A Preset-Trajectory-Based Singularity-Free Preassigned Performance Control Approach

The preassigned performance control (PPC) methods have attracted considerable attention in recent years; however, most of the mainstream PPC methods utilize barrier functions, and thus, may suffer from the singularity problem of the control law under some unexpected conditions, such as sensor faults. In this article, a new robust PPC method without using barrier functions is proposed for second-order vector nonlinear systems, which can completely avoid the singularity problem of the control law and be considered as a complement to these mainstream PPC methods. The control design consists of three steps: first, a performance function is constructed to form the performance envelope according to the performance requirements; second, a preset trajectory (PT) is generated within the performance envelope; third, a robust sliding mode control law is designed to make the actual tracking error evolve in a certain tubular area that contains the PT and is strictly within the performance envelope. Furthermore, the obtained result is extended to the case of adaptive PPC. The effectiveness and the advantages of the proposed robust PPC method are illustrated by simulation results.