Sampled-Data Control Strategies for Nonlinear Dynamic Systems

Sampled‐data control bridges continuous‐time dynamics and digital implementation by applying control inputs at discrete instants while monitoring plant outputs between updates. In nonlinear dynamic systems, this approach must address intersample behaviour, time‐varying sampling intervals and the intrinsic coupling between sampling and system nonlinearity. Two principal design paradigms coexist: emulation, which discretises a continuous‐time controller, and direct design, which derives control laws in the sampled‐data setting. Recent advances encompass event‐based sampling, quantization‐aware schemes and robustification against disturbances. By integrating modern Lyapunov‐based methods, including nonsmooth Control Lyapunov Functions and observer‐based structures, researchers have achieved practical stability, performance guarantees and cost regulation. These developments underpin applications from power converters to autonomous vehicles, highlighting the global importance of sampled‐data strategies in real‐world digital control.

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One recent study introduces an extension of Sontag’s universal formula to design dynamic output‐feedback stabilisers for control‐affine nonlinear time‐delay systems. By defining the Steepest Descent Error Dynamics, the authors derive a sampled‐data controller that guarantees semiglobal practical stability under fast or time‐varying sampling and explicitly accounts for intersample behaviour.

Another work examines the robustness of popular sample‐and‐hold stabilisation schemes against disturbances and measurement noise. Through a combination of nonsmooth Control Lyapunov Function techniques and extensive case studies such as robotic parking, new propositions clarify the resilience of methods including Dini aiming, inf‐convolution stabilisation and optimisation‐based control within digital implementations.

In an automotive context, a quantized sampled‐data approach to ground‐vehicle attitude control employs event‐based sampling to preserve practical stability when replacing continuous‐time trajectories with digital control signals. Conditions for maintaining tracking performance despite quantization and sampling constraints are derived and validated via realistic simulations.

Sampled-Data Control Strategies for Nonlinear Dynamic Systems publication trend

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

Technical terms

Sampled‐data control: A control methodology in which inputs are updated at discrete time instants while continuous‐time dynamics evolve between updates.

Control Lyapunov Function (CLF): A scalar function that decreases along trajectories under a suitable feedback law, certifying stability.

Sample‐and‐hold mechanism: The process by which a control input is held constant between sampling instants.

Event‐based sampling: A scheme that triggers sampling or actuation only when certain state‐dependent events occur, reducing communication load.

Quantization: The finite‐resolution representation of continuous signals or control inputs in digital systems.

Control‐affine system: A nonlinear model whose dynamics are linear in the control input but possibly nonlinear in the state.

Input‐to‐State Stability (ISS): A property ensuring bounded inputs produce bounded state responses and asymptotic regulation under vanishing inputs.

Sontag’s universal formula: A constructive expression for a stabilising feedback derived from a Control Lyapunov Function, applicable in nonlinear settings.

References

1. On Sontag’s formula for the sampled-data observer-based stabilization of nonlinear time-delay systems. Automatica (2023).
2. Some Remarks on Robustness of Sample-and-Hold Stabilization. IEEE Control Systems Letters (2024).
3. Quantized Sampled-Data Attitude Control of Ground Vehicles: An Event-Based Approach. IEEE Control Systems Letters (2022).