LQ optimal control for stochastic systems with infinite Markovian jumps

Infinite horizon LQ Nash Games for SDEs with infinite jumps

“…Then, under the constraint of (34), to minimize J 2 (x 0 , i, u(•), v * (•)) is a standard LQ problem with the control weighting matrix R( t ) = I and the state weighting matrix Q( t ) = C( t ) ′ C( t ). By Theorem 2 [19] and (29), we get u…”

“…is strong detectable, it follows from Theorem 2 [19] that (48) has a solution P 2 (i) ≥ 0, i ∈  and min…”

“…Now observe that (26) is a standard LQ problem with R( t ) = I and Q( t ) = C( t ) ′ C( t ) subject to (34). Using Theorem 2 [19], we say that P 2 = (P 2 (1), P 2 (2), … ) ∈ N n+ ∞ is a stabilizing solution of (29). Moreover,…”

H∞ Control for Nonlinear Infinite Markov Jump Systems

“…Therefore, infinite Markov jump systems deserve our consideration. Recently, some papers on stability [25][26][27] and control problems [28,29] of linear infinite Markov jump systems have appeared. To be specific, infinite horizon 2 / ∞ controller has been obtained by four coupled algebraic Riccati equations in [30].…”