Alejandro Vignoni

Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm

The super-twisting algorithm (STA) has become the prototype of second-order sliding mode algorithm. It achieves finite time convergence by means of a continuous action, without using information about derivatives of the sliding constraint. Thus, chattering associated to traditional sliding-mode observers and controllers is reduced. The stability and finite-time convergence analysis have been jointly addressed from different points of view, most of them based on the use of scaling symmetries (homogeneity), or non-smooth Lyapunov functions. Departing from these approaches, in this contribution we decouple the stability analysis problem from that of finite-time convergence. A nonlinear change of coordinates and a time-scaling are used. In the new coordinates and time-space, the transformed system is stabilized using any appropriate standard design method. Conditions under which the combination of the nonlinear coordinates transformation and the time-scaling is a stability preserving map are given. Provided convergence in the transformed space is faster than O(1/@t)-where @t is the transformed time-convergence of the original system takes place in finite-time. The method is illustrated by designing a generalized super-twisting observer able to cope with a broad class of perturbations.

Multi-objective optimization framework to obtain model-based guidelines for tuning biological synthetic devices: an adaptive network case.

BackgroundModel based design plays a fundamental role in synthetic biology. Exploiting modularity, i.e. using biological parts and interconnecting them to build new and more complex biological circuits is one of the key issues. In this context, mathematical models have been used to generate predictions of the behavior of the designed device. Designers not only want the ability to predict the circuit behavior once all its components have been determined, but also to help on the design and selection of its biological parts, i.e. to provide guidelines for the experimental implementation. This is tantamount to obtaining proper values of the model parameters, for the circuit behavior results from the interplay between model structure and parameters tuning. However, determining crisp values for parameters of the involved parts is not a realistic approach. Uncertainty is ubiquitous to biology, and the characterization of biological parts is not exempt from it. Moreover, the desired dynamical behavior for the designed circuit usually results from a trade-off among several goals to be optimized.ResultsWe propose the use of a multi-objective optimization tuning framework to get a model-based set of guidelines for the selection of the kinetic parameters required to build a biological device with desired behavior. The design criteria are encoded in the formulation of the objectives and optimization problem itself. As a result, on the one hand the designer obtains qualitative regions/intervals of values of the circuit parameters giving rise to the predefined circuit behavior; on the other hand, he obtains useful information for its guidance in the implementation process. These parameters are chosen so that they can effectively be tuned at the wet-lab, i.e. they are effective biological tuning knobs. To show the proposed approach, the methodology is applied to the design of a well known biological circuit: a genetic incoherent feed-forward circuit showing adaptive behavior.ConclusionThe proposed multi-objective optimization design framework is able to provide effective guidelines to tune biological parameters so as to achieve a desired circuit behavior. Moreover, it is easy to analyze the impact of the context on the synthetic device to be designed. That is, one can analyze how the presence of a downstream load influences the performance of the designed circuit, and take it into account.

Sliding mode reference conditioning for coordination in swarms of non-identical multi-agent systems

A novel approach is proposed for coordination of swarms of dynamical systems in order to provide them with a desired collective behavior. The approach is based on the sliding mode reference conditioning technique as local interaction handler among neighbor systems. Neighbor systems become connected when a virtual constraint between them is violated, leading to a time-varying switching topology for the connections in the swarm. The approach addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g. linear and nonlinear, different orders, constraints, etc.), assuming there is no leader. The main idea is to shape the systems local feasible references in order to keep them coordinated. Coordination is understood as invariance of a set defined by some aimed relationship among the references. This implies considering the local goals, the systems constraints and the achievable performances as well. To show the applicability of the approach, the problem of coordinating a swarm of different dynamical systems with control saturations is addressed as a particular case.

