Dynamic-Error-Interval-Based Event-Triggered Adaptive Saturated Tracking Control of Uncertain Nonlinear Systems

This paper investigates the adaptive tracking control of uncertain nonlinear systems with actuator saturation. First, a dynamic interval depending on the saturation bounds is constructed to constrain the tracking error, thereby maintaining satisfactory control performance. More importantly, it is proven that the interval is a subset of the existing one. This means that the result is less conservative. Further, a novel interval transformation technique is proposed. This technique converts the constrained error interval into an unconstrained function, which is then employed in the virtual controller formulation. Compared with the previous results, the unconstrained nature of the function enhances the design flexibility of the controller. To suppress the chattering caused by direct differentiation of virtual control signals (VCSs), a class of improved command filters is designed to filter the VCSs and replace their repeated derivatives. Significantly, the filters are designed with continuous hyperbolic tangent functions instead of the traditional discontinuous jump sign functions, further mitigating chattering. By introducing the auxiliary systems, the actuator saturation output is transformed into unconstrained input and output. Subsequently, a novel event-triggered adaptive control law is constructed based on the above components, thereby accomplishing the desired control objectives. We also prove that the proposed event-triggered mechanism leads to a smaller number of triggered events in comparison with existing results. An example is provided to demonstrate the effectiveness of the approach.