Title :
Impulse control of piecewise-deterministic processes via linear programming
Author_Institution :
Dept. of Electr. Eng., Imperial Coll., London, UK
fDate :
3/1/1991 12:00:00 AM
Abstract :
In previous papers a state-space discretization technique in which the continuous-time discretized piecewise-deterministic Markov process (discretization on the post-jump location) approaches the original process uniformly on compact sets has been presented. Under the assumptions of continuity and boundedness of the cost function, it follows that the total discounted cost will also approach the original total cost, at least for epsilon -optimal strategies, which means that the optimal cost of the discretized process should converge to the original optimal cost. The author considers a time discretization so that the new discretized problem (state space and intervention times discretizations) will be finite-dimensional and linear programming (LP) can be used to solve it. The author presents a method that can considerably reduce the number of inequalities of the LP problem. An application to the maintenance of complex systems is given.
Keywords :
linear programming; maintenance engineering; probability; stochastic systems; complex systems; continuous-time discretized piecewise-deterministic Markov process; epsilon -optimal strategies; impulse control; linear programming; maintenance; optimal cost; state-space discretization technique; total discounted cost; Control theory; Convergence; Cost function; Linear programming; Markov processes; Operations research; Optimal control; Process control; State-space methods; Stochastic processes;
Journal_Title :
Automatic Control, IEEE Transactions on