Polynomial Optimization with Applications to Stability Analysis and Control - Alternatives to Sum of Squares

In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation Linear Techniques, Blossoming and Groebner basis methods, our main focus is on algorithms defined by Polya's theorem, Bernstein's theorem and Handelman's theorem. We first formulate polynomial optimization problems as verifying the feasibility of semi-algebraic sets. Then, we discuss how Polya's algorithm, Bernstein's algorithm and Handelman's algorithm reduce the intractable problem of feasibility of semi-algebraic sets to linear and/or semi-definite programming. We apply these algorithms to different problems in robust stability analysis and stability of nonlinear dynamical systems. As one contribution of this paper, we apply Polya's algorithm to the problem of H_infinity control of systems with parametric uncertainty. Numerical examples are provided to compare the accuracy of these algorithms with other polynomial optimization algorithms in the literature.Comment: AIMS Journal of Discrete and Continuous Dynamical Systems - Series

Firm and industry effects in accounting versus economic profit data

This article presents estimates of firm and industry fixed-effects on profit rates for large US corporations, using both Economic Value Added (EVA), the popular measure of profits produced by Stern Stewart and Company, as well as simple (unadjusted) accounting measures as the dependent variable. We find that the improvement in explanatory power of the fixed-effect model is substantially greater when using EVA than has been documented with alternative measures

The Persistence of Accounting versus Economic Profit

Drawing on Schumpeterian theory, this article presents estimates of a first-order autoregressive model of profit persistence for large US firms, using Economic Value Added (EVA), the popular measure of profits produced by Stern Stewart and Company, and simple (unadjusted) accounting measures from the Compustat database. We hypothesize about the differences we should expect to find between these two sets of estimates, and also provide a fresh normative assessment of the dynamic competitiveness of the US economy

The persistence of accounting versus economic profit

Drawing on Schumpeterian theory, this article presents estimates of a first-order autoregressive model of profit persistence for large US firms, using Economic Value Added (EVA), the popular measure of profits produced by Stern Stewart and Company, and simple (unadjusted) accounting measures from the Compustat database. We hypothesize about the differences we should expect to find between these two sets of estimates, and also provide a fresh normative assessment of the dynamic competitiveness of the US economy.dynamic competition efficiency persistence

Optical Network Virtualisation using Multi-technology Monitoring and SDN-enabled Optical Transceiver

We introduce the real-time multi-technology transport layer monitoring to facilitate the coordinated virtualisation of optical and Ethernet networks supported by optical virtualise-able transceivers (V-BVT). A monitoring and network resource configuration scheme is proposed to include the hardware monitoring in both Ethernet and Optical layers. The scheme depicts the data and control interactions among multiple network layers under the software defined network (SDN) background, as well as the application that analyses the monitored data obtained from the database. We also present a re-configuration algorithm to adaptively modify the composition of virtual optical networks based on two criteria. The proposed monitoring scheme is experimentally demonstrated with OpenFlow (OF) extensions for a holistic (re-)configuration across both layers in Ethernet switches and V-BVTs

A Multi-objective Approach to Optimal Battery Storage in The Presence of Demand Charges

In this paper, we propose an optimization framework for optimal energy storage, in the form of batteries, by residential customers. Our goal is to determine the value of battery storage to those customers whose electricity bills consist of both Time-of-Use charges ($/kWh, with different rates for on-peak and off-peak hours) and demand charges ($/kW, proportional to the peak rate of consumption in a month). The customers may have access to a local power generating source in the form of solar PhotoVoltaic (PV). In order to quantify the benefits from the battery storage, we pose a battery optimization problem which minimizes the monthly electricity bill 30 poff ∑k∈off q(k)Δt + 30 pon ∑k∈on q(k)Δt + pd supk∈on q(k), where poff, pon, pd are the off-peak, on-peak and demand prices, and q(k) is the power delivered by the utility company to the customer. We consider this power to be used according to q(k) = qb(k) + qa(k) - qsolar(k), where qa is the power consumed by the appliances, qsolar is the power provided by the solar PV, and qb is the power given to or taken from the battery. We assume that the rate of the energy stored in the battery is proportional to qb and the stored energy is bounded by the battery’s capacity (kWh). Furthermore, we account for the battery degradation by modeling the battery’s capacity as a function of the number of charging/discharging cycles and the depth of discharge. Because of the presence of demand charges (supk q(k)), the objective function of our battery optimization problem is not separable in time - a property (time separability) which is a sufficient for the dynamic programming algorithm to converge to an optimal solution. We establish a provably convergent algorithm for the non-separable optimization problem in the following two steps. First, we replace supk q(k) in the objective function using the following approximation                                                           supk∈on q(k) = q(k) l∞ = (∑k∈on q(k)p)1/p for some large p. Then, we construct a multi-objective problem (a class of optimization problems involving at least two objective functions to be minimized simultaneously) defined by a parameterized set of dynamic programs expressed in terms of the time-separable functions J1(q) = ∑k q(k) J2(q) = ∑k∈on q(k)p Each of these parameterized dynamic programs can be solved using the standard dynamic programming algorithms. The set of solutions to these parameterized problems form a Pareto front - a set which is guaranteed to contain the solution to the original battery optimization problem as p → ∞. We apply our algorithm to multiple scenarios described by a range battery sizes, solar generation levels and appliances loads to quantify the savings from the batteries for a wide range of residential customers. The proposed approach can be potentially used to: 1) Model customers response to changes in electricity prices; 2) Quantify the benefits of energy storage to utility companies