Risk-sensitive control of stochastic hybrid systems

A stochastic hybrid system of a form arising in various applications and system formulations (e.g. power, manufacturing, fault-tolerant control) is considered. The most common approach in control design for hybrid systems with a random jump parameter is to use optimal control methods. We study risk-sensitive control for hybrid systems with a Markovian jump parameter. In particular, the objective of the control is to minimize an infinite-horizon risk-sensitive cost functional. It is shown that the relationship between H^∞ control, linear differential games and risk-sensitive control does not hold. The main reason for this is that the risk-sensitivity cost functional measures the risk sensitivity of the system to transitions caused by the random jump parameter as well as the noise input. The risk sensitivity of the cost functional to transitions induced by the jump parameter may be of a great value in the design of systems where it is desired to make the system as insensitive to the effects of the jump parameter as possible