Application of nonlinear model predictive control (NMPC) to problems with
hybrid dynamical systems, disjoint constraints, or discrete controls often
results in mixed-integer formulations with both continuous and discrete
decision variables. However, solving mixed-integer nonlinear programming
problems (MINLP) in real-time is challenging, which can be a limiting factor in
many applications. To address the computational complexity of solving mixed
integer nonlinear model predictive control problem in real-time, this paper
proposes an approximate mixed integer NMPC formulation based on value function
approximation. Leveraging Bellman's principle of optimality, the key idea here
is to divide the prediction horizon into two parts, where the optimal value
function of the latter part of the prediction horizon is approximated offline
using expert demonstrations. Doing so allows us to solve the MINMPC problem
with a considerably shorter prediction horizon online, thereby reducing the
online computation cost. The paper uses an inverted pendulum example with
discrete controls to illustrate this approach