A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family

Analytical modeling of vibrations in a damaged beam using Green-Volterra formalism

Structural Health Monitoring of aeronautic composite structures through Lamb waves can advantageously exploit the fact that Lamb wave damage interaction is nonlinear. However, one di culty in this context is to be able to distinguish between nonlinearities due to the propagation (i.e. ma- terial or geometrical nonlinearities) and those due to the damage itself that are of main interest here. This work proposes to use the Green-Volterra formal- ism to build up a model for Lamb Wave propagation and damage interaction that is complex enough to represent both types of nonlinearities, and simple enough to be used for simulation and estimation purposes. This approach is presented for the low frequency S0 mode nonlinear propagation in a dam- aged beam. An analytical model of the nonlinear wave propagation is rst derived, where the damage is represented with a polynomial sti ness char- acteristic acting via boundary conditions. This model is then used to derive the Green-Volterra series describing the nonlinear input-output relationship of the system. A modal decomposition of the Green-Volterra series is also pro- vided. Simulations are presented, and the proposed approach is successfully compared to state-of-the-art methods based on nite-elements models.This work has received funding from the European Union's Horizon 2020 research and innovation program under the REMAP project (grant agreement number 769288)

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.Comment: 1 Figures, 6 page

Scalable Verification of Linear Controller Software

We consider the problem of verifying software implementations of linear time-invariant controllers against mathematical specifications. Given a controller specification, multiple correct implementations may exist, each of which uses a different representation of controller state (e.g., due to optimizations in a third-party code generator). To accommodate this variation, we first extract a controller\u27s mathematical model from the implementation via symbolic execution, and then check input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of C code controller implementation using the combination of techniques such as symbolic execution, satisfiability solving and convex optimization. Through evaluation using randomly generated controller specifications of realistic size, we demonstrate that the scalability of this approach has significantly improved compared to our own earlier work based on the invariant checking method

Automatic Verification of Finite Precision Implementations of Linear Controllers

We consider the problem of verifying finite precision implementation of linear time-invariant controllers against mathematical specifications. A specification may have multiple correct implementations which are different from each other in controller state representation, but equivalent from a perspective of input-output behavior (e.g., due to optimization in a code generator). The implementations may use finite precision computations (e.g. floating-point arithmetic) which cause quantization (i.e., roundoff) errors. To address these challenges, we first extract a controller\u27s mathematical model from the implementation via symbolic execution and floating-point error analysis, and then check approximate input-output equivalence between the extracted model and the specification by similarity checking. We show how to automatically verify the correctness of floating-point controller implementation in C language using the combination of techniques such as symbolic execution and convex optimization problem solving. We demonstrate the scalability of our approach through evaluation with randomly generated controller specifications of realistic size

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory

What Happened to Gray Whales during the Pleistocene? The Ecological Impact of Sea-Level Change on Benthic Feeding Areas in the North Pacific Ocean

Gray whales (Eschrichtius robustus) undertake long migrations, from Baja California to Alaska, to feed on seasonally productive benthos of the Bering and Chukchi seas. The invertebrates that form their primary prey are restricted to shallow water environments, but global sea-level changes during the Pleistocene eliminated or reduced this critical habitat multiple times. Because the fossil record of gray whales is coincident with the onset of Northern Hemisphere glaciation, gray whales survived these massive changes to their feeding habitat, but it is unclear how.We reconstructed gray whale carrying capacity fluctuations during the past 120,000 years by quantifying gray whale feeding habitat availability using bathymetric data for the North Pacific Ocean, constrained by their maximum diving depth. We calculated carrying capacity based on modern estimates of metabolic demand, prey availability, and feeding duration; we also constrained our estimates to reflect current population size and account for glaciated and non-glaciated areas in the North Pacific. Our results show that key feeding areas eliminated by sea-level lowstands were not replaced by commensurate areas. Our reconstructions show that such reductions affected carrying capacity, and harmonic means of these fluctuations do not differ dramatically from genetic estimates of carrying capacity.Assuming current carrying capacity estimates, Pleistocene glacial maxima may have created multiple, weak genetic bottlenecks, although the current temporal resolution of genetic datasets does not test for such signals. Our results do not, however, falsify molecular estimates of pre-whaling population size because those abundances would have been sufficient to survive the loss of major benthic feeding areas (i.e., the majority of the Bering Shelf) during glacial maxima. We propose that gray whales survived the disappearance of their primary feeding ground by employing generalist filter-feeding modes, similar to the resident gray whales found between northern Washington State and Vancouver Island

Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria

In engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices