Forwarding-based immersion and invariance control for \[\varvec{n}\] -dimensional strict-feedback nonlinear systems

• Published in: Nonlinear dynamics Vol. 83; no. 1-2; pp. 483 - 496
• Main Authors: Zhang, Xu, Huang, Xianlin, Lu, Hongqian, Zhang, Hongyang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.01.2016
• Subjects: Algorithms; Asymptotic properties; Computer simulation; Control systems; Control systems design; Control theory; Design engineering; Dynamical systems; Feedback; Immersion; Invariance; Liapunov functions; Magnetic levitation; Magnetic levitation systems; Nonlinear dynamics; Nonlinear systems; Partial differential equations; Stability; Submerging; Theorems
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-015-2342-4

Implementation of immersion and invariance (I&I) theorem becomes increasingly difficult as the degree of freedom increases. This inherent difficulty is mainly driven by the need to solve the partial differential equations in the immersion conditions. For a class of n-dimensional nonlinear systems in strict-feedback form, a novel method for designing asymptotically stabilizing control laws is developed in this work. At each step of the design, by defining a lower-order target system, the required mappings can be transformed into the virtual control inputs and the controlled system is able to exhibit the same responses as the target system. The order of nonlinear systems is reduced step by step by implementing I&I theorem repetitively. Unlike other control methodologies, the proposed algorithm does not require knowledge of Lyapunov functions in principle. In this paper, the design procedure and proof of closed-loop stability are described in detail. The TORA and magnetic levitation system are used to demonstrate the design procedures and controller performance via various simulations.