling the requirements above. In this chapter, we introduce the uncertainty quartet, a.k.a. the \(+-\times \div \) uncertainty (as is simpler to pronounce in oriental languages), which combines in a unifying framework the additive, multiplicative, subtractive and divisive uncertainties. An elementary robust control theory, involving mostly polynomial manipulations, is developed based on the uncertainty quartet. The proposed theory is demonstrated in a case study on controlling an under-sensed and under-actuated linear (USUAL) inverted pendulum system.
In memory of Robert Tempo.
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Acknowledgements
Useful discussions with Dr. Wei Chen on the writing of this chapter are gratefully acknowledged. This work was supported in part by the Research Grants Council of Hong Kong Special Administrative Region, China, under Project 16201115 and Theme-Based Research Scheme T23-701/14-N, and in part by the People’s Government of Pengjiang District, Jiangmen, Guangdong, China.
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Zhao, D., Chen, C., Khong, S.Z., Qiu, L. (2018). Robust Control Against Uncertainty Quartet: A Polynomial Approach. In: Başar, T. (eds) Uncertainty in Complex Networked Systems. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-04630-9_4
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DOI: https://doi.org/10.1007/978-3-030-04630-9_4
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