Dynamic surface control approach to adaptive robust control of nonlinear systems in semi-strict feedback form

This paper consider the adaptive robust control of a class of single-input-single-output (SISO) nonlinear systems in semi-strict feedback form, where nonlinearities can exist in the input channel of each subsystem. To overcome the problem of ``explosion of terms", the recently developed dynamic surface control technique is generalized to the nonlinear systems under study. The design procedure is performed in a step by step manner. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract modelling errors is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptions are introduced to reduce the ultimate error bound. Finally, simulational examples are included to verify the results of theoretical analysis. DYNAMIC SURFACE CONTROL APPROACH TO ADAPTIVE ROBUST CONTROL OF NONLINEAR SYSTEMS IN SEMI-STRICT FEEDBACK FORM Zi-Jiang Yang ∗ Toshimasa Nagai ∗ Shunshoku Kanae ∗ Kiyoshi Wada ∗ ∗ Department of Electrical and Electronic Systems Engineering, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan TEL: (+81)92-642-3904, FAX: (+81)92-642-3939 E-mail: [email protected] Abstract: This paper consider the adaptive robust control of a class of singleinput-single-output (SISO) nonlinear systems in semi-strict feedback form, where nonlinearities can exist in the input channel of each subsystem. To overcome the problem of “explosion of terms”, the recently developed dynamic surface control technique is generalized to the nonlinear systems under study. At each step of design, a feedback controller strengthened by nonlinear damping terms to counteract modelling errors is designed to guarantee input-to-state practical stability of the corresponding subsystem, and then parameter adaptions are introduced to reduce the ultimate error bound. Finally, simulational examples are included to verify the results of theoretical analysis. Copyright c ©2005 IFAC