A switching-dependent prescribed performance adaptive control (SPPAC) scheme is proposed for switched nonlinear systems. The approach constructs mode-specific performance bounds and a dedicated error transformation to resolve switching-induced discontinuities. Combined with adaptive backstepping under average dwell-time condition, it guarantees practical finite-time stability with an explicit settling-time upper bound, and is validated via numerical tests including an aero-engine case.
Switched nonlinear systems are widely used in power systems, chemical process control, and aerospace engineering, where complex dynamic behaviors arise from structural changes and variations in operating conditions. Prescribed performance control (PPC) aims to constrain tracking errors within predefined time-varying bounds, ensuring specified convergence rates, overshoot limits, and steady-state accuracy. However, most existing PPC approaches adopt common performance bounds for all subsystems, which may lead to conservative or infeasible control designs when subsystem dynamics differ significantly. Moreover, switching events can disrupt the Lyapunov decrease conditions required for finite-time convergence. Therefore, achieving flexible tracking performance and practical finite-time stability under unknown nonlinear dynamics and subsystem switching remains a significant challenge.
To address these challenges, Feiyue Wu from Dalian University of Technology proposed a switching-dependent prescribed performance adaptive control (SPPAC) scheme for a class of switched nonlinear systems. The main contributions are summarized as follows.
1. Mode-dependent prescribed performance bounds
The study constructs mode-dependent prescribed performance bounds (PPBs) to accommodate the different transient tracking requirements of individual subsystems. The initial performance bounds are selected offline according to the dynamic characteristics and performance requirements of each subsystem. When the active mode changes, the corresponding performance bound switches accordingly, allowing mode-specific transient tracking performance. After a prescribed convergence time, all performance functions reach a common terminal bound, ensuring consistent steady-state tracking requirements.
2. Switching-dependent error transformation
To address discontinuities in the transformed tracking error caused by changes in performance bounds at switching instants, a switching-dependent model transformation is developed. By establishing a continuous mapping between the transformed errors before and after switching, the original constrained switched system is reformulated as an equivalent unconstrained system, facilitating subsequent controller design and stability analysis.
3. Adaptive backstepping control with an average dwell-time condition
Based on the proposed transformation, an adaptive backstepping controller is designed by incorporating radial basis function (RBF) neural networks and adaptive laws under an average dwell-time (ADT) switching condition. Through Lyapunov stability analysis, sufficient conditions are established to guarantee the boundedness of all closed-loop signals, satisfaction of the prescribed tracking constraints, and practical finite-time convergence. Furthermore, an explicit upper bound on the settling time is derived using the Lambert W function.
4. Numerical validation and aero-engine application
The effectiveness of the proposed SPPAC scheme is evaluated through two numerical examples. The first compares common and switching-dependent performance bounds, illustrating violations of the common bounds near switching instants and the tracking behavior under the proposed mode-dependent design. The second applies the method to an aero-engine control system. Simulation results demonstrate that the system output tracks the reference signal while the tracking error remains within the prescribed bounds. The engine states converge to a bounded region within finite time, and the control input remains bounded throughout the simulation.
Conclusion and Outlook
This study presents a switching-dependent prescribed performance adaptive control framework that accommodates mode-specific transient tracking requirements while ensuring practical finite-time stability. By integrating switching-dependent performance bounds, error transformation, adaptive backstepping, and ADT-based stability analysis, the proposed method provides a flexible approach to balancing tracking performance and convergence requirements in switched nonlinear systems. Future research may further consider input saturation, actuator faults, and more complex multimode interactions to extend the framework toward practical engineering applications.
Wu F. Switching-dependent prescribed performance adaptive control for switched nonlinear systems with finite-time stability. Adv. Equip. 2026(2):0007, https://doi.org/10.55092/ae20260007.
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Switching-dependent prescribed performance adaptive control for switched nonlinear systems with finite-time stability
26-Oct-2026