Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

Trade-off analysis and design of a Hydraulic Energy Scavenger

In the last years there has been a growing interest in intelligent, autonomous devices for household applications. In the near future this technology will be part of our society; sensing and actuating will be integrated in the environment of our houses by means of energy scavengers and wireless microsystems. These systems will be capable of monitoring the environment, communicating with people and among each other, actuating and supplying themselves independently. This concept is now possible thanks to the low power consumption of electronic devices and accurate design of energy scavengers to harvest energy from the surrounding environment. In principle, an autonomous device comprises three main subsystems: an energy scavenger, an energy storage unit and an operational stage. The energy scavenger is capable of harvesting very small amounts of energy from the surroundings and converting it into electrical energy. This energy can be stored in a small storage unit like a small battery or capacitor, thus being available as a power supply. The operational stage can perform a variety of tasks depending on the application. Inside its application range, this kind of system presents several advantages with respect to regular devices using external energy supplies. They can be simpler to apply as no external connections are needed; they are environmentally friendly and might be economically advantageous in the long term. Furthermore, their autonomous nature permits the application in locations where the local energy grid is not present and allows them to be ‘hidden' in the environment, being independent from interaction with humans. In the present paper an energy-harvesting system used to supply a hydraulic control valve of a heating system for a typical residential application is studied. The system converts the kinetic energy from the water flow inside the pipes of the heating system to power the energy scavenger. The harvesting unit is composed of a hydraulic turbine that converts the kinetic energy of the water flow into rotational motion to drive a small electric generator. The design phases comprise a trade-off analysis to define the most suitable hydraulic turbine and electric generator for the energy scavenger, and an optimization of the components to satisfy the systems specification

On the convergence of an algorithm constructing the normal form for lower dimensional elliptic tori in planetary systems

We give a constructive proof of the existence of lower dimensional elliptic tori in nearly integrable Hamiltonian systems. In particular we adapt the classical Kolmogorov's normalization algorithm to the case of planetary systems, for which elliptic tori may be used as replacements of elliptic keplerian orbits in Lagrange-Laplace theory. With this paper we support with rigorous convergence estimates the semi-analytical work in our previous article (2011), where an explicit calculation of an invariant torus for a planar model of the Sun-Jupiter-Saturn-Uranus system has been made. With respect to previous works on the same subject we exploit the characteristic of Lie series giving a precise control of all terms generated by our algorithm. This allows us to slightly relax the non-resonance conditions on the frequencies.Comment: 45 page

A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road

Static Analysis of Run-Time Errors in Embedded Real-Time Parallel C Programs

We present a static analysis by Abstract Interpretation to check for run-time errors in parallel and multi-threaded C programs. Following our work on Astr\'ee, we focus on embedded critical programs without recursion nor dynamic memory allocation, but extend the analysis to a static set of threads communicating implicitly through a shared memory and explicitly using a finite set of mutual exclusion locks, and scheduled according to a real-time scheduling policy and fixed priorities. Our method is thread-modular. It is based on a slightly modified non-parallel analysis that, when analyzing a thread, applies and enriches an abstract set of thread interferences. An iterator then re-analyzes each thread in turn until interferences stabilize. We prove the soundness of our method with respect to the sequential consistency semantics, but also with respect to a reasonable weakly consistent memory semantics. We also show how to take into account mutual exclusion and thread priorities through a partitioning over an abstraction of the scheduler state. We present preliminary experimental results analyzing an industrial program with our prototype, Th\'es\'ee, and demonstrate the scalability of our approach

A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

Metastability in the Furstenberg-Zimmer tower

According to the Furstenberg-Zimmer structure theorem, every measure-preserving system has a maximal distal factor, and is weak mixing relative to that factor. Furstenberg and Katznelson used this structural analysis of measure-preserving systems to provide a perspicuous proof of Szemer\'edi's theorem. Beleznay and Foreman showed that, in general, the transfinite construction of the maximal distal factor of a separable measure-preserving system can extend arbitrarily far into the countable ordinals. Here we show that the Furstenberg-Katznelson proof does not require the full strength of the maximal distal factor, in the sense that the proof only depends on a combinatorial weakening of its properties. We show that this combinatorially weaker property obtains fairly low in the transfinite construction, namely, by the $\omega^{\omega^\omega}$th level

Development of novel orthogonal genetic circuits, based on extracytoplasmic function (ECF) σ factors

