Quantized Control Strategies for Nonlinear Systems

Quantized control strategies address the challenge of implementing feedback laws when signals must be represented with a finite number of bits or discrete levels. In nonlinear systems, quantization arises in digital networks, embedded controllers and sensor limitations, and it can introduce significant distortions or limit cycles if not properly managed. Contemporary approaches combine uniform or dynamic quantizers with adaptive mechanisms, event-triggering schemes and barrier or Lyapunov-based methods to ensure stability and performance despite coarse signal resolution. Finite-time convergence, robustness to disturbances and actuator faults, and handling of input saturation are central objectives. Neural approximators, fuzzy logic systems and backstepping designs are often employed to compensate for unknown dynamics and unmodelled nonlinearities. Applications range from aerial vehicles and robotic manipulators to power electronics and large-scale networked systems, where reduced communication load and guaranteed safety margins are critical. The global significance of quantized control lies in enabling high-performance, resource-constrained automation across industrial, aerospace and energy domains.

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Recent work has advanced finite‐time adaptive control for stochastic nonlinear systems subject to input quantization and actuator faults. By integrating fuzzy logic approximation with backstepping and Lyapunov techniques, controllers achieve rapid convergence despite quantisation errors and unknown faults, maintaining boundedness of all closed-loop signals in simulation studies.

In quadrotor trajectory tracking, a novel finite-time adaptive neural controller employs barrier Lyapunov functions and filter compensation to respect state constraints and mitigate input quantisation effects. A smoothing intermediate function further reduces chattering, and real-world tests confirm precise attitude regulation under discretised control inputs.

For passive nonlinear plants with discrete control sets, a nearest-neighbour static feedback mapping has been proposed that ensures practical stabilisation. The method selects m + 1 discrete inputs to span the equilibrium’s convex hull and provides a constructive algorithm for input design, offering a low-complexity alternative to continuous quantisers.

Quantized Control Strategies for Nonlinear Systems publication trend

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

Technical terms

Quantization: The mapping of continuous signals into a finite set of discrete values, often leading to information loss.

Nonlinear system: A dynamic system whose response cannot be described by a linear superposition of inputs.

Lyapunov stability: A criterion ensuring that small perturbations in state lead to bounded deviations from equilibrium.

Finite-time stability: The property that system states converge to a target set within a predetermined finite interval.

Event-triggered control: A strategy that updates control actions only when a specified state-dependent condition is met, reducing communication and computation load.

References

1. Finite‐Time Adaptive Fuzzy Control for Stochastic Nonlinear Systems with Input Quantization and Actuator Faults. Journal of Mathematics (2024).
2. Nearest neighbor control for practical stabilization of passive nonlinear systems. Automatica (2022).
3. Finite-Time Adaptive Quantized Control for Quadrotor Aerial Vehicle with Full States Constraints and Validation on QDrone Experimental Platform. Drones (2024).