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Guaranteed bounds on the performance cost of a fast real-time suboptimal constrained MPC controller

A fundamental limitation on the implementation of constrained model predictive control (MPC) is the excessive computational time required to evaluate the constrained controls at each sample interval. Prior results show that premature termination of algorithms which solve the quadratic programming (QP) subproblem associated with the computation of the MPC controller at each sampling interval, can be used to decrease the necessary CPU time, with favorable results, but there is no guarantee on the performance of such ad hoc methods. In this paper, a new supervisory algorithm is introduced in order to guarantee bounds on the performance of any non-feasible algorithm, which on solving the QP subproblem is terminated before convergence has occurred. This supervisory algorithm allows for real-time control of a large class of systems using a suboptimal constrained MPC controller with guaranteed bounds on its performance. An example is included to illustrate how this method performs under the limitations of real-time control.