Evaluation of suboptimal real-time control results for model predictive control using improved initial conditions

In the model predictive control (MPC) framework a controller is computed using a finite horizon optimal control cost. When linear constraints are imposed on the system with a quadratic cost function, then the MPC problem can be reformulated as a constrained quadratic programming (QP) problem. In this paper active set methods are used in order to solve the QP problem associated with MPC, and it is shown that it is possible to use information from the previous sample interval in order to provide improved initial conditions for the QP problem which is applied to the subsequent sample interval. Simulations show that when real-time considerations force the used of suboptimal intermediate control values, then improved initial conditions can allow for control values which are closer to the true optimal solution than obtained when using standard initial conditions. These ideas can allow for the implementation of MPC schemes on a greater number of real industrial applications, where standard MPC control cannot be applied due to the excessive CPU time requirements