Performance bounds for min-max uncertain constrained systems

B. Van Parys, P. J. Goulart and M. Morari

@inproceedings{PGM:2012a,
  author = {B. Van Parys and P. J. Goulart and M. Morari},
  title = {Performance bounds for min-max uncertain constrained systems},
  booktitle = {IFAC Workshop on Nonlinear Model Predictive Control},
  year = {2012},
  pages = {107-112},
  url = {http://dx.doi.org/10.3182/20120823-5-NL-3013.00018},
  doi = {10.3182/20120823-5-NL-3013.00018}
}

We present a method to bound the performance of causal controllers for uncertain linear systems with mixed state and input constraints. The performance is measured by the worst-case value (over all possible disturbance inputs) of a convex piecewise linear cost function over a finite horizon. Our method computes a causal affine control policy that satisfies the constraints robustly, while simultaneously providing a lower bound on the achievable performance of this, or any other causal control policy constructed by any other method. The controller and performance guarantee can be found by solving a number of convex conic optimization problems which are closely connected.