Offline model predictive control based on weighted projection over polytopes. (English) Zbl 1342.93057

de Almeida, Fabio Andrade

J. Appl. Math. 2015, Article ID 741348, 14 p. (2015).

Summary: This work presents a novel offline model predictive control technique for tracking of constrained systems. The quadratic programming problem, commonly found in constrained control methods, is replaced by sequential offline set projections based on priority given to the decision variables. If a preference is established in terms of which decision variables are more desirable, the optimization problem can be solved by sequentially choosing the most important variables and performing a membership test with the projection of the constraint closed set over the related dimensions. Thus, real-time optimization is replaced by offline projection operations and online one-dimensional membership tests. This concept of decision variable prioritization is then applied to a form of model predictive control: feasible target tracking. Three quadratic programming problems are replaced by the proposed method. In the first problem, attainable steady-state demands are computed based on the performance of the plant. The reachable target command is then filtered in terms of dynamic admissibility, creating feasible inputs to the plant. Finally, the control is computed considering the current state and disturbance vectors along with the feasible and attainable command. Simulations of the method executing a path-following task are presented, demonstrating its benefits with negligible online computational burden.

MSC:

93B40	Computational methods in systems theory (MSC2010)
90C20	Quadratic programming

Keywords:

model predictive control; weighted projection over polytopes; quadratic programming; decision variable prioritization

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