New adaptive control scheme keeps switched nonlinear systems on prescribed performance bounds

Engineers at Dalian University of Technology have proposed a new control framework that lets switched nonlinear systems track reference signals within user-defined performance bounds, even as the system jumps between different operating modes. The scheme, called switching-dependent prescribed performance adaptive control (SPPAC), is described in a peer-reviewed paper published in Advanced Equipment, and it guarantees practical finite-time stability with an explicit upper bound on the settling time.

Switched nonlinear systems appear throughout power systems, chemical process control and aerospace engineering, where structural changes and varying operating conditions generate complex dynamic behavior. Prescribed performance control (PPC) constrains tracking errors within predefined time-varying bounds so that convergence rates, overshoot limits and steady-state accuracy are specified in advance. The difficulty is that most existing PPC designs impose a single set of common performance bounds on every subsystem. When subsystem dynamics differ significantly, those shared bounds can be conservative or outright infeasible, and switching events can disrupt the Lyapunov decrease conditions needed for finite-time convergence.

The new framework addresses this with mode-dependent prescribed performance bounds. Each subsystem receives its own initial performance bounds, selected offline according to that subsystem’s dynamics and performance requirements. When the active mode changes, the bound switches with it, allowing mode-specific transient tracking performance. After a prescribed convergence time, all performance functions reach a common terminal bound, so steady-state tracking requirements remain consistent across the whole system.

A second innovation handles the discontinuities that arise at switching instants, when the transformed tracking error would otherwise jump because the performance bound changes. The researchers developed a switching-dependent model transformation that establishes a continuous mapping between the transformed errors before and after a switch. This reformulates the original constrained switched system as an equivalent unconstrained one, which simplifies both controller design and stability analysis.

On top of that transformation, the design builds an adaptive backstepping controller that incorporates radial basis function neural networks and adaptive laws under an average dwell-time switching condition. Lyapunov stability analysis yields sufficient conditions guaranteeing that all closed-loop signals remain bounded, that the prescribed tracking constraints are satisfied, and that convergence is practical finite-time. Notably, an explicit upper bound on the settling time is derived using the Lambert W function, giving designers a concrete timing guarantee rather than a purely qualitative one.

The scheme was evaluated through two numerical examples. The first compared common and switching-dependent performance bounds, illustrating violations of the common bounds near switching instants and the tracking behavior achieved under the proposed mode-dependent design. The second applied the method to an aero-engine control system, where simulation results showed the system output tracking the reference signal while the tracking error stayed within the prescribed bounds. The engine states converged to a bounded region within finite time, and the control input remained bounded throughout the simulation.

The study is a computational simulation and modeling effort, and its validation is limited to numerical examples including the aero-engine case; the author notes that future work should consider input saturation, actuator faults and more complex multimode interactions to extend the framework toward practical engineering applications. Within that scope, the framework offers a flexible way to balance tracking performance against convergence requirements in switched nonlinear systems, combining switching-dependent performance bounds, error transformation, adaptive backstepping and average dwell-time-based stability analysis in a single design.

Subject of Research: Adaptive control design for switched nonlinear systems with prescribed performance and finite-time stability

Article Title: Switching-dependent prescribed performance adaptive control for switched nonlinear systems with finite-time stability

Article References: Switching-dependent prescribed performance adaptive control for switched nonlinear systems with finite-time stability. Original publication (Bibliographic details unavailable.)

Image Credits: AI Generated

DOI: Not provided

Keywords: switched nonlinear systems, prescribed performance control, adaptive backstepping, average dwell time, finite-time stability, error transformation, radial basis function neural networks, aero-engine control, Lyapunov stability, settling time bound, Switching-dependent, prescribed