Additive noise effects in active nonlinear spatially extended systems

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first focus on a regime close to the instability onset (primary bifurcation), where the system can be described by a single dominant mode. We show analytically that the resulting noise in the equation describing the amplitude of the dominant mode largely depends on the nature of the stochastic forcing. For a highly degenerate noise, in the sense that it is acting on the first stable mode only, the amplitude equation is dominated by a pure multiplicative noise, which in turn induces the dominant mode to undergo several critical state transitions and complex phenomena, including intermittency and stabilisation, as the noise strength is increased. The intermittent behaviour is characterised by a power-law probability density and the corresponding critical exponent is calculated rigorously by making use of the first-passage properties of the amplitude equation. On the other hand, when the noise is acting on the whole subspace of stable modes, the multiplicative noise is corrected by an additive-like term, with the eventual loss of any stabilised state. We also show that the stochastic forcing has no effect on the dominant mode dynamics when it is acting on the second stable mode. Finally, in a regime which is relatively far from the instability onset, so that there are two unstable modes, we observe numerically that when the noise is acting on the first stable mode, both dominant modes show noise-induced complex phenomena similar to the single-mode case

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure

Frequency-domain subspace identification of nonlinear mechanical systems - Application to a solar array structure

The present paper addresses the experimental identification of a simplified realisation of a solar array structure in folded configuration. To this end, a nonlinear subspace identification technique formulated in the frequency domain, referred to as the FNSI method, is exploited. The frequency response functions of the underlying linear structure and the nonlinear coefficients are estimated by this approach. Nonlinearity is caused by impacts between adjacent panels and friction and gaps appearing in their clamping interfaces. This application is challenging for several reasons, which include high modal density and the complicated nature of the involved nonlinear mechanisms

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Control theory for infinite dimensional dynamical systems and applications to falling liquid film flows

In this thesis, we study the problem of controlling the solutions of various nonlinear PDE models that describe the evolution of the free interface in thin liquid films flowing down inclined planes. We propose a control methodology based on linear feedback controls, which are proportional to the deviation between the current state of the system and a prescribed desired state. We first derive the controls for weakly nonlinear models such as the Kuramoto-Sivashinsky equation and some of its generalisations, and then use the insight that the analytical results obtained there provide us to derive suitable generalisations of the controls for reduced-order long-wave models. We use two long-wave models to test our controls: the first order Benney equation and the first order weighted-residual model, and compare some linear stability results with the full 2-D Navier-Stokes equations. We find that using point actuated controls it is possible to stabilise the full range of solutions to the generalised Kuramoto-Sivashinsky equation, and that distributed controls have a similar effect on both long-wave models. Furthermore, point-actuated controls are efficient when stabilising the flat solution of both long-wave models. We extend our results to systems of coupled Kuramoto-Sivashinsky equations and to stochastic partial differential equations that arise by adding noise to the weakly nonlinear models.Open Acces

Optimal Universal Controllers for Roll Stabilization

Roll stabilization is an important problem of ship motion control. This problem becomes especially difficult if the same set of actuators (e.g. a single rudder) has to be used for roll stabilization and heading control of the vessel, so that the roll stabilizing system interferes with the ship autopilot. Finding the "trade-off" between the concurrent goals of accurate vessel steering and roll stabilization usually reduces to an optimization problem, which has to be solved in presence of an unknown wave disturbance. Standard approaches to this problem (loop-shaping, LQG, $H_{\infty}$-control etc.) require to know the spectral density of the disturbance, considered to be a \colored noise". In this paper, we propose a novel approach to optimal roll stabilization, approximating the disturbance by a polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic optimization problems in presence of polyharmonic disturbances can be solved by means of the theory of universal controllers developed by V.A. Yakubovich. An optimal universal controller delivers the optimal solution for any uncertain amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that provides a realistic vessel's model, we compare our design method with classical approaches to optimal roll stabilization. Among three controllers providing the same quality of yaw steering, OUC stabilizes the roll motion most efficiently

Stabilisation of state-and-input constrained nonlinear systems via diffeomorphisms: A Sontag's formula approach with an actual application

In this work, we provide a new and constructive outlook for the control of state-and-input constrained nonlinear systems. Previously, explicit solutions have been mainly focused on the finding of a barrier-like Lyapunov function, whereas we propose the construction of a diffeomorphism to map all the trajectories of the constrained dynamics into an unconstrained one. Careful analysis has revealed that only some foundations of differential geometry and a technical assumption are necessary to construct the proposed methodology based on the well-established theories of control Lyapunov functions and Sontag's universal formulae. Altogether, it allows us to obtain an explicit solution that even includes bounded constraints in the control action, giving the designer a way to decide (to some extent) the trade-off between control saturations and robustness. Moreover, this approach does not rely on the own structure of the system dynamics, therefore covering a broad class of nonlinear systems. The main advantage of this approach is that the use of a diffeomorphism allows the splitting of the mathematical treatment of the constraint and the Lyapunov controller design. The result has been successfully applied to solve the dynamic positioning of an actual ship, where the nonlinear state constraints describe a strait. This approach enabled us to design a control Lyapunov function and thereby use Sontag's formula to solve the stabilisation problem. Realistic simulations have been executed in a real scenario on the simulator owned by an international shipbuilding company.Postprint (author's final draft