Dynamical Systems Coordination via Sliding Mode Reference Conditioning

Abstract A novel methodology is proposed for coordination of dynamical systems. The scheme is based on the sliding mode reference conditioning technique in a sort of supervisory level. The approach addresses the problem of coordinating dynamical systems with possible different dynamics ( e.g. linear and nonlinear, different orders, constraints, etc. ). To achieve this, the dynamics of each subsystem are hidden from the coordination mechanism. The main idea is to shape the systems local references in order to keep them coordinated. This implies considering the global goals, the systems constraints and the achievable performances as well. Sliding Mode Reference Conditioning (SMRC) is used for this purpose by means of a hierarchical supervisory structure. To show the applicability of the approach, the problem of coordinating a number of different dynamical systems with control saturations is addressed as a particular case. Coordination will be understood as actuating on the systems references to achieve some collective behavior considering the individual restrictions of each system.

Improvement of a CLE stochastic simulation of gene synthetic network with quorum sensing and feedback in a cell population

We investigate the possibility of performing stochastic simulation of a synthetic gene circuit that includes a cell-to-cell communication system with an intracellular feedback control circuit. We propose an implementation of the CLE stochastic simulation method that makes possible to simulate gene synthetic circuits involving cell-to-cell communication. We find the minimum number of samples ensuring the statistic moments over the population do not degrade. This allows us to reduce the total simulation time and improve the efficiency of the method. Also we reveal that one realization of the population of interconnected cells, provided there is enough time to perform the time average, is useful to obtain representatives of the long-term moments of the population. Finally we show the potential of the improved approach by performing an analysis of the influence of the parameters in the LuxR promoter on the noise strength of the population.

Specific Kinetic Rates Regulation in Multi-Substrate Fermentation Processes

Abstract The regulation of the biomass specific growth rate is an important goal in many biotechnological applications. To achieve this goal in fed-batch processes, several control strategies have been developed employing a closed loop version of the exponential feeding law, an estimation of the controlled variable and some error feedback term. Moreover, in some bioprocesses there is more than one feeding flow entering the bioreactor and supplying different nutrients or substrates. Hence, the problem of estimating multiple substrate consumption rates together with the specific growth rate of the microorganism becomes relevant. In this context, the dynamic behavior of fed-batch processes with multiple substrates and Haldane kinetics is further investigated. In particular, a nonlinear PI control law based on a partial state feedback with gain dependent on the output error is used. Then, with a recent developed algorithm for several kinetic rates estimation based on second-order sliding mode (SM) ideas, we extend the mentioned control strategy to a multi-substrate fed-batch bioprocess. The observer provides smooth estimates that converge in finite time to the time-varying parameters and allows independent design of the observer and controller dynamics. The features of the proposed estimation and control strategies are assessed by simulation in different scenarios.

UAV reference conditioning for formation control via set invariance and sliding modes

Abstract A novel methodology is proposed for formation control of UAVs. The scheme is based on the sliding mode reference conditioning technique in a sort of supervisory level. The main idea is to shape the UAVs references in order to keep them coordinated. This implies a virtual leader which has the information of the formation structure, position of the agents in the formation and bounds on the distance between its reference and the ones of the agents. Geometric set invariance techniques together with sliding mode control is used for this purpose in order to make some set, defined from the reference constraints, invariant. To show the applicability of the approach, the problem of coordination and formation a number UAVs in cartesian motion is illustrated through simulation results using non-linear identified models of the UAVs.

Multi-objective identification of synthetic circuits stochastic models using flow flcytometry data

Synthetic biology use mathematical models of biological circuits to predict the behavior of the designed synthetic devices, but also to help in the design of the circuit and for the selection of their biological components. Estimation of these models parameters remains a demanding problem that has been addressed by optimization of a weighted combination of different prediction errors, thus obtaining only one solution. This single-objective approach can be inadequate when trying to incorporate different kinds of experiments or to identify parameters for an ensemble of biological circuit models and even more when dealing with stochastic models and flow cytometry data. Stochasticity in biological systems, often referred to as gene expression noise, is ubiquitous and needs to be taken into account when modeling a biological system. Here we present a methodology based on multi-objective optimization to perform parameter estimation in stochastic models using flow citometry data. It uses a global multi-objective evolutionary algorithm and a multi-criteria decision making strategy to select the most suitable solutions. We obtain an approximation to the Pareto set that corresponds to the model parameters better fitting the experimental data. Then, the Pareto set is clustered according to the different experimental cases, allowing to analyze the sensitivity of model parameters. We show the methodology applicability through the case study of a genetic circuit which controls noisy protein expression in a cell population.

