Simulation-guided parameter synthesis for chance-constrained optimization of control systems

We consider the problem of parameter synthesis for black-box systems whose operations are jointly influenced by a set of “tunable parameters” under the control of designers, and a set of uncontrollable stochastic parameters. The goal is to find values of the tunable parameters that ensure the satisfaction of given performance requirements with a high probability. Such problems are common in robust system design, including feedback controllers, biomedical devices, and many others. These can be naturally cast as chance-constrained optimization problems, which however, are hard to solve precisely. We present a simulation-based approach that provides a piecewise approximation of a certain quantile function for the responses of interest. Using the piecewise approximations as objective functions, a collection of local optima are estimated, from which a global search based on simulated annealing is performed. The search yields tunable parameter values at which the performance requirements are satisfied with a high probability, despite variations in the stochastic parameters. Our approach is applied to three benchmarks: an insulin infusion pump model for type-1 diabetic patients, a robust flight control problem for fixed-wing aircrafts, and an ODE-based apoptosis model from system biology.