Prescribed-Performance-Aware Hybrid-Gain-Based Robust Controller

Abstract: This paper proposes a prescribed performance function aware hybrid gain finite time sliding mode control framework for a class of nonlinear systems subject to matched disturbances. The hybrid gain structure ensures bounded control effort while retaining finite time convergence, and the incorporation of PPFs enables explicit enforcement of transient performance requirements. Theoretical guarantees are first established for first order systems, characterizing finite time convergence, disturbance rejection, and residual bounds. The approach is then extended to second order dynamics, where a sliding manifold is designed using PPF constraints to facilitate controlled shaping of position and velocity transients. Simulation studies illustrate the proposed design under matched peak control conditions. Comparative results for second-order systems demonstrate that, while a well tuned non-PPF hybrid gain controller achieves competitive tracking performance, the PPF-aware formulation strictly enforces prescribed transient constraints and yields consistent reductions of approximately 9 to 12 percent in integral error and control energy metrics without increasing peak actuation effort.