Computational Sensitivity Analysis of State Constrained Control Problems

Stability analysis of parametric control problems has recently been extended to control problems subject to pure state constraints. This paper illustrates the numerical aspects of stability analysis via a specific numerical example: the optimal control of the state constrained Van-der-Pol oscillator. The multiple shooting method is used to determine a nominal solution of high accuracy that satisfies first order necessary conditions. Second order sufficient conditions can be checked by solving an associated Riccati equation. Finally, sensitivity differentials of optimal solutions with respect to parameters are computed.