Affiliations: [a] National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an, Shaanxi, PR China | [b] The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA
Correspondence:
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Corresponding author. Ye-Hwa Chen, Professor in George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. Tel.: +1 404 894 3210; Fax: +1 404 894 9342; E-mail: yehwa.chen@me.gatech.edu.
Abstract: The paper considers an optimal design problem for a class of uncertain systems. The systems are nonlinear and the state is constrained to be positive. The uncertainty of the system is time-varying and bounded, with the bound lies within a prescribed fuzzy set. The control input of the system may also be constrained to be one-sided (i.e., either positive or negative). A transformation of the state is proposed to release the state constraint. Based on a partial sign-definiteness knowledge of the uncertainty, a one-sided robust control is presented. The control structure is deterministic and is not fuzzy if-then rule-based. By using the fuzzy description of uncertainty, the paper proposes an optimal design problem of the one-sided robust control. It is proven that the global solution to this optimal design problem always exists and is unique. The performance of the resulting controlled system is deterministically guaranteed as well as fuzzily optimized. The control design is illustrated by applying to a drug administration problem.
Keywords: Fuzzy dynamic system, state constraint, control constraint, fuzzy set theory, optimal design
