We consider a supply chain in which the underlying demand process can be described in a linear state space form. Inventory is managed at various points of the chain (members), based on local information that each member observes and continuously updates. The key feature of our model is that it takes into account the ability of the members to observe subsets of the underlying state vector, and adopt their forecasting and replenishment policies accordingly. This enables us to model situations in which the members are privy to certain explanatory variables of the demand, with the latter possibly evolving according to a vector autoregressive time series. For each member, we identify an associated demand evolution model, for which we propose an adaptive inventory replenishment policy that utilizes the Kalman filter technique. We then provide a simple methodology for assessing the benefits of various types of information-sharing agreements between members of the supply chain. We also discuss inventory positioning and cost performance assessment in the supply chain. Our performance metrics and inventory target levels are usually presented in matrix forms, allowing them to accommodate a relatively large spectrum of linear demand models, and making them simple to implement. Several illustrations for possible applications of our models are provided.

A Time-Series Framework for Supply-Chain Inventory Management

Statistical arbitrage strategies, such as pairs trading and its generalizations rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. We embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean- reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.

/pdf/dynamic-modeling-of-mean-reverting-spreads-for-statistical-3nvwmn773o.pdf

Dynamic modeling of mean-reverting spreads for statistical arbitrage

The problem of synthesizing a robust controller is considered for a large, flexible space-based antenna by using the linear-quadratic-Gaussian (LQG)/loop transfer recovery (LTR) method. The study is based on a finite-element model of the 122-m hoop/column antenna, which consists of three rigid-body rotational modes and the first 10 elastic modes. A robust compensator design for achieving the required performance bandwidth in the presence of modeling uncertainties is obtained using the LQG/LTR method for loop-shaping in the frequency domain. Different sensor actuator locations are analyzed in terms of the pole/zero locations of the multivariable systems and possible best locations are indicated. The computations are performed by using the LQG design package ORACLS augmented with frequency domain singular value analysis software.

https://ntrs.nasa.gov/api/citations/19860021328/downloads/19860021328.pdf

Application of the LQG/LTR technique to robust controller synthesis for a large flexible space antenna

The linear-quadratic Gaussian/loop-transfer-recovery method is used to synthesize a fine-pointing control system for a large space antenna. A finite-element model for the 122-m hoop/column antenna is employed, and a compensator, utilizing attitudes sensors and torque actuators, is designed which achieves pointing performance while maintaining stability robustness to unmodeled dynamics. Inclusion of the rigid-body modes plus the first three elastic modes is found to be necessary to achieve a 0.1-rad/s bandwidth. Results are obtained by employing a modification of the standard robustness recovery procedure, which reduces the conservative nature of the design methodology. Performance degradation is encountered due to the presence of unavoidable invariant zeros within the design bandwidth.

Robust controller synthesis for a large flexible space antenna

This paper considers the problem of synthesizing a fine-pointing control system for a large flexible space antenna in the presence of modeling uncertainties. The plant to be controlled is a 122-meter diameter, space-based, "Hoop/Column" antenna. The mathematical model, based on a finite element analysis, consists of three rigid-body rotational modes, and the first 10 elastic modes. A preliminary robust compensator design for achieving the required pointing performance is obtained using linear-quadratic-Gaussian (LQG) and loop transfer recovery (LTR) methods for loop-shaping. The computations are performed using the LQG design package "ORACLS," and a recently developed singular value analysis package.

The applicability of the recently developed frequency-domain, matrix-norm robustness margins for physical systems is explored in this paper using a power system example. The power system is modeled using the damping-and synchronizing-torque framework. The robustness margins evaluated at several junctions of the power system model are shown to be useful measures of the system's tolerance for unmodeled shaft torsional dynamics and variations in the effectiveness of power system controllers (e.g., multiterminal high-voltage dc modulators). In addition, the robustness margins are shown to be useful for comparing the robustness of alternate controller designs. This paper ends with general guidelines for applying the matrix-norm robustness margins to physical systems.

https://ieeexplore.ieee.org/iel5/9/24206/01103373.pdf

M. Athans

Papers

Applications of robustness theory to power system models