Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

A model for pH determination during alcoholic fermentation of a grape must by Saccharomyces cerevisiae

A model to predict accurately pH evolution during alcoholic fermentation of must by Saccharomyces cerevisiae is proposed for the first time. The objective at least is to determine if the pH measurement could be used for predictive control. The inputs of the model are: the temperature, the concentrations in sugars, ethanol, nitrogen compounds, mineral elements (magnesium, calcium, potassium and sodium) and main organic acids (malic acid, citric acid, acetic acid, lactic acid, succinic acid). In order to avoid uncertainties coming from the possible precipitation, we studied this opportunity on a grape must without any tartaric acid, known as forming complexes with potassium and calcium during the fermentation. The model is based on thermodynamic equilibrium of electrolytic compounds in solution. The dissociation constants depend on the temperature and the alcoholic degree of the solution. The average activity coefficients are estimated by the Debbye–H¨uckel relation. A fictive diacid is introduced in the model to represent the unmeasured residual species. The molality of hydrogen ions and thus the pH are determined by solving a non-linear algebraic equations system consisted of mass balances, chemical equilibrium equations and electroneutrality principle. Simulation results showed a good capacity of the model to represent the pH evolution during fermentation

Batch fermentation process: Modelling and direct sensitivity analysis

Based on a nonlinear model, this article realizes an investigation of dynamic behaviour of a batch fermentation process using direct sensitivity analysis (DSA). The used nonlinear mathematical model has a good qualitative and quantitative description of the alcoholic fermentation process. This model has been discussed and validated by authors in other studies. The DSA of dynamic model was used to calculate the matrix of the sensitivity functions in order to determine the influence of the small deviations of initial state, control inputs, and parameters from the ideal nominal values on the state trajectory and system output in time. Process optimization and advanced control strategies can be developed based on this work

Reachability Analysis of Neural Networks with Uncertain Parameters

The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with additional uncertainties on their internal parameters (weight matrices and bias vectors of each layer), which may open the field of formal methods on neural networks to new topics, such as safe training or network repair. The first and main method that we propose relies on existing reachability analysis approach based on mixed monotonicity (initially introduced for dynamical systems). The second proposed approach extends the ESIP (Error-based Symbolic Interval Propagation) approach which was first implemented in the verification tool Neurify, and first mentioned in the publication of the tool VeriNet. Although the ESIP approach has been shown to often outperform the mixed-monotonicity reachability analysis in the classical case with uncertainties only on the network's inputs, we show in this paper through numerical simulations that the situation is greatly reversed (in terms of precision, computation time, memory usage, and broader applicability) when dealing with uncertainties on the weights and biases

Nanogram amounts of salicylic acid produced by the rhizobacterium Pseudomonas aeruginosa 7NSK2 activate the systemic acquired resistance pathway in bean

Root colonization by specific nonpathogenic bacteria can induce a systemic resistance in plants to pathogen infections. In bean, this kind of systemic resistance can be induced by the rhizobacterium Pseudomonas aeruginosa 7NSK2 and depends on the production of salicylic acid by this strain. In a model with plants grown in perlite we demonstrated that Pseudomonas aeruginosa 7NSK2-induced resistance is equivalent to the inclusion of 1 nM salicylic acid in the nutrient solution and used the latter treatment to analyze the molecular basis of this phenomenon. Hydroponic feeding of 1 nM salicylic acid solutions induced phenylalanine ammonia-lyase activity in roots and increased free salicylic acid levels in leaves. Because pathogen-induced systemic acquired resistance involves similar changes it was concluded that 7NSK2-induced resistance is mediated by the systemic acquired resistance pathway. This conclusion was validated by analysis of phenylalanine ammonia-lyase activity in roots and of salicylic acid levels in leaves of soil-grown plants treated with Pseudomonas aeruginosa. The induction of systemic acquired resistance by nanogram amounts of salicylic acid is discussed with respect to long-distance signaling in systemic acquired resistance