A New Hot-start Interior-point Method for Model Predictive Control

A. Shahzad and P. J. Goulart

@inproceedings{SG:2011,
  author = {A. Shahzad and P. J. Goulart},
  title = {A New Hot-start Interior-point Method for Model Predictive Control},
  booktitle = {IFAC World Congress},
  year = {2011},
  url = {http://dx.doi.org/10.3182/20110828-6-IT-1002.02817},
  doi = {10.3182/20110828-6-IT-1002.02817}
}

In typical model predictive control applications, a finite-horizon optimal control problem, in the form of a quadratic program (QP), must be solved at each sampling instant with a known initial state. We present a new hot-start strategy to solve such QPs using interior-point methods, where the first interior-point iterate is constructed from a backward time-shifting of the solution to the QP at the previous time-step. There are two difficulties with such a strategy. First, a naive backward shifting of a previous solution can yield an initial iterate on the boundary of the primal-dual feasible region, leading to blocking of the search direction and consequently to very small and inefficient interior-point steps. Second, a backward shifted solution does not provide a set of strictly feasible terminal KKT conditions. In order to address both of these issues, we propose a modification to the basic backward- shifting method which provides simultaneously an initial iterate that satisfies strict feasibility conditions and a strictly feasible set of primal and dual terminal decision variables. Numerical results indicate that the proposed technique yields convergence in fewer iterations than a cold- start interior-point method.