Output-Tracking Quantized Explicit Nonlinear Model Predictive Control Using Multiclass Support Vector Machines

• Published in: IEEE transactions on industrial electronics (1982) Vol. 64; no. 5; pp. 4130 - 4138
• Main Authors: Chakrabarty, Ankush, Buzzard, Gregery T., Zak, Stanislaw H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Constraint modelling; Control surfaces; Data points; Explicit nonlinear model predictive control; finite control set; Mixed integer; multicategory learning; Nonlinear control; Nonlinear programming; Nonlinear systems; output tracking; Predictive control; Predictive models; Programming; Scalability; supervised learning; Support vector machines; support vector machines (SVMs); Tracking; Training
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2016.2638401

In applications involving digital control, the set of admissible control actions is finite/quantized. Coupled with state constraints and fast dynamics, explicit model predictive control (EMPC) provides an attractive control formalism. However, the design of data-driven EMPCs with finite admissible control sets is a challenging and relatively unexplored problem. In this paper, a systematic data-driven method is proposed for the design of quantized EMPCs (Q-EMPCs) for time-varying output tracking in nonlinear systems. The design involves: 1) sampling the admissible state space using low-discrepancy sequences to provide scalability to higher dimensional nonlinear systems; 2) at each sampled data point, solving for optimal quantized model predictive control actions and determining feasibility of the intrinsic mixed-integer nonlinear programming problem; and 3) constructing the Q-EMPC control surface using multiclass support vector machines (MC-SVMs). In particular, four widely used MC-SVM algorithms are employed to construct the proposed data-driven Q-EMPC. Extensive testing and comparison among the different MC-SVM algorithms is performed on 2-D and 5-D benchmark examples to demonstrate the effectiveness and scalability of the proposed methodology.