Optimal control law for fault tolerant control systems in noisy environment

An optimal control law is synthesized for fault tolerant control systems with Markovian parameters (FTCSMP) in noisy environment. Three types of noise are considered: state-dependent, control-dependent and purely additive Gaussian noise. In particular, conditions for the existence of an optimal control law in the finite time horizon are derived. The limiting behavior of the cost function, the Riccati-like and the covariance-like differential equations is studied. The conditions that guarantee the finiteness of the cost function and the existence of steady-state solutions, for both Riccati-like and covariance-like differential equations, are stated and verified. A computational algorithm is constructed for both finite and infinite time horizons. It is shown that under certain conditions, the algorithm converges to constant optimal control gains. The theoretical results are illustrated by a numerical example