Promoter and transcription factor dynamics tune protein mean and noise strength in a quorum sensing-based feedback synthetic circuit

Gene expression is a fundamental cellular process. Its stochastic fluctuations due to intrinsic and extrinsic sources, known generically as ‘gene expression noise’, trigger both beneficial and harmful consequences for the cell behavior. Controlling gene expression noise is of interest in many applications in biotechnology, biomedicine and others. Yet, control of the mean expression level is an equally desirable goal. Here, we analyze a gene synthetic network designed to reduce gene expression noise while achieving a desired mean expression level. The circuit combines a negative feedback loop over the gene of interest, and a cell-to-cell communication mechanism based on quorum sensing. We analyze the ability of the circuit to reduce noise as a function of parameters that can be tuned in the wet-lab, and the role quorum sensing plays. Intrinsic noise is generated by the inherent stochasticity of biochemical reactions. On the other hand, extrinsic noise is due to variability in the cell environment and the amounts of cellular components that affect gene expression. We develop a realistic model of the gene synthetic circuit over the population of cells using mass action kinetics and the stochastic Chemical Langevin Equation to include intrinsic noise, with parameters drawn from a distribution to account for extrinsic noise. Stochastic simulations allow us to quantify the mean expression level and noise strength of all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in E. coli. Our in silico experiments reveal significant noise attenuation in gene expression through the interplay between quorum sensing and the negative feedback, allowing control of the mean expression and variance of the protein of interest. These in silico conclusions are validated by preliminary experimental results. This gene network could have important implications as a robust protein production system in industrial biotechnology. Author Summary Controlling gene expression level is of interest in many applications in biotechnology, biomedicine and others. Yet, the stochastic nature of biochemical reactions plays an important role in biological systems, and cannot be disregarded. Gene expression noise resulting from this stochasticity has been studied over the past years both in vivo, and in silico using mathematical models. Nowadays, synthetic biology approaches allow to design novel biological circuits, drawing on principles elucidated from biology and engineering, for the purpose of decoupled control of mean gene expression and its variance. We propose a gene synthetic circuit with these characteristics, using negative feedback and quorum sensing based cell-to-cell communication to induce population consensus. Our in silico analysis using stochastic simulations with a realistic model reveal significant noise attenuation in gene expression through the interplay between quorum sensing and the negative feedback, allowing control of the mean expression and variance of the protein of interest. Preliminary in vivo results fully agree with the computational ones.

Engineered Control of Genetic Variability Reveals Interplay among Quorum Sensing, Feedback Regulation, and Biochemical Noise

Stochastic fluctuations in gene expression trigger both beneficial and harmful consequences for cell behavior. Therefore, achieving a desired mean protein expression level while minimizing noise is of interest in many applications, including robust protein production systems in industrial biotechnology. Here, we consider a synthetic gene circuit combining intracellular negative feedback and cell-to-cell communication based on quorum sensing. Accounting for both intrinsic and extrinsic noise, stochastic simulations allow us to analyze the capability of the circuit to reduce noise strength as a function of its parameters. We obtain mean expression levels and noise strengths for all species under different scenarios, showing good agreement with system-wide available experimental data of protein abundance and noise in Escherichia coli. Our in silico experiments, validated by preliminary in vivo results, reveal significant noise attenuation in gene expression through the interplay between quorum sensing and negative feedback and highlight the differential role that they play in regard to intrinsic and extrinsic noise.