Sensitivity analysis of the value function for infinite dimensional optimal control problems and its relation to Riccati equations

Abstract

First and second order sensitivities of the value function in optimal control problems constrained by semilinear parabolic equations with respect to the initial condition are considered. Sufficient conditions are given which allow to express these sensitivities in terms of the adjoint equation and a suitably defined Riccati equation.

Keywords:

• Optimal control
• value function
• sensitivity analysis
• Riccati operators
• semilinear parabolic equations

Acknowledgements

We would like to thank the referees for their valuable comments and suggestions, which allowed us to improve the first version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author has been partially supported by the project GNAMPA 2017 ‘Comportamento asintotico e controllo di equazioni di evoluzione non lineari’ funded by INdAM - Istituto Nazionale di Alta Matematica. Reseach partially supported by the Austrian Science Fund (FWF) special research grant SFB-F32 ‘Mathematical Optimization and Applications in Biomedical Sciences’, and by the ERC advanced grant 668998 (OCLOC) under the EU’s H2020 research program.