Variable structure control for three-variable autocatalytic reaction

In this paper, two irreversible exothermic autocatalytic reactions which carry out in continuous stirred tank reactor (CSTR) are considered. A differential-algebraic system is applied to model these chemical reactions. The stability and the dynamic behavior are studied for the differential-algebraic system. The Hopf bifurcation appears when the parameter exceeds a critical value. In order to eliminate this complex behavior, the differential-algebraic system is described by a single-input and single-output system with parameter varying within definite intervals, and then variable structure control with sliding mode based on a special power reaching law is designed to stabilize this chemical system. Numerical simulations are given to illustrate the effectiveness of the method.     

Exact computation of amplification for a class of nonlinear systems arising from cellular signaling pathways

A commonly employed measure of the signal amplification properties of an input/output system is its induced L² norm, sometimes also known as H_∞ gain. In general, however, it is extremely difficult to compute the numerical value for this norm, or even to check that it is finite, unless the system being studied is linear. This paper describes a class of systems for which it is possible to reduce this computation to that of finding the norm of an associated linear system. In contrast to linearization approaches, a precise value, not an estimate, is obtained for the full nonlinear model. The class of systems that we study arose from the modeling of certain biological intracellular signaling cascades, but the results should be of wider applicability.     

Global exponential stabilisation of acyclic traffic networks

This work is devoted to the construction of explicit feedback control laws for the robust global exponential stabilisation of general uncertain discrete-time acyclic networks. We consider discrete-time uncertain network models, which satisfy very weak assumptions. The construction of the controllers and the rigorous proof of the robust global exponential stability for the closed-loop system are based on recently proposed vector-Lyapunov function criteria, as well as the fact that the network is acyclic. It is shown, in this study, that the latter requirement is necessary for the existence of a robust global exponential stabiliser of the desired uncongested equilibrium point of the network. Our main focus is on traffic networks and all assumptions are related to features appearing in traffic models. An illustrative example demonstrates the applicability of the obtained results to realistic traffic flow networks.     

Synchronization of complex switched networks with two types of delays

In this paper, a general switched model of complex network with two types of delays is presented. The complex switched network (CSN) contains switching behaviors on both its nodes and topology configuration. Different from those CSNs studied in the existing literatures, the two switching signals dominating the nodes and topology are desynchronized. The two types of delays are the time-varying system delay in nodes and the time-varying coupling delay between nodes and they have different values. The inherent synchronization properties of the CSN have been studied not subject to any controllers. By defining a piecewise Lyapunov-Krasovskii function and by using the improved free-weighting matrix method, global exponential synchronizations are obtained. Illustrated example is presented to show the effectiveness of the proposed result.     

Existence criteria of periodic oscillations in cyclic gene regulatory networks

In this paper, we consider the existence conditions of periodic oscillations in large-scale cyclic gene regulatory networks. Using the Poincaré–Bendixson theorem for cyclic systems, we first show that the local instability of an equilibrium point implies the existence of periodic oscillations. We then derive the graphical and its equivalent analytic criteria for the existence of periodic oscillations based on local instability analysis. These criteria have a remarkable feature that they can be applied systematically to a large-scale cyclic gene regulatory network consisting of any number of genes. The latter part of this paper is devoted to analyze the relation between an equilibrium point and the biochemical parameters. This leads to an analytic existence criterion that explicitly takes the dependence of the equilibrium state on biochemical parameters into account, which is often overlooked in nonlinear system analyses. In particular, the novel physical quantities that are essential for determining the existence of periodic oscillations are obtained based on the rigorous analytic criterion.     

Analysis of partial stability problems using sum of squares techniques

A methodology for algorithmic construction of Lyapunov functions for problems concerning the stability of an equilibrium with respect to part of the system variables is proposed. This methodology utilizes the previously developed sum of squares technique to determine Lyapunov certificates. Conditions for stability with respect to part of the variables are developed that allow for Lyapunov functions to be determined in terms of a sum of squares. Asymptotic stability conditions in terms of sum of squares polynomials are developed for autonomous and non-autonomous systems. An example is presented which demonstrates the methodology and gives insight into the new stability conditions.     

Modeling,estimation, and analysis of epidemics over networks: An overview

We present and discuss a variety of mathematical models that have been proposed to capture the dynamic behavior of epidemic processes. We first present traditional group models for which no underlying graph structures are assumed, thus implying that instantaneous mixing between all members of a population occurs. Then we consider models driven by similar principles, but involving non-trivial networks where spreading occurs between connected nodes. We present stability analysis results for selected models from both classes, as well as simple least squares approaches for estimating the spreading parameters of the virus from data for each basic networked model structure. We also provide some simulation models. The paper should serve as a succinct, accessible guide for systems and control research efforts toward understanding and combating COVID-19 and future pandemics.     

Model decomposition and reduction tools for large-scale networks in systems biology

Biological system models are routinely developed in modern systems biology research following appropriate modelling/experiment design cycles. Frequently these take the form of high-dimensional nonlinear Ordinary Differential Equations that integrate information from several sources; they usually contain multiple time-scales making them difficult even to simulate. These features make systems analysis (understanding of robust functionality) — or redesign (proposing modifications in order to improve or modify existing functionality) a particularly hard problem. In this paper we use concepts from systems theory to develop two complementary tools that can help us understand the complex behaviour of such system models: one based on model decomposition and one on model reduction. Our aim is to algorithmically produce biologically meaningful, simplified models, which can then be used for further analysis and design. The tools presented are applied on a model of the Epidermal Growth Factor signalling pathway.     

