Prescribed-time stabilization for high-order nonlinear systems with a pre-specified asymmetric output constraint |
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| Affiliation: | 1. Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 70101, Taiwan;2. Institute of Automation, Qufu Normal University, Qufu, Shandong Province 273165, China;3. Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, Taiwan;4. Advanced Manufacturing Research Center, National Taiwan University of Science and Technology, Taiwan;1. College of Mathematics and Computer Science, Tongling University, Tongling, 244000, China;2. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, 212013, China;1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;2. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, Missouri 65211, USA;1. Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150006, China;2. Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China;1. School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, P.R. China;2. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering, University of Kragujevac, 36000 Kraljevo, Serbia |
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| Abstract: | This article considers the problem of prescribed-time stabilization for a class of uncertain high-order nonlinear systems (i.e., systems in the -normal form) with a pre-specified asymmetric output constraint. A core ingredient, tangent-type barrier function, is proposed first by skillfully excavating and assimilating the inherent properties of system nonlinearities. Based on the barrier function, as well as a serial of nested signum functions, the celebrated technique of adding a power integrator is renovated finely to establish a new design approach by which a continuous state feedback prescribed-time stabilizer, along with a tangent-type asymmetric barrier Lyapunov function, can be constructed in a systematic fashion, thereby guaranteeing the performance of prescribed-time state convergence and ensuring the fulfillment of pre-specified output constraints surely. Benefiting from the composite characteristics of the presented tangent-type barrier Lyapunov function and the signum functions, the proposed approach further offers a unified nature in design enabling us to organize a prescribed-time stabilizer that is simultaneously valid and executable for the system undergone or free from output constraints, without the need of changing the controller structure. The effectiveness and superiority of the developed approach are illustrated by a numerical example. |
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