Stability Of Nonlinear Systems Research Articles

Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer

One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x-direction and between two concurrent plates at z=0 and z=d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (Nu), Sherwood number proportional to mass transfer of solute 1 (Sh1) and Sherwood number proportional to mass transfer of solute 2 (Sh2) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

Correction to: Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

Correction to: Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

Fault tolerant control for a class of nonlinear systems with multiple faults using neuro-dynamic programming

Considering the multiple fault scenario, i.e., both actuator and sensor faults occur simultaneously, this paper develops a neuro-dynamic programming (NDP)-based fault tolerant control (FTC) scheme for a class of nonlinear systems. By combining a descriptor observer with an adaptive observer, system states and multiple faults are estimated simultaneously. For the nominal system, i.e., the fault-free system, a critic neural network (NN) is employed to solve the Hamilton–Jacobi-Bellman (HJB) equation, and the approximate optimal control policy is obtained. To eliminate the influence of sensor faults, the accurate estimations of system states are used instead of system states from faulty sensors to construct the approximate optimal control policy. Then, by combining the estimations of actuator faults with the approximate optimal control policy, an FTC law is developed to suppress the influence of actuator faults. The stability of the closed-loop nonlinear system is analyzed to be uniformly ultimately bounded via the Lyapunov stability theorem. The effectiveness of the present FTC scheme is demonstrated by two simulation examples.

Dynamic event‐triggered dissipative control of nonlinear networked control systems with deception attacks

AbstractFor nonlinear networked control systems with deception attacks, the problem of dynamic event‐triggered dissipative control is researched in this article. First, on the basis of nonlinear networked control systems model, a dynamic event triggered scheme is proposed to save impact of network bandwidth. Second, considering the impact of time delay, a networked time‐delay system model under deception attacks is established. Third, by constructing a new and less conservative Lyapunov function, using linear matrix inequality and unilateral Lipschitz condition, we derive some new sufficient conditions to guarantee the asymptotically stability of nonlinear networked control systems and strictly ‐dissipative performance. Besides, a cooperative design strategy of dynamic event triggered scheme parameters and controller gain is put forward. Finally, a simulation example is given to prove feasibility and rationality of the proposed strategy.

Robust stabilization of uncertain nonlinear systems with infinite distributed input delays

This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua’s circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers.

Finite/nearly fixed-time stability of nonlinear impulsive systems with destabilizing impulses and its application to neural networks

This paper investigated the finite-time stability (FTS) and nearly fixed-time stability (nFxTS) of nonlinear impulsive systems with destabilizing impulses. The concept of nFxTS is different from FxTS, as the former may be just asymptotically stable but the latter must be FTS. A Lyapunov inequality with linear terms has been used to derive sufficient conditions based on the dwell time (DT) and average dwell time (ADT) properties of impulsive sequences to ensure FTS/FxTS of the system. Theorems are constructed based on the initial state of the system, which belongs to either δ-neighborhood(nbh) or outside δ-nbh of the origin. When the system starts within δ−nbh of the origin then FTS can be achieved by the system following conditions on DT and ADT of impulsive sequences. The same is true for nFxTS of the system when it starts outside δ-nbh of the origin. We investigated the condition on DT for which nFxTS is not possible, but FTS is possible only if δ>0 is bounded. The main results of this paper are applied to the synchronization problem of impulsive neural networks with destabilizing impulses. Finally, a numerical example of an impulsive neural network is given to illustrate the validity of the proposed theoretical results.

Finite/fixed-time input-to-state stability of impulsive nonlinear systems

In this paper, we investigate the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems involving hybrid impulses which have time-dependent multiple jump maps. Under unified average dwell-time conditions, several criteria for finite-time and fixed-time input-to-state stability are established by virtue of the Lyapunov function with linear rate and nonlinear rate of jump maps. It shows that, when the finite/fixed-time input-to-state stable continuous systems are subject to hybrid impulses, the finite-time and fixed-time input-to-state stability can be ascertained under the requirement that the accumulative effect of hybrid impulses is non-destabilizing or the accumulative effect of hybrid impulses is destabilizing and the impulses are not activated too frequently. Finally, the effectiveness of theoretical results is verified by two numerical examples and an application example about an axisymmetric circular spacecraft.

Exponential stability for nonlinear time-varying systems on time scales

In this paper, some less conservative sufficient conditions for uniform exponential stability, local uniform exponential stability and uniform practical exponential stability of nonlinear time-varying systems on time scales are proposed. Compared with the traditional exponential stability results, the negative definiteness of the time derivatives of Lyapunov functions is weakened, that is, the time derivatives of related Lyapunov functions in this paper are allowed to be indefinite. The main tools used are some Gronwall's inequalities on time scales. Two examples are also included to verify the effectiveness of the results obtained.

Practical stability of fractional-order nonlinear fuzzy systems

In this paper, we present a practical Mittag–Leffler stability for a new class of fractional-order nonlinear Takagi–Sugeno fuzzy uncertain systems. Based on fractional-order Lyapunov stability theory and the parallel distributed compensation (PDC) controller techniques, we show the convergence of the solutions of the closed-loop considered system toward a neighborhood of the origin. Furthermore, a numerical example is given to show the applicability of the main result.

Semi-global exponential stability of stochastic nonlinear functional sampling systems by emulation approach

In this paper, the semi-global exponential stability is studied for the stochastic nonlinear functional systems by emulation of sampled-data controller. In consideration of the stochastic factor, a novel definition of the right and upper Dini’s derivative of the constructed functional is given. Based on this novel definition, combining with stochastic analysis techniques and Lyapunov method, some sufficient criteria for the semi-global exponential stability of the stochastic nonlinear functional systems by suitably fast sampling are given. As a special case, a class of stochastic nonlinear functional systems with multiple time delays is studied and two coefficient type theorems that lead to the semi-global exponential stability of the sampling system are derived. Finally, a practical application about parallel active suspension systems with time delay and stochastic disturbance is discussed at length and the corresponding numerical example is given to illustrate the feasibility of the theoretical results.

