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1.
A predator–prey model with prey-dependent functional response is considered. The set of all points in the positive quadrant of the state plane that can be made equilibrium points by means of an affine state-feedback control law is determined, and the values of the control parameters ensuring the desired equilibria are provided. It is shown how the asymptotic stability of the equilibrium points depends on simple geometric conditions. The problem of stabilizing unstable equilibrium points is also briefly discussed.  相似文献   

2.
In this paper, we investigate the cooperative control problem of high-order integrators under heterogeneous couplings. A new class of distributed control algorithms are developed for the designated convergence rate (DCR) problem of high-order integrators, which could explicitly show the convergence margin of the closed-loop system, and has better robustness than conventional consensus algorithms. We first propose state consensus control algorithms for high-order integrators, where necessary and sufficient convergence conditions are proposed by theoretical analysis. Then we extend the results to the case of output leaderless consensus of heterogeneous high-order integrators with heterogeneous couplings. Finally, simulation examples are given to validate the effectiveness of the proposed algorithms.  相似文献   

3.
In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.  相似文献   

4.
In this paper, we consider the finite-time scaled consensus tracking of a class of high-order nonlinear multiagent systems(MASs)who owns unstable modes in its Jacobian linearized system. The presence of unstable linearization makes the high-order MASs in question essentially different from those in the existing works. Under a directed interaction topology, to overcome the difficulties caused by the asymmetry property of Laplacian matrix, the finite-time scaled consensus control scheme is developed by the modified addition of a power integrator method. Based on finite-time Lyapunov stability theorem and algebra graph theory, for high-order MASs with unstable linearization even in the presence of non-lipschitz nonlinear dynamic, all system states are bounded and the output tracking errors are finite-time uniformly ultimately bounded(FUUB). Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.  相似文献   

5.
《Journal of The Franklin Institute》2022,359(18):10628-10652
Control of a water hyacinth-fish ecological system is required for a healthy and sustainable environment. This paper aims to investigate the global dynamics of a water hyacinth fish ecological system under ratio-dependent state impulsive control. First, we study the positivity and boundedness of the solution of the controlled system. By studying the local stability of the equilibrium, we find that the system has two situations. One is that there are two equilibria, namely a saddle point and a boundary equilibrium. In the second case, there are four equilibria, namely, two saddle points, a boundary equilibrium, and a focus point. For the first case, when we select an appropriate ratio-dependent control threshold, the trajectory will globally converge to the boundary equilibrium. For the second case, when the control line is located below the focus point, by using Poincare mapping method, flip bifurcation theory, and vector field analysis techniques, we find that the solution of the controlled system either globally converges to the boundary equilibrium, order-1 periodic solution, or order-2 periodic solution under certain conditions. When the control line is located above the focus point, the solution of the controlled system either globally converges to the focus point, order-1 or order-2 periodic solution. Finally, we use examples to verify the correctness and validity of the theoretical results.  相似文献   

6.
This paper addresses an output tracking problem for discrete-time high-order fully actuated (DHOFA) systems and its application in the control of air-bearing spacecraft (ABS) simulator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of discrete-time control systems. Accordingly, a HOFA predictive control scheme is presented to deal with this problem, which is composed of a HOFA feedback for stabilization and a HOFA predictive control for tracking. In this scheme, a Diophantine equation is exploited to construct an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, and then a cost function involving tracking performance is minimized by using multi-step output predictions. A sufficient and necessary condition is proposed to discuss the stability and tracking performance of the closed-loop DHOFA systems, it is simple to utilize in system analysis and extend in practice. Two experiments of the control of ABS simulator are shown to illustrate the feasibility of the presented HOFA predictive control scheme.  相似文献   

7.
This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.  相似文献   

8.
Sylvester quaternion tensor equations have a wide range of applications in image processing and system and control theory. In this paper, by the Kronecker product and vectorization operator and the properties of quaternion tensors, we focus mainly on proposing the tensor form of the generalized product-type biconjugate gradient method for solving generalized Sylvester quaternion tensor equations. As an application, we apply the proposed method to restore a blurred and noisy-free color video. The obtained numerical results illustrate the effectiveness of our method compared with some existing methods.  相似文献   

