Efficient Constrained Algebraic Model Predictive Control for Aerospace Applications

Abstract

The major drawback of MPC is the computational burden associated with the large number of parameters it can be optimised over. One method that improves the computational efficiency of the control algorithm is Algebraic Model Predictive Control (AMPC). In this method the optimal control problem can be formulated with a non-uniform distribution of points in the prediction horizon. The most efficient case is one where the prediction horizon is reduced down to a single prediction point, thus removing any additional and redundant calculations. The drawback of this prediction point reduction is loss of system information and hence degraded performance while the system is constrained. This thesis extends the AMPC framework, improving the constraint handling performance. This is achieved by introducing additional points across the time horizon at which the constraints are checked. The computational efficiency of the original method is retained by recognising that the critical constraint is the peak location, the time along the prediction horizon at which the peak of the response occurs, with a method developed for calculating its location. By constraining this peak time location, an equivalent constrained response can be achieved as though every point across the horizon length was considered, however, at a significantly reduced computational cost. This thesis also develops a method of expressing the optimal AMPC law explicitly. This further improves the computational efficiency of the algorithm. By combining the improved constraint method with the explicit control law, stability properties of the constrained, closed loop system can be guaranteed a priori. Analysis of the algorithms and the computational cost is performed on several different numerical simulations including an aircraft model, demonstrating the capabilities of the algorithm being used in aerospace applications.