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Hybrid model predictive control (MPC) with both continuous and discretevariables is widely applicable to robotic control tasks, especially thoseinvolving contact with the environment. Due to the combinatorial complexity,the solving speed of hybrid MPC can be insufficient for real-time applications.In this paper, we proposed a hybrid MPC solver based on Generalized BendersDecomposition (GBD) with continual learning. The algorithm accumulates cuttingplanes from the invariant dual space of the subproblems. After a shortcold-start phase, the accumulated cuts provide warm-starts for the new probleminstances to increase the solving speed. Despite the randomly changingenvironment that the control is unprepared for, the solving speed maintains. Weverified our solver on controlling a cart-pole system with randomly moving softcontact walls and show that the solving speed is 2-3 times faster than theoff-the-shelf solver Gurobi.

Generalized Benders Decomposition with Continual Learning for Hybrid Model Predictive Control in Dynamic Environment