Non-switching control strategies for continuous-time jump linear quadratic systems

For continuous-time linear systems with random jumps in parameter values, an optimal control problem is formulated in terms of a quadratic cost-function. The random changes of the model are described by a new variable, called the plant mode, that behaves like a Markov chain. Previous work established the optimal solution when the control is allowed to feedback both the plant state and the plant mode. One obtains a linear feedback law with switching gains. In this paper, non-switching control strategies are considered. They are more realistic since they do not require that the plant mode is measurable. The system performance is first computed for such a strategy. Then an optimization problem is solved that yields the best non-switching strategy. Optimality conditions and computationnal algorithms are given. On an example, non-switching strategies are compared to the optimal switching one. If one takes into account the random nature of the realized cost-function, it is shown that nonswitching strategies may be preferable.