Search results for "nonlinear"
showing 10 items of 3684 documents
Observer-based adaptive stabilization of a class of uncertain nonlinear systems
2014
In this paper, an adaptive output feedback stabilization method for a class of uncertain nonlinear systems is presented. Since this approach does not require any information about the bound of uncertainties, this information is not needed a priori and a mechanism for its estimation is exploited. The adaptation law is obtained using the Lyapunov direct method. Since all the states are not measurable, an observer is designed to estimate unmeasurable states for stabilization. Therefore, in the design procedure, first an observer is designed and then the control signal is constructed based on the estimated states and adaptation law with the σ-modification algorithm. The uniformly ultimately bou…
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
2015
The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a {hidden attractor} in the case of multistability as well as a classical {self-excited attractor}. The hidden attractor in this system can be localized by analytical-numerical methods based on the {continuation} and {perpetual points}. For numerical study of the attractors' dimension the concept of {finite-time Lyapunov dimension} is developed. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of {exact Lyapunov dimension} are discussed. A comparative survey on the computation of the finite-time Lyapunov expon…
Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
2014
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance…
Stability analysis and H<inf>&#x221E;</inf> controller design of a class of switched discrete-time fuzzy systems
2011
In this paper, the problems of stability analysis and H ∞ controller design of a class of switched nonlinear systems are investigated. In a classical way, the modeling of the systems is approached by switched fuzzy systems, and both fast switching and slow switching are considered there. In particular, for slow switching scheme, a new mode-dependent average dwell time switching is proposed for the underlying switched fuzzy systems. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the H ∞ state-feedback controller is derived. A numerical example is given to show the validity and potential of the theoretical results.
Adaptive Neural Stabilizing Controller for a Class of Mismatched Uncertain Nonlinear Systems by State and Output Feedback
2015
In this paper, first, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is proposed. By using a radial basis function NN (RBFNN), a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. Then, an observer-based adaptive controller based on RBFNN is designed to stabilize uncertain nonlinear systems with immeasurable states. The state-feedback and observer-based controllers are based on Lyapunov and strictly positive real-Lyapunov stability theory, respectively, and it is shown that the asymptotic convergence of the closed-loop system to ze…
Design on fuzzy control for a class of stochastic nonlinear systems
2014
The problem of Hankel-norm output feedback control is solved for a class of T-S fuzzy stochastic systems. The dynamic output feedback controller design technique is proposed by employing fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms Refereed/Peer-reviewed
Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System
2015
In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system. peerReviewed
Input-Output Feedback Linearization Control with On-Line Inductances Estimation of Synchronous Reluctance Motors
2021
This paper proposes an adaptive input-output Feedback Linearization (FL) techniques for Synchronous Reluctance Motor (SynRM) drives, taking into consideration the iron losses. As a main original content, this work proposes a control law based on a new dynamic model of the SynRM including iron losses as well as the on-line estimation of the static inductances. The on-line estimation of the SynRM static inductances permits to inherently take into consideration the magnetic saturation phenomena occuring on both axes. The estimation law is obtained thanks to a Lyapunov-based analysis and thus the stability of the entire control system, including the estimation algorithm, is intrinsically guaran…
Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction
2014
Abstract This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. …
The chaotic Dadras–Momeni system: control and hyperchaotification
2015
In this paper a novel three-dimensional autonomous chaotic system, the so called Dadras-Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. Firstly, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin’s minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of t…