Stability and sensitivity analysis for linear-quadratic optimal control subject to state constraints

Abstract

A family of parametric linear-quadratic optimal control problems is considered. The problems are subject to state constraints. The conditions are derived, under which the solutions and Lagrange multipliers are locally Lipschitz continuous and directionally differentiable functions of the parameter. These conditions consist of constraint qualifications and weakened second order sufficient optimality conditions.

Keywords:

• Linear-quadratic optimal control
• State constraints
• Parametric problems
• Second order sufficient conditions
• Lipschitz stability
• Directional differentiability of the solutions

Keywords:

• 49K40
• 49K30
• 49K15
• 49N10

Acknowledgment

Supported by the Polish Ministry of Scientific Research and Information Technology grant 3 T11C 051 28.