Engine control unit PID controller calibration by means of local model networks

In this work a new approach for a fully automated calibration of nonlinear PID controllers and feedforward maps is introduced. Controller design poses a particularly challenging task in the application to internal combustion engines due to the nonlinear controller structure, which is usually prescribed by the manufacturer of the engine control unit (ECU). A dynamic local model network is used to represent the actual physical process as its architecture can beneficially be adopted for scheduling of the nonlinear controller parameters. The presented calibration technique uses a genetic algorithm to calibrate the nonlinear PID controller and a static model inversion to determine the feedforward map. Closed-loop stability is taken into account by incorporating a Lyapunov function. Finally, an example demonstrates the effectiveness of the proposed method.     

Decentralized control of a class of large-scale nonlinear systems using neural networks

This paper designs a decentralized neural network (NN) controller for a class of nonlinear large-scale systems, in which strong interconnections are involved. NNs are used to handle unknown functions. The proposed scheme is proved guaranteeing the boundedness of the closed-loop subsystems using only local feedback signals.     

Multiple models switching control based on recurrent neural networks

This paper presents a novel approach in designing adaptive controller to improve the transient performance for a class of nonlinear discrete-time systems under different operating modes. The proposed scheme consists of generalized minimum variance (GMV) controllers and a compensating controller. GMV controllers are based on the known nominal linear multiple models, while the compensating controller is based upon a recurrent neural network. The adaptation law of network weight is derived from Lyapunov stability theory. A suitable switching control strategy is applied to choose the best controller by the performance indices at every sampling instant. Simulations are discussed in order to illustrate the merits of the proposed method.     

Analysis of input-to-state stability for discrete time nonlinear systems via dynamic programming

The input-to-state stability (ISS) property for systems with disturbances has received considerable attention over the past decade or so, with many applications and characterizations reported in the literature. The main purpose of this paper is to present analysis results for ISS that utilize dynamic programming techniques to characterize minimal ISS gains and transient bounds. These characterizations naturally lead to computable necessary and sufficient conditions for ISS. Our results make a connection between ISS and optimization problems in nonlinear dissipative systems theory (including L₂-gain analysis and nonlinear H_∞ theory). As such, the results presented address an obvious gap in the literature.     

Neural networks for nonlinear state estimation

Estimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non-recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.     

Behavioural equivalences and interference metrics for mobile ad-hoc networks

Connectivity and communication interference are two key aspects in mobile ad-hoc networks (MANETs). This paper proposes a process algebraic model targeted at the analysis of both such aspects. The framework includes a probabilistic process calculus and a suite of analytical techniques based on a probabilistic observational congruence and an interference-sensitive preorder. The former enables the verification of behavioural equivalences; the latter makes it possible to evaluate the interference level of behaviourally equivalent networks. The result is a comprehensive and effective framework for the behavioural analysis and a quantitative assessment of interference for wireless networks in the presence of node mobility. We show our techniques at work on two realistic case studies.     

Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics

The objective of this paper is to analyze the finite-time convergence of a nonlinear but continuous consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis are more challenging than those under the well-studied consensus algorithms for known linear systems. For this purpose, we propose a novel comparison based tool. By using this tool, it is shown that the proposed nonlinear consensus algorithm can guarantee finite-time convergence if the directed switching interaction graph has a directed spanning tree at each time interval. Specifically, the finite-time convergence is shown by comparing the closed-loop system under the proposed consensus algorithm with some well-designed closed-loop system whose stability properties are easier to obtain. Moreover, the stability and the finite-time convergence of the closed-loop system using the proposed consensus algorithm under a (general) directed switching interaction graph can even be guaranteed by the stability and the finite-time convergence of some well-designed nonlinear closed-loop system under some special directed switching interaction graph. This provides a stimulating example for the potential applications of the proposed comparison based tool in the stability analysis of linear/nonlinear closed-loop systems by making use of known results in linear/nonlinear systems.     

Nonlinear robust performance analysis using complex-step gradient approximation

In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The method is applied to two robust performance analysis problems. The accuracy and convergence rate of the solutions computed using the proposed approach are seen to be significantly better than those achieved using standard gradient approximation methods.     

Multi-agent compositional stability exploiting system symmetries

This paper considers nonlinear symmetric control systems. By exploiting the symmetric structure of the system, stability results are derived that are independent of the number of components in the system. This work contributes to the fields of research directed toward compositionality and composability of large-scale system in that a system can be “built-up” by adding components while maintaining system stability. The modeling framework developed in this paper is a generalization of many existing results which focus on interconnected systems with specific dynamics. The main utility of the stability result is one of scalability or compositionality. If the system is stable for a given number of components, under appropriate conditions stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system. The results are general and applicable to a wide class of problems. The examples in this paper focus on the formation control problems for multi-agent robotic systems.     

Synchronization in complex networks of phase oscillators: A survey

The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.     

Nonlinear systems identification using dynamic multi-time scale neural networks

In this paper, two Neural Network (NN) identifiers are proposed for nonlinear systems identification via dynamic neural networks with different time scales including both fast and slow phenomena. The first NN identifier uses the output signals from the actual system for the system identification. The on-line update laws for dynamic neural networks have been developed using the Lyapunov function and singularly perturbed techniques. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the neuron networks. The on-line identification algorithm with dead-zone function is proposed to improve nonlinear system identification performance. Compared with other dynamic neural network identification methods, the proposed identification methods exhibit improved identification performance. Three examples are given to demonstrate the effectiveness of the theoretical results.