9.
In this paper, the problem of output feedback stabilization for high-order nonlinear systems with more general low-order and high-order nonlinearities multiplied by a polynomial-type output-dependent growth rate is studied. By constructing the novel Lyapunov function and observer, based on the homogeneous domination and adding a power integrator methods, an output feedback controller is developed to guarantee that the equilibrium of the closed-loop system is globally uniformly asymptotically stable.  相似文献   

10.
In this paper, we investigate the stability and periodicity of a class of state-dependent switched systems with all unstable subsystems by means of energy analysis. We firstly transform the unstable subsystems reversibly into the form of second order mechanical systems, and then construct energy functions by calculating the sum of kinetic and potential energies of each subsystem. After that, two switching lines, derived from the lines with the largest and smallest energy drops, make the stable phase trajectory approach to the equilibrium point at the fastest speed. In addition, we explore possible dynamic behaviors of the switched system under a pair of switching line including asymptotic stability, instability and periodicity. Furthermore, based on the bisection method and nested intervals theorem, we design a state-dependent switching law, which makes the switched system periodic initiated from a stable switching law. Finally, numerical simulation examples are provided to illustrate the effectiveness and less conservativeness of the proposed method with practical significance.  相似文献   

11.
The main results of this paper are concentrated on the nonlinear model predictive control (MPC) tracking optimization based on high-order fully actuated (HOFA) system approaches. The proposed HOFA MPC strategy makes full use of full-actuation property to eliminate the nonlinear dynamics of the system, and then the nonlinear optimization problem is equivalently transformed into a series of easy-solve linear convex optimization problems. Different from general nonlinear MPC methods and the current optimal control of the HOFA system approach, an analytical controller with smooth and less energy is obtained by the moving horizon optimization. And it is proven that the proposed controller can stabilize the corresponding tracking error closed-loop system. Finally, not limited to FA systems, as examples, a nonlinear numerical under-actuated model in the mathematical sense and a benchmark nonlinear under-actuated mechanical system are transformed into corresponding equivalent HOFA systems, the simulation results are given to verify the effectiveness of the proposed strategy.  相似文献   

12.
This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.  相似文献   

13.
Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by making use of statistical properties—types of diversity—of the data. Two popular types of diversity that have proven useful for many applications are statistical independence and sparsity. Although many methods have been proposed for the solution of the BSS problem that take either the statistical independence or the sparsity of the data into account, there is no unified method that can take into account both types of diversity simultaneously. In this work, we provide a mathematical framework that enables direct control over the influence of these two types of diversity and apply the proposed framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity. In addition, due to its importance in biomedical applications, we propose a new model reproducibility framework for the evaluation of the proposed algorithm. Using simulated functional magnetic resonance imaging (fMRI) data, we study the trade-offs between the use of sparsity versus independence in terms of the separation accuracy and reproducibility of the algorithm and provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.  相似文献   

14.
A smooth periodic delayed feedback (SPDF) control scheme is proposed for the fixed-time stabilization problem of linear periodic systems subject to input delay. By investigating the monodromy matrix of the periodic system, it is proved that the SPDF controller can achieve the fixed-time stabilization of linear periodic systems with arbitrarily long yet bounded input delays under the condition that the original system is uniformly completely controllable. The proposed controller is continuously differentiable and smooth. The SPDF control scheme is then applied to the elliptical spacecraft rendezvous problem. The effectiveness of the established method is verified on numerical simulations.  相似文献   

15.
This paper concentrates on computing the stabilizing region of PDμ controller for fractional order system with general interval uncertainties and an interval delay. The stabilizing region means the complete/approximate set of PDμ controllers that stabilize the given closed-loop control system. General interval uncertainties refer to both coefficients and orders of the fractional system suffer from interval uncertainties. Interval delay indicates that the delay also vary in a specified interval.Firstly, a method is presented to calculate the stabilizing region for general interval fractional system with an interval time-constant delay. Based on a novel mapping function and the concept of critical controller parameters, the stabilizing region can be determined numerically. Secondly, the stabilizing region computation problem for general interval fractional system with an interval time-varyingdelay is considered. By applying a revised small-gain theorem, the stabilizing region can be calculated like the time-constant delay case. Thirdly, two alternative methods are proposed to improve the computational efficiency of stabilizing region calculation. Both methods can reduce the number of polynomials which are used to determine the stabilizing region. Examples are followed to illustrate the proposed results.  相似文献   

