Immersion‐ and invariance‐based adaptive stabilization of switched nonlinear systems |
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| Authors: | Zhi‐E Lou Jun Zhao |
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| Affiliation: | 1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China;2. College of Information Science and Engineering, Northeastern University, Shenyang, China |
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| Abstract: | This paper presents a novel framework to asymptotically adaptively stabilize a class of switched nonlinear systems with constant linearly parameterized uncertainty. By exploiting the generalized multiple Lyapunov functions method and the recently developed immersion and invariance (I&I) technique, which does not invoke certainty equivalence, we design the error estimator, continuous state feedback controllers for subsystems, and a switching law to ensure boundedness of all closed‐loop signals and global asymptotical regulation of the states, where the solvability of the I&I adaptive stabilization problem for individual subsystems is not required. Then, along with the backstepping method, the proposed design technique is further applied to a class of switched nonlinear systems in strict‐feedback form with an unknown constant parameter so that the I&I adaptive stabilization controllers for the system is developed. Finally, simulation results are also provided to demonstrate the effectiveness of the proposed design method. |
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| Keywords: | adaptive stabilization generalized multiple Lyapunov functions (GMLFs) immersion and invariance (I&I) switched nonlinear systems |
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