An accelerated dual gradient-projection algorithm for linear model predictive control

This paper proposes a dual fast gradient-projection method for solving quadratic programming problems that arise in linear model predictive control with general polyhedral constraints on inputs and states. The proposed algorithm is quite suitable for embedded control applications in that: (1) it is extremely simple and easy to code; (2) the number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution can be estimated quite tightly; (3) the computational cost per iteration increases only linearly with the prediction horizon; and (4) the algorithm is also applicable to linear time-varying (LTV) model predictive control problems, with an extra on-line computational effort that is still linear with the prediction horizon.