Joint Spectral Radius and Path-Complete Graph Lyapunov Functions

We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of graphs called path-complete graphs, and show that any such graph gives rise to a method for proving stability of the switched system. This enables us to derive several asymptotically tight hierarchies of semidefinite programming relaxations that unify and generalize many existing techniques such as common quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov functions. We compare the quality of approximation obtained by certain classes of path-complete graphs including a family of dual graphs and all path-complete graphs with two nodes on an alphabet of two matrices. We provide approximation guarantees for several families of path-complete graphs, such as the De Bruijn graphs, establishing as a byproduct a constructive converse Lyapunov theorem for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has gone through two major rounds of revision. In particular, a section on the performance of our algorithm on application-motivated problems has been added and a more comprehensive literature review is presente

A Complete Characterization of the Gap between Convexity and SOS-Convexity

Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity, its first order characterization, and its second order characterization, are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\tilde{C}_{n,d}$ and $\tilde{\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\tilde{C}_{n,d}=\tilde{\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\Sigma C_{n,d}$ of sos-convex forms if and only if $n=2$ or $d=2$ or $(n,d)=(3,4)$. To prove these results, we present in particular explicit examples of polynomials in $\tilde{C}_{2,6}\setminus\tilde{\Sigma C}_{2,6}$ and $\tilde{C}_{3,4}\setminus\tilde{\Sigma C}_{3,4}$ and forms in $C_{3,6}\setminus\Sigma C_{3,6}$ and $C_{4,4}\setminus\Sigma C_{4,4}$, and a general procedure for constructing forms in $C_{n,d+2}\setminus\Sigma C_{n,d+2}$ from nonnegative but not sos forms in $n$ variables and degree $d$. Although for disparate reasons, the remarkable outcome is that convex polynomials (resp. forms) are sos-convex exactly in cases where nonnegative polynomials (resp. forms) are sums of squares, as characterized by Hilbert.Comment: 25 pages; minor editorial revisions made; formal certificates for computer assisted proofs of the paper added to arXi

Modeling and PSO Optimization of Humidifier-Dehumidifier Desalination

The aim of this study is modeling a solar-air heater humidification-dehumidification unit with applying particle swarm optimization to find out the maximum gained output ratio with respect to the mass flow rate of water and air entering humidifier, mass flow rate of cooling water entering dehumidifier, width and length of solar air heater and terminal temperature difference (TTD) of dehumidifier representing temperature difference of inlet cooling water and saturated air to dehumidifier as its decision variable. A sensitivity analysis, furthermore, is performed to distinguish the effect of operating parameters including mass flow rate and streams' temperature. The results showed that the optimum productivity decreases by decreasing the ratio of mass flow rate of water entering humidifier to air ones.Article History: Received: July 12th 2017; Revised: December 15th 2017; Accepted: 2nd February 2018; Available onlineHow to Cite This Article: Afshar, M.A., Naseri, A., Bidi, M., Ahmadi, M.H. and Hadiyanto, H. (2018) Modeling and PSO Optimization of Humidifier-Dehumidifier Desalination. International Journal of Renewable Energy Development, 7(1),59-64.https://doi.org/10.14710/ijred.7.1.59-6

Assessing the Potential of Plug-in Electric Vehicles in Active Distribution Networks

A multi-objective optimization algorithm is proposed in this paper to increase the penetration level of renewable energy sources (RESs) in distribution networks by intelligent management of plug-in electric vehicle (PEV) storage. The proposed algorithm is defined to manage the reverse power flow (PF) from the distribution network to the upstream electrical system. Furthermore, a charging algorithm is proposed within the proposed optimization in order to assure PEV owner's quality of service (QoS). The method uses genetic algorithm (GA) to increase photovoltaic (PV) penetration without jeopardizing PEV owners' (QoS) and grid operating limits, such as voltage level of the grid buses. The method is applied to a part of the Danish low voltage (LV) grid to evaluate its effectiveness and capabilities. Different scenarios have been defined and tested using the proposed method. Simulation results demonstrate the capability of the algorithm in increasing solar power penetration in the grid up to 50%, depending on the PEV penetration level and the freedom of the system operator in managing the available PEV storage

Graphene Bioelectronic Nose for the Detection of Odorants with Human Olfactory Receptor 2AG1

A real-time sensor for the detection of amyl butyrate (AB) utilising human olfactory receptor 2AG1 (OR2AG1), a G-protein coupled receptor (GPCR) consisting of seven transmembrane domains, immobilized onto a graphene resistor is demonstrated. Using CVD graphene as the sensor platform, allows greater potential for more sensitive detection than similar sensors based on carbon nanotubes, gold or graphene oxide platforms. A specific graphene resistor sensor was fabricated and modified via non-covalent π–π stacking of 1,5 diaminonaphthalene (DAN) onto the graphene channel, and subsequent anchoring of the OR2AG1 receptor to the DAN molecule using glutaraldehyde coupling. Binding between the target odorant, amyl butyrate, and the OR2AG1 receptor protein generated a change in resistance of the graphene resistor sensor. The functionalized graphene resistor sensors exhibited a linear sensor response between 0.1–500 pM and high selectively towards amyl butyrate, with a sensitivity as low as 500 fM, whilst control measurements using non-specific esters, produced a negligible sensor response. The approach described here provides an alternative sensing platform that can be used in bioelectronic nose applications

Finite element analysis of axial fan blade with different chord lengths

Nowadays, improving energy efficient systems is one of the most controversial and significant global focuses. However, this trend in the field of engineering concentrates on the optimization of the existing technologies more than implementing new ones. Meanwhile, fans are one of the potent devices to be more efficient. Improvement in fan efficiency can be achieved by reducing material that is used in the fan blades. Due to this, decreasing the airfoil chord length to optimum value, leads to a decline in the amount of used materials in the blade design and manufacturing. In fan designing, Factor of safety should be considered. This factor changes by varying the chord length of the airfoil. However, this paper attempts to analyze the factor of safety in an axial fan blade with different chord lengths by use of finite element method. Due to this, axial fan blade with NACA5514 airfoil that is made by Aluminum 6061-T91 will be analyzed to find the correlation between the factor of safety and chord length in various pressure loads. The load values are determined by the experimental test