Sequential Quadratic Programming Algorithm for Real-Time Mixed-Integer Nonlinear MPC

Nonlinear model predictive control (NMPC) has grown mature and algorithmic techniques exist, e.g., based on sequential quadratic programming (SQP) methods, to handle relatively complex constrained control systems. In addition, model predictive control for hybrid dynamical systems, including both continuous and discrete decision variables, can be implemented efficiently based on state of the art mixed-integer quadratic programming (MIQP) algorithms. This paper proposes a novel mixed-integer SQP (MISQP) optimization algorithm as a heuristic search technique to find feasible, but possibly suboptimal, solutions for real-time implementations of mixed-integer NMPC (MINMPC). Two variants of the MISQP algorithm are described and motivated. Based on a preliminary software implementation, the real-time MISQP performance is illustrated for closed-loop MINMPC simulations on a nontrivial vehicle control case study, featuring worst-case computation times below 30 milliseconds.