The synthetic biology field aims to apply the engineering 'design-build-test-learn' cycle for the implementation of synthetic genetic circuits modifying the behavior of biological systems. In order to reach this goal, synthetic biology projects use a set of fully characterized biological parts that subsequently are assembled into complex synthetic circuits following a rational, model-driven design. However, even though the bottom-up design approach represents an optimal starting point to assay the behavior of the synthetic circuits under defined conditions, the rational design of such circuits is often restricted by the limited number of available DNA building blocks. These usually consist only of a handful of transcriptional regulators that additionally are often borrowed from natural biological systems. This, in turn, can lead to cross-reactions between the synthetic circuit and the host cell and eventually to loss of the original circuit function. Thus, one of the challenges in synthetic biology is to design synthetic circuits that perform the designated functions with minor cross-reactions (orthogonality). To overcome the restrictions of the widely used transcriptional regulators, this project aims to apply extracytoplasmic function (ECF) σ factors in the design novel orthogonal synthetic circuits. ECFs are the smallest and simplest alternative σ factors that recognize highly specific promoters. ECFs represent one of the most important mechanisms of signal transduction in bacteria, indeed, their activity is often controlled by anti-σ factors. Even though it was shown that the overexpression of heterologous anti-σ factors can generate an adverse effect on cell growth, they represent an attractive solution to control ECF activity. Finally, to date, we know thousands of ECF σ factors, widespread among different bacterial phyla, that are identifiable together with the cognate promoters and anti-σ factors, using bioinformatic approaches. All the above-mentioned features make ECF σ factors optimal candidates as core orthogonal regulators for the design of novel synthetic circuits. In this project, in order to establish ECF σ factors as standard building blocks in the synthetic biology field, we first established a high throughput experimental setup. This relies on microplate reader experiments performed using a highly sensitive luminescent reporter system. Luminescent reporters have a superior signal-to-noise ratio when compared to fluorescent reporters since they do not suffer from the high auto-fluorescence background of the bacterial cell. However, they also have a drawback represented by the constant light emission that can generate undesired cross-talk between neighboring wells on a microplate. To overcome this limitation, we developed a computational algorithm that corrects for luminescence bleed-through and estimates the “true” luminescence activity for each well of a microplate. We show that the correcting algorithm preserves low-level signals close to the background and that it is universally applicable to different experimental conditions. In order to simplify the assembly of large ECF-based synthetic circuits, we designed an ECF toolbox in E. coli. The toolbox allows for the combinatorial assembly of circuits into expression vectors, using a library of reusable genetic parts. Moreover, it also offers the possibility of integrating the newly generated synthetic circuits into four different phage attachment (att) sites present in the genome of E. coli. This allows for a flawless transition between plasmid-encoded and chromosomally integrated genetic circuits, expanding the possible genetic configurations of a given synthetic construct. Moreover, our results demonstrate that the four att sites are orthogonal in terms of the gene expression levels of the synthetic circuits. With the purpose of rationally design ECF-based synthetic circuits and taking advantage of the ECF toolbox, we characterized the dynamic behavior of a set of 15 ECF σ factors, their cognate promoters, and relative anti-σs. Overall, we found that ECFs are non-toxic and functional and that they display different binding affinities for the cognate target promoters. Moreover, our results show that it is possible to optimize the output dynamic range of the ECF-based switches by changing the copy number of the ECFs and target promoters, thus, tuning the input/output signal ratio. Next, by combining up to three ECF-switches, we generated a set of “genetic-timer circuits”, the first synthetic circuits harboring more than one ECF. ECF-based timer circuits sequentially activate a series of target genes with increasing time delays, moreover, the behavior of the circuits can be predicted by a set of mathematical models. In order to improve the dynamic response of the ECF-based constructs, we introduced anti-σ factors in our synthetic circuits. By doing so we first confirmed that anti-σ factors can exert an adverse effect on the growth of E. coli, thus we explored possible solutions. Our results demonstrate that anti-σ factors toxicity can be partially alleviated by generating truncated, soluble variants of the anti-σ factors and, eventually, completely abolished via chromosomal integration of the anti-σ factor-based circuits. Finally, after demonstrating that anti-σ factors can be used to generate a tunable time delay among ECF expression and target promoter activation, we designed ECF/AS-suicide circuits. Such circuits allow for the time-delayed cell-death of E. coli and will serve as a prototype for the further development of ECF/AS-based lysis circuits