Nonlinear Model Predictive Control for Electric Bus Operations Based on Generalized Disjunctive Programming Method

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This article investigates the nonlinear model predictive control (NMPC) for electric bus operations (EBOs) under dynamic environments, based on the generalized disjunctive programming (GDP) method. Specifically, we construct discrete-event model to capture the dynamic of bus traffic, passenger load, and current electricity. With the safety constraints, we incorporate algebraic equations, disjunctions, and logical propositions to formulate a nonconvex GDP model, for the nonlinear optimal control problem with both discrete and continuous components. Tailored to the nonlinearity and disjunctions, we design a GDP-based branch and bound (GDPB) algorithm with domain reduction under the model prediction control scheme. The main idea entails branching on constraints regarding disjunctive terms and spatial disjunctions, to convert the complex original problem with discrete and continuous variables as well as nonlinear and nonconvex constraints and cost functions into quadratic programming (QP) subproblems with reduced domains. It can ensure the rapid attainment of exact solutions for embedded applications. Extensive experiments confirm the effectiveness of the proposed control (PC) method. Additionally, the solution algorithm demonstrates desirable computational efficiency, suitable for online implementations.