ECS-9629866 Runolfsson Dynamic systems that depend on a auxiliary parameter that characterizes the mode of operation of the system arise in many applications. In some applications this parameter can be measured, in others it can be estimated and in still others it is completely unknown except for, perhaps, some apriori estimate about its size. The methods that are chosen in incorporating the auxiliary parameter in the design of a control systems depends on the characteristic of the parameter. If the parameter is deterministic and can be measured, gain scheduling methods are frequently employed in the design of real systems. If the parameter is (deterministic) unknown and not measurable, robust design methods are usually used. If, on the other hand, the parameter is stochastic with known statistic, stochastic methods are usually employed. A particular case of this situation is the case when the auxiliary parameter can be modelled as finite state continuous time Markov chain. Such systems arise in various applications and system formulations such as power systems, manufacturing systems and fault-tolerant control system. In this research we study risk-sensitive control for hybrid systems with a Markovian jump parameter. In particular, the objective of the control is to minimize the infinite-horizon risk-sensitive cost functional. Preliminary investigations show that the relationship between H(_ control, linear differential games and risk-sensitive control does not hold for hybrid systems. The main reason for this appears to be 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 performance as insensitive to the effects of the jump parameter as possible. In this research we will develop risk sen sitive control of hybrid stochastic systems and study in detail both system theoretic properties and design techniques for such systems. Furthermore, the benefits of the developed techniques will be evaluated for the applications described above.
