Fixed-time quasi-passivity of switched nonlinear systems and its application to adaptive tracking control

This paper develops a fixed-time quasi-passivity theory for switched nonlinear systems through a multiple storage functions approach and applies this theory to address the adaptive tracking control problem. First, fixed-time control is introduced to define fixed-time quasi-passivity, which permits the storage functions to increase at each switching time and requires only that each subsystem exhibits the fixed-time quasi-passivity property during its active time interval. Unlike passive systems, quasi-passive systems can generate energy independently. Second, a more general switching law is designed using state information to achieve fixed-time quasi-passivity, even if none of the subsystems are inherently fixed-time quasi-passive. This switching law operates based on continuous functions rather than storage functions, which provides us with more design freedom. Third, a novel multiple storage function is introduced to obtain practical fixed-time output feedback stabilization for switched nonlinear systems. It represents a generalization of the existing fixed-time stability criterion. Finally, a new switching adaptive backstepping technique is developed to address the fixed-time output tracking issue of uncertain switched strict-feedback systems. This method combines fixed-time quasi-passivation with fuzzy adaptive backstepping, thereby eliminating the restriction that the relative order must be one. The efficiency of the proposed control approach is demonstrated through simulation examples.