Formal Controller Synthesis from Specifications Given by Discrete-Time Hybrid Automata

This paper deals with formal controller synthesis for discrete-time dynamical systems. For a specification under the form of a discrete-time hybrid automaton, we aim at synthesizing controllers such that the trajectories of the closed-loop system are also trajectories of the hybrid automaton. We first show that the existence of an alternating simulation relation from the specification to the open-loop system is a necessary and sufficient condition for the existence of such controllers. Then, we propose an approach based on the use of symbolic (i.e. finite-state) abstractions of both the system and the specification. Effective computations are discussed for systems that are monotone and for specifications given by piecewise affine hybrid automata. We extend our approach to handle specifications with additional safety or reachability requirements. Finally, we illustrate our approach with examples from autonomous vehicle control

Ozone and nitrogen dioxide above the northern Tien Shan

The results of systematic perennial measurements of the total ozone (since 1979) and nitrogen dioxide column (since 1983) in the atmosphere in the European-Asian continent center above the mountainmass of the Tien Shan are given. This region is distinguished by a great number of sunny days during a year. The observation station is at the Northern shore of Issyk Kul Lake (42.56 N 77.04 E 1650 m above the sea level). The measurement results are presented as the monthly averaged atmospheric total ozone and NO2 stratospheric column abundances (morning and evening). The peculiarities of seasonal variations of ozone and nitrogen dioxide atmospheric contents, their regular variances with a quasi-biennial cycles and trends have been noticed. Irregular variances of ozone and nitrogen dioxide atmospheric contents, i.e. their positive and negative anomalies in the monthly averaged contents relative to the perennial averaged monthly means, have been analyzed. The synchronous and opposite in phase anomalies in variations of ozone and nitrogen dioxide atmospheric contents were explained by the transport and zonal circulation in the stratosphere (Kamenogradsky et al., 1990)

Sequence-specific DNA cleavage mediated by bipyridine polyamide conjugates

The design of molecules that damage a selected DNA sequence provides a formidable opportunity for basic and applied biology. For example, such molecules offer new prospects for controlled manipulation of the genome. The conjugation of DNA-code reading molecules such as polyamides to reagents that induce DNA damages provides an approach to reach this goal. In this work, we showed that a bipyridine conjugate of polyamides was able to induce sequence-specific DNA breaks in cells. We synthesized compounds based on two polyamide parts linked to bipyridine at different positions. Bipyridine conjugates of polyamides were found to have a high affinity for the DNA target and one of them produced a specific and high-yield cleavage in vitro and in cultured cells. The bipyridine conjugate studied here, also presents cell penetrating properties since it is active when directly added to cell culture medium. Harnessing DNA damaging molecules such as bipyridine to predetermined genomic sites, as achieved here, provides an attractive strategy for targeted genome modification and DNA repair studies

Universal Oligonucleotide Microarray for Sub-Typing of Influenza A Virus

A universal microchip was developed for genotyping Influenza A viruses. It contains two sets of oligonucleotide probes allowing viruses to be classified by the subtypes of hemagglutinin (H1–H13, H15, H16) and neuraminidase (N1–N9). Additional sets of probes are used to detect H1N1 swine influenza viruses. Selection of probes was done in two steps. Initially, amino acid sequences specific to each subtype were identified, and then the most specific and representative oligonucleotide probes were selected. Overall, between 19 and 24 probes were used to identify each subtype of hemagglutinin (HA) and neuraminidase (NA). Genotyping included preparation of fluorescently labeled PCR amplicons of influenza virus cDNA and their hybridization to microarrays of specific oligonucleotide probes. Out of 40 samples tested, 36 unambiguously identified HA and NA subtypes of Influenza A virus

Abstraction of Continuous-time Systems Based on Feedback Controllers and Mixed Monotonicity

International audienceIn this paper, we consider the problem of the computation of efficient symbolic abstractions for continuous-time control systems. The new abstraction algorithm builds symbolic models with the same number of states but fewer transitions in comparison to the one produced by the standard algorithm. At the same time, the new abstract system is at least as controllable as the standard one. The proposed algorithm is based on the solution of a region-to-region control synthesis problem. This solution is formally obtained using the theory of viscosity solutions of the dynamic programming equation and the theory of differential equations with discontinuous righthand side. In the new abstraction algorithm, the symbolic controls are essentially the feedback controllers that solve this control synthesis problem. The improvement in the number of transitions is achieved by reducing the number of successors for each symbolic control. For a certain class of control systems, with a suitable set of discretization parameters, the new algorithm may even produce deterministic abstract systems or systems with a singleton input alphabet. The approach is illustrated by examples that compare the two abstraction algorithms

Controller Synthesis for Nonlinear Systems with Reachability Specifications Using Monotonicity

International audienceIn this paper, we consider a control synthesis problem for a continuous-time nonlinear system. The problem under consideration consists in driving the state of the system to some target interval at a given time instant. We propose a solution based on candidate under-approximations of the backward reachable sets using multi-dimensional intervals. We show that a suitable controller can be designed by enforcing a monotonicity property of the closed-loop system on these intervals. For this purpose, we utilize the monotonicity conditions for nonlinear systems with inputs in the infinitesimal form. From these differential inequalities on the control strategy, we design some particular controllers which are time-varying, linear with respect to the state. The approach is illustrated by two examples

Abstraction of Continuous-time Systems Based on Feedback Controllers and Mixed Monotonicity

International audienceIn this paper, we consider the problem of the computation of efficient symbolic abstractions for continuous-time control systems. The new abstraction algorithm builds symbolic models with the same number of states but fewer transitions in comparison to the one produced by the standard algorithm. At the same time, the new abstract system is at least as controllable as the standard one. The proposed algorithm is based on the solution of a region-to-region control synthesis problem. This solution is formally obtained using the theory of viscosity solutions of the dynamic programming equation and the theory of differential equations with discontinuous righthand side. In the new abstraction algorithm, the symbolic controls are essentially the feedback controllers that solve this control synthesis problem. The improvement in the number of transitions is achieved by reducing the number of successors for each symbolic control. For a certain class of control systems, with a suitable set of discretization parameters, the new algorithm may even produce deterministic abstract systems or systems with a singleton input alphabet. The approach is illustrated by examples that compare the two abstraction algorithms

Abstraction of Monotone Systems Based on Feedback Controllers

International audienceIn this paper, we consider the problem of computation of efficient symbolic abstractions for a certain subclass of continuous-time monotone control systems. The new abstraction algorithm utilizes the properties of such systems to build symbolic models with the same number of states but fewer transitions in comparison to the one produced by the standard algorithm. At the same time, the new abstract system is at least as controllable as the standard one. The proposed algorithm is based on the solution of a region-to-region control synthesis problem. This solution is formally obtained using the theory of viscosity solutions of the dynamic programming equation and the theory of differential equations with discontinuous right-hand side. In the new abstraction algorithm the symbolic controls are essentially the feedback controllers which solve this control synthesis problem. The improvement in the number of transitions is achieved by reducing the number of successors for each symbolic control. The approach is illustrated by an example which compares the two abstraction algorithms