Secure control for remote networked stochastic systems via integral sliding mode

This paper deals with the secure control problem for a class of networked stochastic systems with false data injection attacks via an integral sliding mode control technique. The networked control system is with a hierarchical structure, and the main controller and a remote controller are considered to realize the secure control against false data injection attacks on the network between a main controller and the plant. A mode-shared event-triggering controller is designed as the main controller, by utilizing a time delay approach. An input-output model based on a two-term approximation is applied to cope with the formulated time-varying delay. Then, the scaled small gain theory is employed to analyze the stability of the resulting system. Sufficient conditions on ensuring the desired system performance are derived and then the controller parameters are synthesized. Moreover, an elaborated sliding mode control law is proposed for the desired secure control action. Finally, two simulation examples are permitted to verify the effectiveness of the theoretical derivations.

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

This paper investigates the issue of event-triggered adaptive optimal tracking control for uncertain nonlinear systems with stochastic disturbances and dynamic state constraints. To handle the dynamic state constraints, a novel unified tangent-type nonlinear mapping function is proposed. A neural networks (NNs)-based identifier is designed to cope with the stochastic disturbances. By utilizing adaptive dynamic programming (ADP) of identifier-actor-critic architecture and event triggering mechanism, the adaptive optimized event-triggered control (ETC) approach for the nonlinear stochastic system is first proposed. It is proven that the designed optimized ETC approach guarantees the robustness of the stochastic systems and the semi-globally uniformly ultimately bounded in the mean square of the NNs adaptive estimation error, and the Zeno behavior can be avoided. Simulations are offered to illustrate the effectiveness of the proposed control approach.

A Markovian model for the spread of the SARS-CoV-2 virus

We propose a Markovian stochastic approach to model the spread of a SARS-CoV-2-like infection within a closed group of humans. The model takes the form of a Partially Observable Markov Decision Process (POMDP), whose states are given by the number of subjects in different health conditions. The model also exposes the different parameters that have an impact on the spread of the disease and the various decision variables that can be used to control it (e.g, social distancing, number of tests administered to single out infected subjects). The model describes the stochastic phenomena that underlie the spread of the epidemic and captures, in the form of deterministic parameters, some fundamental limitations in the availability of resources (hospital beds and test swabs). The model lends itself to different uses. For a given control policy, it is possible to verify if it satisfies an analytical property on the stochastic evolution of the state (e.g., to compute probability that the hospital beds will reach a fill level, or that a specified percentage of the population will die). If the control policy is not given, it is possible to apply POMDP techniques to identify an optimal control policy that fulfils some specified probabilistic goals. Whilst the paper primarily aims at the model description, we show with numeric examples some of its potential applications.

Constraints on Hebbian and STDP learned weights of a spiking neuron

We analyse mathematically the constraints on weights resulting from Hebbian and STDP learning rules applied to a spiking neuron with weight normalisation. In the case of pure Hebbian learning, we find that the normalised weights equal the promotion probabilities of weights up to correction terms that depend on the learning rate and are usually small. A similar relation can be derived for STDP algorithms, where the normalised weight values reflect a difference between the promotion and demotion probabilities of the weight. These relations are practically useful in that they allow checking for convergence of Hebbian and STDP algorithms. Another application is novelty detection. We demonstrate this using the MNIST dataset.

Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.

Parameter inference for stochastic single-cell dynamics from lineage tree data

Background

With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference with this type of data. Most of currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by the population structure. However, this information is essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle.

Results

In this work, we propose a Bayesian framework for parameter inference on single-cell time-lapse data from lineage trees. Our method relies on a combination of Sequential Monte Carlo for approximating the parameter likelihood function and Markov Chain Monte Carlo for parameter exploration. We demonstrate our inference framework on two simple examples in which the lineage tree information is crucial: one in which the cell phenotype can only switch at cell division and another where the cell state fluctuates slowly over timescales that extend well beyond the cell-cycle duration.

Conclusion

There exist several examples of biological processes, such as stem cell fate decisions or epigenetically controlled phase variation in bacteria, where the cell ancestry is expected to contain important information about the underlying system dynamics. Parameter inference methods that discard this information are expected to perform poorly for such type of processes. Our method provides a simple and computationally efficient way to take into account single-cell lineage tree data for the purpose of parameter inference and serves as a starting point for the development of more sophisticated and powerful approaches in the future.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0425-1) contains supplementary material, which is available to authorized users.

A data driven nonlinear stochastic model for blood glucose dynamics

The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.

Modeling Excitable Dynamics of Chemotactic Networks

The study of chemotaxis has benefited greatly from computational models that describe the response of cells to chemoattractant stimuli. These models must keep track of spatially and temporally varying distributions of numerous intracellular species. Moreover, recent evidence suggests that these are not deterministic interactions, but also include the effect of stochastic variations that trigger an excitable network. In this chapter we illustrate how to create simulations of excitable networks using the Virtual Cell modeling environment.

The stochastic system approach for estimating dynamic treatments effect

The problem of assessing the effect of a treatment on a marker in observational studies raises the difficulty that attribution of the treatment may depend on the observed marker values. As an example, we focus on the analysis of the effect of a HAART on CD4 counts, where attribution of the treatment may depend on the observed marker values. This problem has been treated using marginal structural models relying on the counterfactual/potential response formalism. Another approach to causality is based on dynamical models, and causal influence has been formalized in the framework of the Doob-Meyer decomposition of stochastic processes. Causal inference however needs assumptions that we detail in this paper and we call this approach to causality the "stochastic system" approach. First we treat this problem in discrete time, then in continuous time. This approach allows incorporating biological knowledge naturally. When working in continuous time, the mechanistic approach involves distinguishing the model for the system and the model for the observations. Indeed, biological systems live in continuous time, and mechanisms can be expressed in the form of a system of differential equations, while observations are taken at discrete times. Inference in mechanistic models is challenging, particularly from a numerical point of view, but these models can yield much richer and reliable results.

A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model

We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks.

Optimal scheduling of multiple sensors in continuous time

This paper considers an optimal sensor scheduling problem in continuous time. In order to make the model more close to the practical problems, suppose that the following conditions are satisfied: only one sensor may be active at any one time; an admissible sensor schedule is a piecewise constant function with a finite number of switches; and each sensor either doesn't operate or operates for a minimum non-negligible amount of time. However, the switching times are unknown, and the feasible region isn't connected. Thus, it's difficult to solve the problem by conventional optimization techniques. To overcome this difficulty, by combining a binary relaxation, a time-scaling transformation and an exact penalty function, an algorithm is developed for solving this problem. Numerical results show that the algorithm is effective.