This work is concerned with the proof-complexity of certifying that optimization problems do not have good solutions. Specifically we consider bounded-degree “Sum of Squares” (SOS) proofs, a powerful algebraic proof system introduced in 1999 by Grigoriev and Vorobjov. Work of Shor, Lasserre, and Parrilo shows that this proof system is automatizable using semidefinite programming (SDP), meaning ...

This paper proposes the control design of a nonlinear polynomial fuzzy system with ∞ H performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the ∞ H performance objective. The desi...

System of Systems (SoS) are a relatively recent phenomenon and present a whole new set of challenges for systems engineers. The system elements of an SoS are often managed and operated in a predominantly independent manner, over widely distributed geographic locations and are subject to evolution with various rates of change. The goals of the SoS itself often change over time. One purpose of th...

This study aimed to evaluate the ability of speed of sound (SOS) measured at the phalanges to estimate simulated wrist fracture load and stress. SOS was measured along the proximal phalanges of the second, third and fourth fingers using an ultrasound (US) system operating in axial transmission mode. The bone mineral density (BMD) of the radius and the phalanges was also measured with quantitati...

concurrent distributed systems, systems of systems, Communicating Structures, object-oriented modeling, visualization By Systems of Systems (SoS) we mean large-scale concurrent and distributed systems the components of which are complex systems themselves (e.g. enterprise intranets). Communicating Structures are hierarchical structures that represent SoS in a uniform, systematic way as composit...

This thesis proposes a value robustness approach to architect defense systems and Systems of Systems (SoS). A value robust system or SoS has the ability to provide continued value to stakeholders by performing well to meet the mission intent under a variety of future contexts. The proposed approach encompasses three methods, namely “Needs to Architecture” framework, Multi-Attribute Tradespace E...

An M x /G/1 queueing system with second optional service (SOS)is studied under N policy and Bernoulli Vacation. The system remains idle until the queue size reaches or exceeds N ( ≥ 1). When the queue size reaches at leastN, the server may begin his setup operation with probability s or may start the service with probability (1-s). The server provides two phases of heterogeneous services, of wh...

The emerging class of systems known as Systems of Systems (SoS) are composed of many distributed, heterogeneous and autonomous components. Such systems are typically separately designed and manufactured and evolve throughout their lifetime. However, they are expected to work together, often in safety-critical areas of operation such as civil transportation, military operations and space explora...