Model Predictive Control in Nonlinear Systems

Model predictive control (MPC) has emerged as a leading methodology for steering nonlinear processes by solving a constrained optimisation problem at each sampling instant. By forecasting future states over a finite prediction horizon and enforcing input and state constraints, MPC offers a systematic means to handle actuator limits, safety requirements and performance objectives. Nonlinear MPC variants approximate complex dynamics through successive linearisation, explicit polynomial models or data-driven surrogates, while ensuring recursive feasibility and closed-loop stability via terminal constraints or robustifying elements. Applications span chemical reactors, renewable-energy integration, autonomous vehicles and aerospace systems, where fast real-time computation and reliable handling of uncertainties are paramount. Recent advances focus on decentralised architectures, resilience to communication disruptions and reduction of computational and communication load through adaptive sampling strategies.

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Research from all publishers

Recent work has advanced the field in three key directions. First, distributed robust MPC frameworks have been introduced for cyber-physical and multi-agent systems subject to denial-of-service attacks and bounded disturbances. These schemes embed novel robustness constraints and sequence-transmission strategies to preserve stability and recursive feasibility when network links fail. Second, sensitivity-based self-triggered control strategies for general nonlinear systems maximise sampling intervals by analysing gradients of the MPC cost function. A computationally efficient Taylor approximation of future cost enables explicit bounds on inter-sampling times, reducing processor load without compromising closed-loop stability. Third, event-driven MPC architectures employing error-gradient and accumulation thresholds have been proposed for perturbed nonlinear plants with input and state constraints. These controllers guarantee input-to-state practical stability and exclude Zeno behaviour while significantly decreasing communication and computation through state-dependent triggering.

Model Predictive Control in Nonlinear Systems publication trend

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

Technical terms

Model Predictive Control: A control strategy that solves an optimisation problem online at each sampling instant to compute future control actions over a prediction horizon while respecting constraints.

Receding Horizon: A moving time window over which future system behaviour is predicted and optimised, updated at each control interval.

Nonlinear System: A dynamical system whose behaviour cannot be represented by a linear function, often exhibiting complex phenomena such as saturation and bifurcation.

Self-Triggered Control: A strategy that computes the next sampling instant based on system state and performance metrics, reducing unnecessary controller updates.

Event-Triggered Control: A scheme that initiates control updates when predefined state or error thresholds are crossed, rather than at fixed time intervals.

Robustness Constraint: A design requirement within the optimisation ensuring performance under model uncertainties and external disturbances.

References

1. Robust and Resilient Distributed MPC for Cyber-Physical Systems Against DoS Attacks. IEEE Transactions on Industrial Cyber-Physical Systems (2023).
2. A Sensitivity-Based Approach to Self-Triggered Nonlinear Model Predictive Control. IEEE Access (2024).
3. An error gradient and accumulation‐type event‐driven model predictive control with relative thresholds for perturbed nonlinear systems. IET Control Theory and Applications (2022).