Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Stochastic hybrid system : modelling and verification

Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult. One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization. In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis. We propose a powerful unifying paradigm that combines analytical and formal methods. Its applications vary from air traffic control to communication networks and healthcare systems. The stochastic hybrid system paradigm has an explosive development. This is because of its very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems. Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability analysis, model checking). These constitute the major motivations of our research. We investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural way. The concrete contribution of this thesis has four major milestones: 1. A new and a very general model for stochastic hybrid systems; 2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities; 3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated. 4. Considering the communication issue, we extend the modelling paradigm

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Leader-following consensus for lower-triangular nonlinear multi-agent systems with unknown controller and measurement sensitivities

summary:In this paper, a novel consensus algorithm is presented to handle with the leader-following consensus problem for lower-triangular nonlinear MASs (multi-agent systems) with unknown controller and measurement sensitivities under a given undirected topology. As distinguished from the existing results, the proposed consensus algorithm can tolerate to a relative wide range of controller and measurement sensitivities. We present some important matrix inequalities, especially a class of matrix inequalities with multiplicative noises. Based on these results and a dual-domination gain method, the output consensus error with unknown measurement noises can be used to construct the compensator for each follower directly. Then, a new distributed output feedback control is designed to enable the MASs to reach consensus in the presence of large controller perturbations. In view of a Lyapunov function, sufficient conditions are presented to guarantee that the states of the leader and followers can achieve consensus asymptotically. In the end, the proposed consensus algorithm is tested and verified by an illustrative example

Fault-tolerant Synchronization of Autonomous Underwater Vehicles

The main objective of this thesis is to develop a fault-tolerant and reconfigurable synchronization scheme based on model-based control protocols for stern and sail hydroplanes that are employed as actuators in the attitude control subsystem (ACS) of an autonomous underwater vehicle (AUV). In this thesis two control approaches are considered for synchronization, namely i) state feedback synchronization, and ii) output feedback synchronization. Both problems are tackled by proposing a passive control approach as well as an active reconfiguration (re-designing the control gains). For the ”state feedback” synchronization scheme, to achieve consensus the relative/absolute measurements of the AUV’s states (position and attitude) are available. The states of a longitudinal model of an AUV are mainly heave, pitch, and their associated rates. For the state feedback problem we employ a static protocol, and it is shown that the multi-agent system will synchronize in the stochastic mean square sense in the presence of measurement noise. However, the resulting performance index defined as the accumulated sum of variations of control inputs and synchronization errors is high. To deal with this problem, Kalman filtering is used for states estimation that are used in synchronization protocol. Moreover, the e�ffects of parameter uncertainty of the agent’s dynamics are also investigated through simulation results. By employing the static protocol it is demonstrated that when a loss of e�ffectiveness (LOE) or float fault occurs the synchronization can still be achieved under some conditions. Finally, one of the main problems that is tackled in the state feedback scenario is our proposed proportional-integral (PI) control methodology to deal with the lock in place (LIP) fault. It is shown that if the LIP fault occurs, by employing a PI protocol the synchronization could still be achieved. Finally, our proposed dynamic synchronization protocol methodology is applied given that the fault (LOE/float) severity is known. Since after a fault occurrence the agents become heterogeneous, employing the dynamic scheme makes the task of reconfiguration (redesigning the gains) more e�ffective. For the ”output feedback” synchronization approach, to achieve consensus relative/absolute measurements of the AUV’s states except the pitch rate are available. For the output feedback problem a dynamic protocol through a Luenberger observer is first employed for state estimation and the synchronization achievement is demonstrated. Then, a system under state and measurement noise is considered, and it is shown that by employing a Kalman filter for the state estimation; the multi-agent system will synchronize in the stochastic mean square sense. Furthermore, by employing the static protocol, it is shown that when a LOE/float fault occurs the synchronization is still achieved under certain conditions. Finally, one of the main problems that is tackled in the output feedback scenario is our proposed dynamic controller methodology. The results of this scheme are compared with another approach that exploits both dynamic controller and dynamic observer. The former approach has less computational e�ort and results in more a robust control with respect to the actuator fault. The reason is that the later method employs an observer that uses the control input matrix information. When fault occurs, this information will not be correct any more. However, if there is a need to redesign the synchronization gains under faulty scenario, the later methodology is preferred. The reason is that the former approach becomes complicated when there is a fault even though its severity is known. In this thesis, fault-tolerant synchronization of autonomous underwater vehicles is considered. In the first chapter a brief introduction on the motivation, problem definition, objectives and the methodologies that are used in the dissertation are discussed. A literature review on research dedicated to synchronization, fault diagnosis, and fault-tolerant control is provided. In Chapter 2, a through literature review on unmanned underwater vehicles is covered. It also comprises a comprehensive background information and definitions including algebraic graph theory, matrix theory, and fault modeling. In the problem statement, the two main problems in this thesis, namely state feedback synchronization and output feedback synchronization are discussed. Chapters 3 and 4 will cover these two problems, their solutions, and the corresponding simulation results that are provided. Finally, Chapter 5 includes a discussion of conclusions and future work

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

State of the art of cyber-physical systems security: An automatic control perspective

Cyber-physical systems are integrations of computation, networking, and physical processes. Due to the tight cyber-physical coupling and to the potentially disrupting consequences of failures, security here is one of the primary concerns. Our systematic mapping study sheds light on how security is actually addressed when dealing with cyber-physical systems from an automatic control perspective. The provided map of 138 selected studies is defined empirically and is based on, for instance, application fields, various system components, related algorithms and models, attacks characteristics and defense strategies. It presents a powerful comparison framework for existing and future research on this hot topic, important for both industry and academia

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area