This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain...This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.展开更多
This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, th...This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous （nonsmooth） output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.展开更多
基金the National Natural Science Foundation of China (Grant No.60674036)the Science and Technique Development Plan of Shandong Province (Grant No.2004GG4204014)+2 种基金the Program for New Century Excellent Talents in University of China (Grant No.NCET-07-0513)the Excellent Young and Middle-Aged Scientist Award Grant of Shandong Province of China (Grant No.2007BS01010)the Key Science and Technique Foundation of Ministry of Education (Grant No.108079)
文摘This paper considers the problem of global stabilization by output feedback for a class of nonlinear systems with uncertain control coefficients and with unmeasured states dependent growth. Mainly due to the uncertain control coefficients, the problem has remained unsolved and its major difficulty stems from the inapplicability of the commonly used high-gain like observer. By introducing an appropriate state transformation and a thoroughly novel observer based on high-gain K-filters, the backstepping design approach is successfully proposed to the output-feedback controller for this class of systems. It is shown that the global asymptotic stability of the closed-loop system can be guaranteed by the appropriate choice of the control parameters.
基金supported by the National Natural Science Foundations of China (Nos. 60974003, 61143011, 61273084, 61233014)the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China (No. JQ200919)the Independent Innovation Foundation of Shandong University (No. 2012JC014)
文摘This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous （nonsmooth） output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.