16.
Rejection of periodic disturbance and/or tracking of periodic reference is of importance in high-precision control systems. Conventional repetitive control is often used to solve the problem, but it cannot precisely set effective frequency points and adversely amplify the non-periodic component disturbance. Therefore, it is not applicable in actual systems where external disturbances exist in the whole frequency domain. In this paper, we propose an improved discrete-time repetitive control method based on the disturbance observer to correct the undesired deviation at repetitive frequencies and mitigate the amplification of the non-components. Moreover, in the observer structure, an intuitive and flexible Q-filter design is presented to suppress low-frequency broadband and intermediate-frequency narrowband disturbances. The conditions of closed-loop stability, performance analysis, and the implementation of the proposed scheme are provided in detail. Finally, the effectiveness of the method is verified by simulation and experimentation on an optoelectronic precision positioning system under the condition of disturbances, and the disturbance suppression and tracking error attenuation are improved.  相似文献   

17.
This paper studies the high-order moment control problem for discrete-time Markov jump linear systems (MJLSs) with certain dynamic response performance and disturbance rejection specifications. An appropriate cumulant generating function is employed to express the original stochastic system in high-order component form. This facilities the high-order moment stabilization of MJLSs. Moreover, a pole region assignment approach is utilized to ensure desired dynamic response specifications with a certain attenuation rate. An arithmetic and geometric inequality approach is utilized to extract sufficient conditions ensuring the designed controller existence. These conditions ensure the high-order moment steady-state property and certain dynamic specifications for the MJLSs. The effectiveness of the proposed method is demonstrated through numerical and practical examples.  相似文献   

18.
In this paper, the boundary stabilization problem of a class of unstable reaction–advection–diffusion (RAD) systems described by a scalar parabolic partial differential equation (PDE) is considered. Different the previous research, we present a new gradient-based optimization framework for designing the optimal feedback kernel for stabilizing the unstable PDE system. Our new method does not require solving non-standard Riccati-type or Klein–Gorden-type PDEs. Instead, the feedback kernel is parameterized as a second-order polynomial whose coefficients are decision variables to be tuned via gradient-based dynamic optimization, where the gradients of the system cost functional (which penalizes both kernel and output magnitude) with respect to the decision parameters are computed by solving a so-called “costate” PDE in standard form. Special constraints are imposed on the kernel coefficients to ensure that the optimized kernel yields closed-loop stability. Finally, three numerical examples are illustrated to verify the effectiveness of the proposed approach.  相似文献   

19.
This paper addresses the design of a sampled-data model predictive control (MPC) strategy for linear parameter-varying (LPV) systems. A continuous-time prediction model, which takes into account that the samples are not necessarily periodic and that plant parameters vary continuously with time, is considered. Moreover, it is explicitly assumed that the value of the parameters used to compute the optimal control sequence is measured only at the sampling instants. The MPC approach proposed by Kothare et al. [1], where the basic idea consists in solving an infinite horizon guaranteed cost control problem at each sampling time using linear matrix inequalities (LMI) based formulations, is adopted. In this context, conditions for computing a sampled-data stabilizing LPV control law that provides a guaranteed cost for a quadratic performance criterion under input saturation are derived. These conditions are obtained from a parameter-dependent looped-functional and a parameter-dependent generalized sector condition. A strategy that consists in solving convex optimization problems in a receding horizon policy is therefore proposed. It is shown that the proposed strategy guarantees the feasibility of the optimization problem at each step and leads to the asymptotic stability of the origin. The conservatism reduction provided by the proposed results, with respect to similar ones in the literature, is illustrated through numerical examples.  相似文献   

20.
The paper is concerned with the modeling and stabilization problem of networked control systems under simultaneous consideration of bounded packet dropouts and occasionally missing control inputs. In particular, the focus of the paper is to capture the case where the packet dropouts and control inputs missing are subject to multiple sampling periods, and not periodic as in existing results. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original linear system is firstly transformed to a switched stochastic time-delay system. Meanwhile, the probability distribution values of stochastic delay taking values in m(m ≥ 2) given intervals can be explicitly obtained, which is of vital importance to analyse the stabilization problem of considered system. Secondly, by means of the average dwell time technique, some sufficient conditions in terms of linear matrix inequalities for the existence of desired stabilizing controller are derived. Finally, an illustrative example is given to illustrate the effectiveness of the proposed stabilizing controller and some less conservative results are obtained.  相似文献   

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