Stabilization of Triangular Nonlinear Systems With Multiplicative Stochastic State Sensing Noise

We present new state-feedback control designs for lower-triangular/upper-triangular nonlinear systems with multiplicative stochastic sensor uncertainty. For lower-triangular nonlinear systems with small sensor noise, we develop a novel control design where the control gains are suitably constructed to simultaneously dominate the nonlinear functions and sensor noise of sufficiently small multiplicative gain. For upper-triangular nonlinear systems, we propose a new low-gain domination design, the advantage of which is that it can effectively deal with the sensor noise with arbitrarily large intensities. These two designs can both ensure that closed-loop system has an almost surely unique global solution, the origin of the closed-loop system is mean-square stable, and the states can be regulated to zero almost surely. Finally, two simulation examples are given to illustrate the designs.

A Multiobjective Feedback Linearization Control of a Cuk Converter

Cuk converter is one of the most common power electronic converters, but its controller design has always been a challenging problem due to its fourth-order nonlinear and nonminimum phase characteristics. In order to solve this problem, this paper proposes a multi-objective feedback linearization control method, which selecting the variables of interest to rebuild the output function to linearize the nonlinear system into a combination of a linear subsystem and a nonlinear subsystem. According to the structural characteristics of these two subsystems, the linear optimal control theory is adopted for the control design of the linear subsystem to make the original nonlinear system have a good output performance, while for the nonlinear subsystem, the coefficient of the output function is adjusted to ensure the stability of the original nonlinear system. The results of simulation and experiment show the feasibility and superiority of using the multi- objective feedback linearization control method to design the nonlinear control law of the Cuk converter.

A new robust SIDA-PBC approach to control a DFIG

Credible control and overall stabilization of closed-loop nonlinear systems presented in a port-controlled hamiltonian structure (PCH-D) were forever the development of the simultaneous interconnection and damping assignment passivity-based control (SIDA-PBC) method. The robustness and reliability of the method called into question against noise and certainly modelling errors. Indeed, a new scheme has been presented to control a doubly fed induction generator (DFIG) based on the energy form and exploiting the electrical parameters of the closed loop system. The results obtained provide a new technique and implement more freedom when designing the diagram of the advanced controller during the production of active power. The contribution of this paper is researching on the advanced nonlinear methodes used, many simulations were carried out in simulation using the MATLAB/Simulink environment under important operating conditions, allowing to demonstrate the feasibility of the proposed method and verify the performance considering the robustness.

On the partial stability of nonlinear impulsive Caputo fractional systems

On the partial stability of nonlinear impulsive Caputo fractional systems

Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

Adaptive asymptotic stabilization of uncertain nonstrict feedback nonlinear HOFA systems with time delays

Practical semiglobal uniform exponential stability of nonlinear nonautonomous systems

UDC 517.9 We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for practical uniform exponential stability of nonlinear perturbed systems under different conditions for the perturbed term. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability for parametrized nonlinear time-varying systems. We establish the possibility of application of a perturbed parametrized system, by using Lyapunov theory, to the investigation of the robustness properties that may provide practical semiglobal uniform exponential stability with respect to perturbations.

Finite‐time adaptive fuzzy tracking control for stochastic nonlinear systems with time‐delay via output‐feedback

AbstractIn this paper, the finite‐time adaptive fuzzy tracking control issue for stochastic nonlinear systems with time‐delay via output‐feedback is studied. Firstly, a state observer and fuzzy logic systems with infinite approximation capability are utilized to estimate the unmeasured states and identify unknown nonlinear characteristics, respectively. Then, a finite‐time adaptive fuzzy tracking controller is devised by the backstepping technology. It is shown that the presented control scheme can ensure the finite‐time square stability of the stochastic nonlinear systems with time‐delay, that is, the output tracking error converges to a sufficiently small neighborhood around the origin in finite‐time, and all signals of the closed‐loop system are bounded. Finally, the effectiveness of the presented control strategy is illustrated via two simulation examples.

Partial stability of nonlinear dissipative feedback systems

Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system's states. In this paper, we develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems.

Estimation and stochastic control of nonlinear dynamic systems over the AWGN channel: Application in tele‐presence and tele‐operation of autonomous vehicles

AbstractThis paper is concerned with tele‐presence and tele‐operation of autonomous vehicles over the Additive White Gaussian Noise (AWGN) channel. This wireless communication channel is subject to transmission noise and transmission power constraint. An encoder, decoder and controller are proposed by implementing a novel linearization method for linearizing the nonlinear dynamic systems at operating points. For the linearized systems, the encoder, decoder and controller are implemented that were previously proposed for output tracking as well as stability of linear dynamic systems. Two novel linearization methods are proposed and their satisfactory performances are proved for output tracking as well as stability of nonlinear dynamic system. The first method is based on the fixed linearization rate and the second one is based on the variable (optimal) linearization rate. The decoder that is based on the second method is in fact the extended Kalman filter with the optimal linearization rate. The performances of these two methods are compared with each other and the other proposed methods by implementing them to the problems of the tele‐presence and tele‐operation of autonomous vehicles over the AWGN channel. Their satisfactory performances are illustrated. It is illustrated that the second method has higher computational complexity with slightly better performance and is applicable to a larger class of reference trajectories.

Global Output Feedback Stabilization for Stochastic Nonlinear Systems with Multiple Uncertainties

Global Output Feedback Stabilization for Stochastic Nonlinear Systems with Multiple Uncertainties