N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

This paper presents a distributed finite-time adaptive integral-sliding-mode (ISM) control approach for a platoon of vehicles consisting of a leader and multiple followers subjected to bounded unknown disturbances. In order to avoid collisions among the vehicles, control protocols have to be designed to ensure string stability of the whole vehicle platoon. First, the constant time headway (CTH) policy known to improve string stability is applied to the case of zero initial spacing errors. Contrary to requiring zero initial spacing and zero initial velocity errors simultaneously in existing methods based on constant spacing (CS) policy, initial velocity errors here are not required to be zero. Then, since string stability condition can fail at the initial conditions, a modified CTH policy is constructed to overcome string instability caused by nonzero initial spacing errors. Moreover, the proposed adaptive ISM control schemes can be implemented without the requirement that the bounds of the disturbances be known in advance. In addition, one effective method is proposed to reduce the chattering phenomenon caused by the indicator function. Finally, simulation results are included to demonstrate its effectiveness and advantages over existing methods.

Distributed Adaptive Integrated-Sliding-Mode Controller Synthesis for String Stability of Vehicle Platoons

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Duality and network theory in passivity-based cooperative control

We present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs. Heterogeneous systems may have totally different dynamical models, albeit of the same dimension, or may possess equal models with different lumped parameters. We show that their behavior, when network-interconnected, is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces: on one hand, we have the so-called emergent dynamics and, on the other, the synchronization error dynamics. Based on this premise, we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior. To illustrate our main theoretical findings we broach a brief case-study on mutual synchronization of heterogeneous chaotic oscillators.

/pdf/synchronization-and-dynamic-consensus-of-heterogeneous-4upixc957v.pdf

Synchronization and Dynamic Consensus of Heterogeneous Networked Systems

This paper addresses formation control problems for heterogeneous groups of unicycle type mobile agents with fixed cruising speed. The heterogeneity in the group is caused by the cruising speeds being nonidentical, which complicates the motion coordination problem but is of practical relevance, for example, in unmanned aerial vehicle applications. We show that two different types of collective circular motion are possible in such groups: 1) a circular motion with common angular frequency and different radius for each agent; or 2) a circular motion with common radius but different angular frequency for each agent. For the first motion type, the orientation of all vehicles can additionally be coordinated such that an agreement or a balanced configuration is achieved. We present suitable control laws for each of these motion coordination tasks. These control laws explicitly take into account the nonidentical velocities and guarantee convergence to the desired configurations. Numerical examples illustrate all results.

Collective Circular Motion of Unicycle Type Vehicles With Nonidentical Constant Velocities

We investigate the problem of synchronizing nonidentical nonlinear dynamical systems by means of generalized diffusive couplings. The focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing nonidentical models. We show that for the problem to be solvable a synchronous steady state needs to exist. This condition leads to the requirement that all individual system models need to embed an internal model of some common endosystem. The latter condition is expressed in terms of nonlinear partial differential equations. The conditions derived in this paper are related to those known from the theory of output regulation.

On Synchronous Steady States and Internal Models of Diffusively Coupled Systems

This paper studies a design and analysis of distributed Kalman-Bucy filter in sensor networks. When observability of the target system from each sensor is lost, boundedness of the covariance matrices for the individual Riccati equations are not guaranteed. In order to overcome this difficulty and to recover the optimality of the centralized Kalman-Bucy filter, we introduce exchange of covariance matrices with other agents. Then, since those Riccati equations and estimators are heterogenous, achieving consensus among them becomes the question. We employ the recently introduced notion of averaged dynamics, which is the average of all distributed Kalman-Bucy filters' dynamics, and show that sufficiently strong coupling gains guarantee arbitrarily precise recovery of optimality and the estimation error converges to zero when there is no noise. Numerical simulations show the performance of the proposed scheme.

On distributed optimal Kalman-Bucy filtering by averaging dynamics of heterogeneous agents

Background: Cellular transformations which involve a significant phenotypical change of the cell’s state use bistable biochemical switches as underlying decision systems. Some of these transformations act over a very long time scale on the cell population level, up to the entire lifespan of the organism. Results: In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occuring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism’s lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. Conclusions: Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale. Background

/pdf/bridging-time-scales-in-cellular-decision-making-with-a-inko4td0am.pdf

Bridging time scales in cellular decision making with a stochastic bistable switch

The problem of output synchronization in a network of interconnected, heterogeneous linear systems is considered. The task is to find local controllers that guarantee synchronization using relative information only. Based on the Internal Model Principle for Synchronization, sufficient conditions are presented that lead to a constructive method for designing local dynamic controllers, which achieve this goal. Both time-invariant and time-varying networks are considered.

Jingbo Wu

Papers

Collective Circular Motion of Unicycle Type Vehicles With Nonidentical Constant Velocities

On Synchronous Steady States and Internal Models of Diffusively Coupled Systems

On distributed optimal Kalman-Bucy filtering by averaging dynamics of heterogeneous agents

Bridging time scales in cellular decision making with a stochastic bistable switch

A constructive approach to Synchronization using relative information