Model Predictive Control for Uncertain Dynamic Systems

Model Predictive Control (MPC) is a versatile optimisation-based methodology that computes control actions by solving a finite-horizon optimisation problem at each sampling instant, using an explicit model of the system dynamics to forecast future behaviour. When applied to uncertain dynamic systems—where parameters, external disturbances or modelling errors may compromise performance—MPC frameworks incorporate robust or stochastic formulations to ensure stability, constraint satisfaction and performance guarantees in the face of uncertainty. Key strategies include tube-based approaches that enclose all possible state trajectories within precomputed invariant tubes, linear parameter-varying embeddings that cast nonlinear dynamics into parameter-dependent linear forms, and fuzzy or interval-type methods that represent uncertainty through membership functions or bounded sets. Recent advances have also explored machine-learning surrogates to alleviate computational burden while preserving predictive accuracy. Such developments have broadened the global impact of MPC, with practical applications spanning automotive cruise control, energy-efficient building climate management, chemical process optimisation and autonomous aerial vehicles. By balancing real-time tractability with rigorous treatment of uncertainty, modern MPC continues to bridge theoretical rigour and industrial utility in complex, safety-critical environments.

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One contemporary advance reformulates nonlinear systems within a linear parameter-varying (LPV) framework and employs a time-varying tube-based MPC. By embedding nonlinearity into an LPV model and constructing convex invariant sets around predicted trajectories, this method achieves recursive feasibility and stability without requiring repeated linearisation, while outer approximations based on interval analysis keep computational complexity manageable.

Another line of inquiry addresses large-scale interconnected systems subject to time-varying delays and persistent disturbances by integrating interval type-2 fuzzy Takagi–Sugeno models into a hierarchical MPC architecture. The system is decomposed into subsystems represented by fuzzy rules, and robust positive invariance is enforced using linear matrix inequalities. A multi-level optimisation ensures both global stability and reduced online burden, demonstrating effectiveness on representative large-scale processes.

Recent work in autonomous driving has demonstrated how deep neural networks (DNNs) can be trained on closed-loop data from a nonlinear MPC to serve as high-fidelity surrogates. This data-driven controller replicates the performance characteristics of the original MPC while drastically lowering the computation time per control update. Experimental evaluations on an instrumented scale-car platform validate that the DNN-based controller maintains tracking accuracy and robustness to disturbances, paving the way for real-time deployment in resource-constrained vehicle-automation systems.

Model Predictive Control for Uncertain Dynamic Systems publication trend

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

Technical terms

Model Predictive Control (MPC): An optimisation-based control strategy that solves a finite-horizon prediction problem at each time step to determine control inputs while respecting constraints.

Robustness: The capacity of a control system to maintain stability and performance in the presence of modelling uncertainties and external disturbances.

Linear Parameter-Varying (LPV) system: A dynamic system whose linear state-space matrices depend on measurable time-varying parameters, enabling tractable handling of nonlinearity.

Tube-based MPC: A robust MPC technique that confines all possible trajectories under uncertainty within precomputed invariant tubes, ensuring constraint adherence.

Takagi–Sugeno fuzzy model: A representation of nonlinear dynamics through a weighted aggregation of linear subsystem models governed by fuzzy membership functions.

References

1. Stabilizing non‐linear model predictive control using linear parameter‐varying embeddings and tubes. IET Control Theory and Applications (2021).
2. Decentralized robust interval type-2 fuzzy model predictive control for Takagi–Sugeno large-scale systems. Automatika (2021).
3. Performance Analysis of Deep Neural Network Controller for Autonomous Driving Learning from a Nonlinear Model Predictive Control Method. Electronics (2021).