Speedup for the quadratic programming problem and other issues in model predictive control.

摘要

Model predictive control (MPC) is based on optimal cost minimization over a finite-horizon window. When considering discrete LTI systems, with a quadratic performance cost, over a finite horizon, with linear constraints, the resulting MPC cost minimization can be converted into a quadratic programming (QP) problem. Solving this constrained QP problem forms the basis for MPC control. This computation is computationally intensive, and for systems with fast dynamics, it is often not possible to compute an optimal constrained solution in real-time.; Three contributions which focus on the QP problem are made; a new active set method is proposed, the concept of premature termination is introduced and a supervisory algorithm is proposed. Two contributions to the formulation of the MPC controller are also made: a framework which allows for natural step disturbance rejection is presented, and a modified performance index, which allows for optimal transient shaping of the closed-loop response, is proposed.; The proposed active set method uses a vastly different approach from existing methods in that the intermediate solutions of the algorithm do not enforce all constraints, leading to a "non-feasible active set method". Experimental results show that the proposed algorithm can converge faster than existing algorithms by as much as 26 times.; Often, the proposed algorithm is still too slow to be run in real-time. The concept of "premature termination", where an algorithm is stopped after a maximum fixed number of iterations, is therefore studied. In this case, no guarantee can be made about the quality of the resulting solution. In particular, a supervisory algorithm which provides guaranteed bounds on the MPC horizon cost while maintaining real-time computation is introduced.; In solving the above MPC problem, it is shown that the plant's equations can be formulated to provide a framework for step tracking and disturbance rejection where no knowledge of the structure or magnitude of disturbances is needed. The output feedback problem is similarly addressed. Finally, a modified performance index is applied to the MPC problem; simulation results show that in conjunction with MPC, the new performance index achieves excellent transient response characteristics compared to the "standard" performance index.