Stability analysis of genetic regulatory networks via a linear parameterization approach

This paper investigates the problem of finite-time stability (FTS) for a class of delayed genetic regulatory networks with reaction-diffusion terms. In order to fully utilize the system information, a linear parameterization method is proposed. Firstly, by applying the Lagrange’s mean-value theorem, the linear parameterization method is applied to transform the nonlinear system into a linear one with time-varying bounded uncertain terms. Secondly, a new generalized convex combination lemma is proposed to dispose the relationship of bounded uncertainties with respect to their boundaries. Thirdly, sufficient conditions are established to ensure the FTS by resorting to Lyapunov Krasovskii theory, convex combination technique, Jensen’s inequality, linear matrix inequality, etc. Finally, the simulation verifications indicate the validity of the theoretical results.

On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

This paper formulates the properties of point reachability and approximate point reachability of either a targeted state or output values in a general dynamic system which possess a linear time-varying dynamics with respect to a given reference nominal one and, eventually, an unknown structured nonlinear dynamics. Such a dynamics is upper-bounded by a function of the state and input. The results are obtained for the case when the time-invariant nominal dynamics is perfectly known while its time-varying deviations together with the nonlinear dynamics are not precisely known and also for the case when only the nonlinear dynamics is not precisely known. Either the controllability gramian of the nominal linearized system with constant linear parameterization or that of the current linearized system (which includes the time-varying linear dynamics) are assumed to be non-singular. Also, some further results are obtained for the case when the control input is eventually saturated and for the case when the controllability gramians of the linear parts are singular. Examples of the derived theoretical results for some epidemic models are also discussed.

Identification of the platform with electric drive using a differentiating filters

The paper presents an example of solving the parameter identification problem in case of platform with one degrees of freedom has been also presented. The parameter identification algorithm based on linear parameterization of the platform model and the least square criteria is developed. The desired derivatives of measured signals are estimated by means of designed differentiation filters. The required derivative order depends on the order of differential equations describing the object. The model was identified and verified using measurement results obtained for a real system.

Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

Methods for Estimating Climate Anomaly Forcing Patterns

Inverse methods for determining the anomalous mean forcing functions responsible for climate change are investigated. First, an iterative method is considered, and it is shown to successfully reproduce forcing functions for various idealized and observed climate states using quasigeostrophic simulations. Second, a new inverse method that is more computationally efficient is presented. This method closes the mean-field equations by representing the second-order statistical moments, the transient eddy heat and momentum (or potential vorticity) fluxes, as linear functions of the mean field. The coefficients of the linear parameterization are determined by least squares regression. It is shown that the new method also successfully reproduces the anomalous forcing functions responsible for climatic changes in quasigeostrophic simulations.