Uniform Convergence of the Solutions of Riccati Equations for a Family of Optimal Control Problems

The uniform convergence of the solutions of a parameterized family of Riccati differential equations which arise in the context of optimal control problems for systems described by a family of linear time-varying evolution equations is considered on the infinite time interval in Hilbert space. Some sufficient conditions and an illustrative example are given for uniform convergence of the solutions of a family of the Riccati differential equations. The uniform convergence of the solutions of the Riccati differential equations with respect to parameters is important for applications to problems in adaptive control of stochastic evolution systems.