No abstract

This paper demonstrates the utility of systems and control theory in the analysis of economic systems. Two applications demonstrate how the analysis of simple dynamic models sheds light on important practical problems. The first problem considers the design of a retail laboratory, where the small gain theorem enables the falsification of pricing policies. The second problem explores industrial organization using the equilibria of profit-maximizing dynamics to quantify the percentage of a firm's profits due strictly to the cooperative effects among its products. This "Value of Cooperation" suggests an important measure for both organizational and antitrust applications.

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these "t-step" approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.

Diode lasers have many useful properties and have found a variety of uses including CD and DVD players, barcode scanners, laser surgery, water purification, quantum-key cryptography, spectroscopic sensing, etc. Nevertheless, their intrinsic linewidth or the precision of their emitted wavelengths, is not good enough for many cutting-edge applications such as atomic interferometry or high-performance atomic clocks. Using active feedback control, we can narrow the linewidth of a diode laser by not allowing the frequency of emitted light to drift away from a reference value. Nevertheless, such feedback designs are challenging because of a lack of first principles models and difficult sensor dynamics. This brief describes our diode laser system and reports our results identifying the system using black-box techniques, validating the empirical models, and designing controllers to achieve desired performance while preserving stability and satisfying implementation constraints.

No abstract

Abstract-We present a systematic method for model reduction of a class of input-quantized systems in the max-plus algebra. We consider a generalization of the flow shop with finite intermediate storage. These systems are useful in modeling chemical processes and manufacturing systems, including pharmaceutical manufacturing, construction, propellant manufacturing and assembly lines. The makespan minimization problem we consider is N P-complete. Our method of model reduction reduces the number of states that a system can reach, thus reducing the search space for the optimization problem. This allows us to construct a smaller N P-complete problem to approximate the solution to the larger problem. We show that the error of the approximation is bounded and that as the approximated system approaches the true system, that the error of the approximation goes to zero.

No abstract