Abstract
The most important part of the control design for nonlinear dynamical systems is to guarantee the stability . Then, the control is quantitatively designed to meet multiple and often conflicting performance objectives. The performance of the closed-loop system is a function of various system and control parameters. The quantitative design using multiple parameters to meet multiple conflicting performance objectives is a challenging task. In this chapter, we present the recent results of Pareto optimal design of controls for nonlinear dynamical systems by using the advanced algorithms of multi-objective optimization. The controls can be of linear PID type or nonlinear feedback such as sliding mode. The advanced algorithms of multi-objective optimization consist of parallel cell mapping methods with sub-division techniques. Interesting examples of linear and nonlinear controls are presented with extensive numerical simulations.
Keywords
Honorary Professor of Tianjin University.
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Acknowledgments
The material in this chapter is based on work supported by grants (11172197, 11332008 and 11572215) from the National Natural Science Foundation of China, and a grant from the University of California Institute for Mexico and the United States (UC MEXUS) and the Consejo Nacional de Ciencia y Tecnología de México (CONACYT) through the project “Hybridizing Set Oriented Methods and Evolutionary Strategies to Obtain Fast and Reliable Multi-objective Optimization Algorithms”.
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Qin, ZC., Xiong, FR., Sardahi, Y., Naranjani, Y., Schütze, O., Sun, J.Q. (2017). Multi-objective Optimal Design of Nonlinear Controls. In: Schütze, O., Trujillo, L., Legrand, P., Maldonado, Y. (eds) NEO 2015. Studies in Computational Intelligence, vol 663. Springer, Cham. https://doi.org/10.1007/978-3-319-44003-3_9
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