In this work, we develop a new control design approach to deal with saturated polynomial nonlinear systems by using higher order Lyapunov functions. By combining power transformation with Sum-of-Squares (SOS) techniques, we can augment the systems with more state variables representing higher order combinations of the original ones. Then, the search of higher order Lyapunov functions for original systems can be recast to the design of quadratic Lyapunov functions for augmented systems. By computing for higher order Lyapunov functions using norm-bounded differential inclusion (NDI) LMI conditions, the flexible representations of augmented systems can help us to achieve better performance than quadratic based method. Two examples illustrate the improvements to enlarge the region of attraction and to improve the ℋ∞ performance for nonlinear systems subjected to saturation nonlinearity, respectively.
- Dynamic Systems and Control Division
Feedback Design for Saturated Polynomial Nonlinear Systems via Higher Order Lyapunov Functions
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Yang, S, & Wu, F. "Feedback Design for Saturated Polynomial Nonlinear Systems via Higher Order Lyapunov Functions." Proceedings of the ASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference. Volume 2: Legged Locomotion; Mechatronic Systems; Mechatronics; Mechatronics for Aquatic Environments; MEMS Control; Model Predictive Control; Modeling and Model-Based Control of Advanced IC Engines; Modeling and Simulation; Multi-Agent and Cooperative Systems; Musculoskeletal Dynamic Systems; Nano Systems; Nonlinear Systems; Nonlinear Systems and Control; Optimal Control; Pattern Recognition and Intelligent Systems; Power and Renewable Energy Systems; Powertrain Systems. Fort Lauderdale, Florida, USA. October 17–19, 2012. pp. 645-652. ASME. https://doi.org/10.1115/DSCC2012-MOVIC2012-8644
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