TY - JOUR
T1 - Risk-sensitive control, differential games, and limiting problems in infinite dimensions
AU - Charalambous, Charalambos D.
AU - Naidu, Subbaram
AU - Moore, Kevin L.
PY - 1994
Y1 - 1994
N2 - In this paper we present the solutions of the stochastic finite and infinite horizon risk-sensitive control problems in infinite dimensions, with μ, ε > 0, respectively, representing the risk-sensitivity and small noise parameters. Invoking a logarithmic transformation, a stochastic differential game equivalent to the risk-sensitive problem is obtained. In the limit as ε ↓ 0, the deterministic differential game associated with the H∞-disturbance attenuation control problem of distributed parameter systems is recovered. In the limit as μ ↓ 0 (resp. μ ↓ 0, ε ↓ 0) the usual stochastic (resp. deterministic) control problem with integral cost is recovered. Both finite and infinite horizon cases are treated. This article extends the recent relations [1] and [2] between risk-sensitive and H∞-robust control from finite to infinite dimensional spaces.
AB - In this paper we present the solutions of the stochastic finite and infinite horizon risk-sensitive control problems in infinite dimensions, with μ, ε > 0, respectively, representing the risk-sensitivity and small noise parameters. Invoking a logarithmic transformation, a stochastic differential game equivalent to the risk-sensitive problem is obtained. In the limit as ε ↓ 0, the deterministic differential game associated with the H∞-disturbance attenuation control problem of distributed parameter systems is recovered. In the limit as μ ↓ 0 (resp. μ ↓ 0, ε ↓ 0) the usual stochastic (resp. deterministic) control problem with integral cost is recovered. Both finite and infinite horizon cases are treated. This article extends the recent relations [1] and [2] between risk-sensitive and H∞-robust control from finite to infinite dimensional spaces.
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M3 - Conference article
AN - SCOPUS:0028749149
VL - 3
SP - 2184
EP - 2186
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
T2 - Proceedings of the 2nd IEEE International Symposium on Requirements Engineering
Y2 - 27 March 1995 through 29 March 1995
ER -