Filtering for nonlinear genetic regulatory networks with stochastic disturbances

In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures

State estimation of a solar direct steam generation mono-tube cavity receiver using a modified Extended Kalman Filtering scheme

State estimation plays a key role in the development of advanced control strategies for Concentrating Solar Thermal Power (CSP) systems, by providing an estimate of process variables that are otherwise infeasible to measure. The present study proposes a state estimation scheme for a once-through direct steam generation plant, the SG4 steam generation system at the Australian National University. The state estimation scheme is a modified Extended Kalman Filter that computes an estimate of the internal variables of the mono-tube cavity receiver in the SG4 system, from a dynamic non-linear model of the receiver. The proposed scheme augments the capabilities of a Continuous-Direct Extended Kalman Filter to deal with the switched nature of the receiver, in order to produce estimates during system start-up, cloud transients and operation of the plant. The estimation process runs at regular sample intervals and happens in two stages, a prediction and a correction stage. The prediction stage uses the receiver model to calculate the evolution of the system and the correction stage modifies the predicted estimate from measurements of the SG4 system. The resulting estimate is a set of internal variables describing the current state of the receiver, termed the state vector. This paper presents a description of the modified Extended Kalman Filter and an evaluation of the scheme using computer simulations and experimental runs in the SG4 system. Simulations and experimental results in this paper show that the filtering scheme improves a receiver state vector estimation purely based on the receiver model and provides estimates of a quality sufficient for closed loop control.This work has been supported by the Australian Renewable Energy Agency (ARENA)

Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays (FPGAs). This architecture allows the design of appropriate filters and multiple time delays which greatly extend the possibilities for exploring synchronization patterns in arbitrary topological networks. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony

Online Discrimination of Nonlinear Dynamics with Switching Differential Equations

How to recognise whether an observed person walks or runs? We consider a dynamic environment where observations (e.g. the posture of a person) are caused by different dynamic processes (walking or running) which are active one at a time and which may transition from one to another at any time. For this setup, switching dynamic models have been suggested previously, mostly, for linear and nonlinear dynamics in discrete time. Motivated by basic principles of computations in the brain (dynamic, internal models) we suggest a model for switching nonlinear differential equations. The switching process in the model is implemented by a Hopfield network and we use parametric dynamic movement primitives to represent arbitrary rhythmic motions. The model generates observed dynamics by linearly interpolating the primitives weighted by the switching variables and it is constructed such that standard filtering algorithms can be applied. In two experiments with synthetic planar motion and a human motion capture data set we show that inference with the unscented Kalman filter can successfully discriminate several dynamic processes online

Tunable n-path notch filters for blocker suppression: modeling and verification

N-path switched-RC circuits can realize filters with very high linearity and compression point while they are tunable by a clock frequency. In this paper, both differential and single-ended N-path notch filters are modeled and analyzed. Closed-form equations provide design equations for the main filtering characteristics and nonidealities such as: harmonic mixing, switch resistance, mismatch and phase imbalance, clock rise and fall times, noise, and insertion loss. Both an eight-path single-ended and differential notch filter are implemented in 65-nm CMOS technology. The notch center frequency, which is determined by the switching frequency, is tunable from 0.1 to 1.2 GHz. In a 50- environment, the N-path filters provide power matching in the passband with an insertion loss of 1.4–2.8 dB. The rejection at the notch frequency is 21–24 dB,P1 db> + 2 dBm, and IIP3 > + 17 dBm