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Coupled matrix Riccati equations in minimal cost variance control problems. (English) Zbl 0986.93072
In the first part of the paper, the authors present an algorithm for the solution of a coupled system of algebraic matrix Riccati equation $$0= -A^T P- PA- Q+ PBR^{-1} B^T P- \gamma^2 VBR^{-1} B^T V,\tag 1$$ $$0= - A^T V- VA+ 2\gamma VBR^{-1} B^TV+ PBR^{-1} B^TV+ VBR^{-1} B^T P- 4PEWE^T P,\tag 2$$ where $P$ and $V$ are solutions of equations (1) and (2). The authors use the standard Lyapunov iteration approach and prove the convergence of the algorithm. In the second part of the paper, they derive sufficient conditions ensuring that the solutions of coupled matrix Riccati differential equations with the terminal values can not blow up on a given interval $[t_0, t_f]$.

93E20Optimal stochastic control (systems)
15A24Matrix equations and identities
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