the problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. in this paper we present a new mixed integer non linear program (minlp) and a heuristic meth...

Motivated by the objective to further reduce the storage and computation time required by finite-horizon discrete-time optimal reduced-order LQG compensators, this paper introduces the modified reachability canonical form of a minimal finite-horizon discrete-time compensator and an algorithm to compute it. Next recursive algorithms for efficient storage and recovery of the compensator matrices ...

In this paper, the finite horizon H∞ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of sampled-data measurements. The methodology adopted involves a certain equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, by solving the finite horizon H∞ control problem for the equivalent stochastic problem ...

In this paper, finite and infinite horizon stochastic H2/H∞ control problems with all state, control input and external disturbance-dependent noise are studied. It is shown that the existence condition of finite horizon stochastic H2/H∞ control is equivalent to the solvability of four coupled matrix-valued differential equations, and that of infinite horizon stochastic H2/H∞ control is equivale...

We address in this paper the challenge of solving a nonhomogeneous infinite horizon Markov Decision Process (MDP) problem. More precisely, we seek an algorithm that, when given a finite subset of the problem’s potentially infinite data set, delivers an optimal first period policy. Such an algorithm can thus recursively generate within a rolling horizon procedure an infinite horizon optimal solu...

This paper steps back from the standard infinite horizon formulation of reinforcement learning problems to consider the simpler case of finite horizon problems. Although finite horizon problems may be solved using infinite horizon learning algorithms by recasting the problem as an infinite horizon problem over a state space extended to include time, we show that such an application of infinite ...

The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An o...

We analyze losses resulting from uncertain transition probabilities in Markov decision processes with bounded nonnegative rewards. We assume that policies are pre-computed using exact dynamic programming with the estimated transition probabilities, but the system evolves according to different, true transition probabilities. Our approach analyzes the growth of errors incurred by stepping backwa...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...