Model-Free Adaptive Control for Nonlinear Dynamic Systems

Model-free adaptive control (MFAC) has emerged as a transformative paradigm for governing nonlinear dynamic systems without relying on explicit mathematical models. By utilising only measured input and output data, MFAC algorithms dynamically estimate system behaviour through online pseudo-gradient or pseudo-Jacobian constructs and update control laws in real time. This data-driven approach circumvents parameter identification and model uncertainty, offering robust performance under varying operating conditions and external disturbances. Core developments include dynamic linearisation techniques, adaptive dynamic programming frameworks and event-triggered strategies to reduce computational burden and communication overhead. Applications span robotics, automotive powertrains, energy conversion units and autonomous vehicles, where rapid adaptation and fault tolerance are vital. Recent advances have further integrated neural network elements and fuzzy observers to enhance tracking precision and disturbance rejection in multi-input multi-output settings. The global significance of MFAC lies in its capacity to accelerate deployment of advanced control in industrial systems with limited modelling resources, while theoretical underpinnings grounded in Lyapunov stability ensure predictable convergence and safety across diverse environmental conditions.

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Recent studies have demonstrated an event-triggered adaptive dynamic programming scheme for hydraulic servo actuators, in which an online learning controller derives optimal inputs solely from measured I/O data. By introducing an event-based feedback mechanism, the number of control updates is minimised and communication resources are conserved without sacrificing convergence guarantees. Simulation results confirm high accuracy in load-bearing tasks and resilience against model uncertainties.

In autonomous underwater vehicles, a fuzzy-state observer has been combined with a model-free adaptive predictive control algorithm to address uncertain disturbances and time delays. A Takagi–Sugeno fuzzy model estimates state errors, while a predicted pseudo-Jacobian matrix supports trajectory tracking under varying currents. Stability analysis via Lyapunov methods and simulation of realistic AUV scenarios reveal improved robustness and precision compared with conventional predictive schemes.

A data-driven fault-tolerant control framework for general nonlinear systems with output saturation employs a modified observer to approximate sensor faults and an adaptive dynamic programming–based controller to compensate in real time. A triggering rule balances control performance with computational effort, and uniform ultimate boundedness of the closed-loop error is ensured by Lyapunov analysis. Comparative examples illustrate effective fault mitigation and stable operation under severe sensor degradation.

Model-Free Adaptive Control for Nonlinear Dynamic Systems publication trend

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

Technical terms

Model-free adaptive control: A control methodology that adjusts inputs online using only measured input/output data, without requiring a priori mathematical models of the system.

Adaptive dynamic programming: A data-driven optimisation technique that iteratively approximates value functions and control policies to achieve near-optimal regulation of dynamic systems.

Pseudo-Jacobian matrix: An online estimate of the system’s sensitivity to control inputs, constructed from recent I/O samples to guide parameter updates in model-free schemes.

Event-triggered control: A strategy that updates control actions only when a predefined condition is met, reducing unnecessary computations and communication exchanges.

Fuzzy-state observer: A state estimation tool based on fuzzy logic, which captures nonlinearities and uncertainties by blending multiple local linear models.

Lyapunov stability: A theoretical criterion ensuring that system trajectories remain bounded and converge to desired setpoints, used to verify robustness of adaptive and predictive controllers.

References

1. Data-driven control of hydraulic servo actuator: An event-triggered adaptive dynamic programming approach. Mathematical Biosciences and Engineering (2023).
2. Date-Driven Tracking Control via Fuzzy-State Observer for AUV under Uncertain Disturbance and Time-Delay. Journal of Marine Science and Engineering (2023).
3. Data-driven fault-tolerant control for nonlinear systems with output saturation. Chaos Solitons & Fractals (2023).