Piecewise non-linear model predictive control with bounded disturbance

• Published in: Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering Journal of systems and control engineering, 2024-08, Vol.238 (7), p.1321-1336
• Main Authors: Shokrollahi, Ali, Shamaghdari, Saeed
• Format: Article
• Language: English
• Subjects: Control systems; Convex analysis; Convexity; H-infinity control; L2 gain; Linear matrix inequalities; Nonlinear control; Nonlinear systems; Optimization; Predictive control; Robust control; Systems stability
• ISSN: 0959-6518; 2041-3041
• DOI: 10.1177/09596518241227273

This work addresses the problem of robust H ∞ model predictive control for constrained piecewise non-linear systems corrupted by norm-bounded disturbances for the first time. In this approach, the system can have different operating points with different subregions. In each subregion, the system is made up of an affine model disturbed by an additive non-linear term that is locally Lipschitz. The employment of the piecewise non-linear model leads to a non-convex optimization problem, which is far more difficult to solve. It is also much more challenging to develop the H ∞ model predictive control for piecewise non-linear systems. The proposed method introduces a control strategy in the form of a convex optimization problem subject to linear matrix inequality constraints, with the ability to minimize the L2 gain between the disturbance input and the controlled output. The proposed controller guarantees system stability with a prescribed H ∞ disturbance attenuation level under switching between subregions. Simulations on a highly non-linear chemical process are conducted to demonstrate the efficacy of the proposed approach.