Neural network hybrid adaptive control for nonlinear uncertain impulsive dynamical systems

A neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.     

State feedback for uncertain dynamical systems

We consider a linear dynamical system in which the system and input matrices, as well as the input, are uncertain. We present a control system consisting of a linear control to stabilize the nominal system, a nonlinear control to cope with the uncertainties, and an insensitive observer for the state estimation. Practical stability is guaranteed for uncertainties with known bounds. Furthermore, the control system is designed to achieve insensitivity against parameter variations. The theoretical results are illustrated by an application to the suspension control of a maglev vehicle.     

Robust stability of uncertain impulsive dynamical systems

This paper studies robust stability of uncertain impulsive dynamical systems. By introducing the concepts of uniformly positive definite matrix functions and Hamilton–Jacobi/Riccati inequalities, several criteria on robust stability, robust asymptotic stability and robust exponential stability are established. An example is also worked through to illustrate our results.     

Stability analysis of quasilinear uncertain dynamical systems

In this paper, we establish new conditions of uniform asymptotic stability for uncertain quasilinear systems. Also, a new class of Lyapunov functions: canonical matrix-valued Lyapunov functions is presented and used for stability analysis. Illustrative examples are given.     

On observing the states of uncertain dynamical systems

For the implementation of a stable asymptotic reduced-order Luenberger observer, which is not sensitive to unknown disturbances entering the system, it is shown that specific columns of the measurement matrixC must be different from zero.This research was supported by the Technion VPR Fund, L. Rogow Aeronautical Research Fund.The author wishes to thank E. P. Ryan, G. Leitmann, and S. Gutman for helpful discussions.     

Zeno phenomenon in hybrid dynamical systems

A way to prolong Zeno solutions to hybrid dynamical system beyond Zeno time is proposed. Additionally, we provide a new definition of asymptotic stability that is equipped with sufficient conditions for its verification. It allows to investigate long-term behavior of the prolonged solutions to hybrid dynamical systems. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One approach to the control of uncertain dynamical systems

We present a controller design methodology for uncertain systems which is based on the constructive use of Lyapunov stability theory. The uncertainties, which are deterministic, are characterized by certain structural conditions and known as well as unknown bounds. As a consequence of the Lyapunov approach, the methodology is not restricted to linear or time-invariant systems. The robustness of these controllers in the presence of singular perturbations is considered. The situation in which the full state of the system is not available for measurement is also considered as are other generalizations.     

Modelling framework for artificial hybrid dynamical systems

Many current industry branches use hybrid approaches to solve complex application problems. Over the last decades, different tools for the simulation of such hybrid systems (e.g. Hysdel and YAMLIP) as well as the identification of hybrid systems (e.g. HIT, MLP and OAF NN) have been developed. The framework presented in this work facilitates the integration of artificial feed-forward neural networks in the modelling process of hybrid dynamical systems (HDS). Additionally, the framework provides a structured language for characterising these feed-forward networks itself. Therefore, an interdisciplinary exchange in the field of neural networks and its integration into hybrid dynamical systems is enabled. Focusing on hybrid systems with autonomous events, two different approaches, namely the artificial hybrid model and the artificial hybrid dynamics, are introduced. Challenges of the modelling process of HDS are reflected and advantages as well as disadvantages are discussed. The case study includes two common examples of HDS and analyses the simulation results and examines limitations of the modelling framework.     

Newton's method and complex dynamical systems

This article is devoted to the discussion of Newton's method. Beginning with the old results of A.Cayley and E.Schröder we proceed to the theory of complex dynamical systems on the sphere, which was developed by G.Julia and P.Fatou at the beginning of this century, and continued by several mathematicians in recent years.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters

This paper investigates the adaptive synchronization in the drive-response fractional-order dynamical networks with uncertain parameters. By means of both the stability theory of fractional-order differential system and the adaptive control technique, a novel adaptive synchronization controller is developed with a more general and simpler analytical expression, which does not contain the parameters of the complex network, and effective adaptive laws of parameters. Furthermore, the very strong and conservative uniformly Lipschitz condition on the node dynamics of complex network is released. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyper-chaotic node dynamics are presented.     

Synchronization of uncertain hybrid switching and impulsive complex networks

This paper considers the asymptotic synchronization problem for a class of uncertain complex networks (CNs) with hybrid switching and impulsive effects. The switches and impulses occur by following a time sequence which is characterized by dwell-time constraint. By designing Lyapunov function with time-varying matrix parameter, two general synchronization criteria formulated by matrix inequalities are first given, which unify synchronizing and desynchronizing impulses. Then specific conditions in terms of linear matrix inequalities (LMIs) are given by partitioning the dwell time and using convex combination technique. Compared with those criteria which are only applicable to pure synchronizing impulses or pure desynchronizing impulses, our results are more practical. It is shown that the switched impulsive CNs (SICNs) can be synchronized by desynchronizing impulses even though CNs without impulse are unsynchronized. Numerical examples are given to show the effectiveness of our new results.     

Energy dissipating hybrid control for impulsive dynamical systems

A novel class of fixed-order, energy-based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in nonsmooth Euler–Lagrange, hybrid port-controlled Hamiltonian, and lossless impulsive dynamical systems. These dynamic controllers combine a logical switching architecture with hybrid dynamics to guarantee that the system plant energy is strictly decreasing across switchings. The general framework leads to hybrid closed-loop systems described by impulsive differential equations. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and an illustrative numerical example is given to demonstrate the efficacy of the proposed approach.     

Guaranteed asymptotic stability for a class of uncertain linear dynamical systems

We consider a class of linear dynamical systems with bounded, Lebesgue-measurable uncertainties in the system and input matrices as well as in the input itself. A state feedback control is derived, which guarantees global, uniform asymptotic stability of the zero state; this control is continuous, except at the zero state.This paper is based in part on research supported by the National Science Foundation.     

Practical stabilizability of uncertain dynamical systems: Application to robotic tracking

The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to . The theory is illustrated in a numerical example of a robot with two degrees of freedom.This paper is based on research supported by the National Science Foundation and the Air Force Office of Scientific Research under Grant ECS-8210324 and by the UK Science and Engineering Research Council under Grants GR/B/32047 and GR/C/43658. This research was carried out, in part, while G. Leitmann was the recipient of a US Senior Scientist Award of the Alexander von Humboldt Foundation.     

Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling

This paper proposes an adaptive control method to achieve the lag synchronization between uncertain complex dynamical network having delayed coupling and a non-identical reference node. Unknown parameters of both the network and reference node are estimated by adaptive laws obtained by Lyapunov stability theory. With the estimated parameters, the proposed method guarantees the globally asymptotical synchronization of the network in spite of unknown bounded disturbances. The effectiveness of our work is verified through a numerical example and simulation.     

Sliding mode control experiments of uncertain dynamical systems with time delay

This article presents the simulation and experimental studies for the nonlinear time-delayed dynamical systems with uncertainties. A rotary flexible joint made by Quanser is chosen as the model system to investigate the method for sliding mode control design. We considered the geometric nonlinearity of the flexible joint consisting of two linear springs. The system is assumed to have constant delay time and uncertain parameters with known upper and lower bounds. We also design an optimal sliding surface for the sliding mode control. Simulations and experiments are carried out to demonstrate the utility of the control method. Finally, the results from the simulations and experiments are in excellent agreement.