Set membership approximations of predictive control laws: the tradeoff between accuracy and complexity

This study proposes two new techniques, in the framework of set membership (SM) theory, to derive off-line an approximation of a given non-linear model predictive control (NMPC) law. The obtained approximated control laws satisfy input constraints and guarantee a bounded worst-case approximation error. Such a bound can be tuned to obtain a tradeoff between closed-loop performance, on-line evaluation complexity, off-line computational burden and memory usage. The presented techniques are suboptimal, since their worst-case approximation error is not minimal; however, they are able to obtain good accuracy with efficient on-line computation. Both approaches are based on the prior information given by a finite number ν of nominal control moves, computed off-line and stored. The first technique relies on the piecewise linear interpolation of the off-line computed data, while the second approach is based on the computation of the (suboptimal) upper and lower bounds of the nominal NMPC law, on the basis of the partial information given by a subset of the whole off-line computed data. A numerical example and an automotive case study are presented in order to show the effectiveness of the proposed approaches and to compare their performance.