Approximate robust optimal control of nonlinear dynamic systems under process noise

Authors

• D. Telen, M. Vallerio, L. Cabianca, B. Houska, J. Van Impe, F. Logist

Reference

• In Proceedings of the European Control Conference 2015,
  Linz, Austria, July 15-17, 2015.

Abstract

Dynamic optimization techniques for nonlinear systems can provide the process industry with sustainable and efficient operating regimes. These regimes can lie close to the process limits. It is therefore critical that these operating conditions are robust with respect to process noise, i.e, an unmodeled time-varying random disturbance. Besides the uncertainty in the constraints, also uncertainty in the objective function should be considered. However, including robustness in an optimization problem typically leads to semiinfinite optimization problems which are challenging to solve in practice. In this paper several computationally tractable methods are exploited to approximately solve the robust optimal control problem. The presented approaches allow the use of fast deterministic gradient based optimization techniques. The first method is based on a linearization approach while the second method exploits the unscented transformation to construct an estimate of the uncertainty propagation. Both methods yield an approximation of the variance-covariance matrix of the critical constraints and of the objective function. These variance-covariance matrices are employed in the optimization routine. The illustrative case study is a jacketed tubular reactor.

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