Adaptive Almost Passivity and Boundedness for Uncertain Switched Nonlinear Systems

This article proposes an almost passivity concept to describe the practical passivity property of switched nonlinear systems, whose subsystems are only passive outside a ball on their active time intervals. Based on this almost passivity concept, adaptive almost passification and boundedness property of a class of switched nonlinearly parameterized systems are studied. First, adaptive almost passification is achieved by the design of adaptive controllers and a switching law dependent on state for the systems whose subsystems have the relative degree one, even if each subsystem is not adaptive feedback almost passive. Second, for the system with any relative degree, the constructive design methods of adaptive controllers and switching law dependent on state are provided to achieve almost passivity by recursive feedback almost passification technique. Third, the ultimate boundedness of adaptive feedback almost passive system is proved using multiple storage functions method under the restricted condition on the energy changing of inactive subsystems. Finally, a continuous stirred tank reactor system is taken as an example to illustrate the effectiveness of the established theory.