Adaptive Control Methods for High-Order Nonlinear Systems

Adaptive control of high-order nonlinear systems has emerged as a pivotal discipline in modern control engineering, addressing the challenges posed by dynamics of elevated differential order, strong nonlinearities and parametric uncertainty. Such systems are characterised by multiple integrator chains or complex power-type terms, which render classical linear techniques inadequate. Contemporary adaptive schemes employ recursive design methodologies—most notably backstepping—to construct stabilising controllers and update laws that compensate for unknown functions or time-varying parameters. Neural-network and fuzzy-logic approximators are routinely integrated to estimate unmodelled dynamics, while barrier Lyapunov functions enforce state or output constraints throughout the transient phase. Moreover, finite-time and fixed-time convergence criteria have been introduced to guarantee rapid error attenuation independent of initial conditions. Recent advances also explore event-triggered mechanisms to reduce computational load and communication demands, and prescribed-performance frameworks to ensure predefined tracking accuracy. Collectively, these developments have broadened the applicability of adaptive control to fault-tolerant systems, aerospace vehicles, robotic manipulators and energy networks, underscoring its global significance and practical impact.

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Research from all publishers

Recent studies have advanced barrier Lyapunov function-based fixed-time fault-tolerant controllers for high-order nonlinear plants under asymmetric state constraints, ensuring predefined tracking accuracy and robustness to actuator faults. Parallel work has introduced adaptive fuzzy tracking control laws that leverage fuzzy-logic systems to approximate unknown dynamics and Nussbaum functions to address uncertain control gains, thereby achieving asymptotic reference tracking and semi-global boundedness. Event-triggered stabilisation strategies combining barrier functions and homogeneity theory have also been proposed, delivering fixed-time convergence while precluding output constraint violations and reducing unnecessary control updates.

Adaptive Control Methods for High-Order Nonlinear Systems publication trend

The graph below shows the total number of articles in adaptive control methods for high-order nonlinear systems across all publications each year (not limited to Nature Index journals).

Technical terms

High-order nonlinear system: A dynamical system in which the highest derivative order exceeds one and whose evolution equations include nonlinear functions of states or inputs.

Adaptive control: A control methodology that adjusts controller parameters in real time to accommodate unknown or time-varying system dynamics.

Backstepping: A recursive design technique that systematically constructs stabilising controllers and Lyapunov functions for systems in strict-feedback form.

Barrier Lyapunov function: A specialised Lyapunov function incorporating barrier terms to ensure that state or output constraints are never violated during transient or steady-state operation.

Fixed-time stability: A convergence property guaranteeing that system states reach an equilibrium in a time bound independent of initial conditions.

References

1. Barrier Lyapunov function-based fixed-time FTC for high-order nonlinear systems with predefined tracking accuracy. Nonlinear Dynamics (2022).
2. Neural Network-Based Adaptive Fault-Tolerant Control for a Class of High-Order Strict-Feedback Nonlinear Systems. IEEE Access (2020).
3. Tracking Control of High-Order Nonlinear Systems With Unknown Control Gains and Its Application: An Adaptive Fuzzy Control Method. IEEE Access (2024).
4. Fixed-Time Event-Triggered Stabilization of High-Order Nonlinear Systems With Asymmetric Output Constraints. IEEE Access (2024).