Optimal Prioritized Infeasibility Handling in Model Predictive Control: Parametric Preemptive Multiobjective Linear Programming Approach

Linear MPC with optimal prioritized infeasibility handling: application, computational issues and stability

“…In (Vada et al 2001), an algorithm which solves the OWDP is presented. In order to give an intuitive understanding of this algorithm, we give in the following an outline of the main ideas behind the algorithm.…”

“…Recall that the problem stated in the OWDP is to design c in (8) (or, more preciselyc, since c i = 0 i 2 I + N m +m 2 +m 3 ) such that for each x t 2 X, a n y optimal solution to (8) has the property that the z t -part of this solution is equal to the lexicographically least feasible z t 0. By using theory from parametric programming, it can be shown that X c a n b e c o vered by a set of polytopes, where each of the polytopes is uniquely de ned as X B LP := fx t 2 X j B LP ;1 g 1 (x t ) g 2 (x t ) g 3 (x t ) 0g the lexicographically minimum of Z(x t ) are equal to corresponding elements of the vector B LP ;1 (g 1 (x t ) g 2 (x t ) g 3 (x t )) : Let B denote the set of bases such that X is covered by the corresponding set of X B LP s. In (Vada et al 2001) it is shown that each basis in B de nes a set of linear constraints onc in (6) in order forc to solve the OWDP. The main idea is to compute ac which satis es the set of constraints de ned by all bases in B.…”

“…In the research literature, the few contributions to this eld include (Rawlings and Muske 1993), (Scokaert and Rawlings 1999), (Garcia and Morshedi 1986), (Kerrigan et al 2000), (Tyler and Morari 1999), (Scokaert 1994), (Alvarez and de Prada 1997), and (Vada et al 2001). To the bestof the authors knowledge, the strategy presented in (Vada et al 2001) is the only optimal infeasibility handler which considers hard prioritized constraints without the use of a sequential solution approach. The focus in the present paper is on the application of this infeasibility handler, including guidelines for adressing computational e ciency.…”

“…3 Optimal weight design problem (OWDP) In this section we formulate the problem of computing optimal constraint violations subject to hard prioritization as a single LP problem to besolved on-line at each sample, see also (Vada et al 2001). …”

“…Note that since we have assumed that d h > 0, (A B) stabilizable, and N max fn u 1g we have that X 6 = and 0 2 intX: In (Vada et al 2001), existence of a solution to the OWDP under these assumptions is established. A consequence of this result is: At each sample, if i) the state x t has a value making (2) infeasible, and ii) x t 2 X that is, with the given x t there exists a relaxation of the relaxable hard constraints such that (2) becomes feasible, then an optimal relaxation z t can be computed by solving the LP problem in (6).…”