Efficient algorithms for online tracking of set points in robust model predictive control

• Published in: International journal of systems science Vol. 48; no. 8; pp. 1635 - 1645
• Main Authors: Razi, M., Haeri, M.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 11.06.2017; Taylor & Francis Ltd
• Subjects: Algorithms; Computational efficiency; Control stability; Controllers; Dynamical systems; Feasibility; Linear matrix inequalities; linear matrix inequality; Mathematical analysis; Mathematical models; Matrix methods; Nonlinear dynamics; optimisation; Predictive control; Robust control; robust model predictive control; Robustness (mathematics); Stability; Switching; Tracking
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207721.2017.1280551

This paper presents some computationally efficient algorithms for online tracking of set points in robust model predictive control context subject to state and input constraints. The nonlinear systems are represented by a linear model along with an additive nonlinear term which is locally Lipschitz. As an unstructured uncertainty, this term is replaced in the robust stability constraint by its Lipschitz coefficient. A scheduled control technique is employed to transfer the system to desired set points, given online, by designing local robust model predictive controllers. This scheme includes estimating the regions of feasibility and stability of the related equilibriums and online switching among the local controllers. The proposed optimisation problems for calculating the regions of feasibility and stability are defined as linear matrix inequalities that can be solved in polynomial time. The effectiveness of the proposed algorithms is illustrated by an example.