In the class of piecewise deterministic systems such as presented by Richel [1975b], [1975c], one considers continuous-time systems disturbed by a jump process with a discrete and finite state space. This disturbance is modeled by a Markov chain with constant transition rates.
The objectivs of this thesis are as follows:
1. A generalization of Richel's formalism by consideration of more general disturbances. The disturbances are modeled by a controlled markov chain with transition rates dependent on the system state and control.
2. Under the new formalism, an extension of the Olsder & Suri model of production scheduling in flexible manufacturing systems. Our model includes the wear of the workstation in the transition rates, and considers preventive maintenance actions.
3. The development of a numerical scheme based on the technique of successive approximations associated with the discretization of the synamic programming equation.
Optimal control problems associated with minimizing the cost on both finite and infinite horizons are considered and optimality conditions are derived.
Paru en janvier 1988 , 283 pages