Boundedness Control Research Articles

Output Feedback Ultimate Boundedness Control with Decentralized Event-Triggering

Output Feedback Ultimate Boundedness Control with Decentralized Event-Triggering

Robust ultimately boundedness control of uncertain delayed systems under time-varying reference and external disturbance

In the set-point following, the asymptotic property of the stability would disappear in the presence of time-varying references and disturbances. Hence, the boundedness of state variables is an essential issue in the regulation. To this aim, in light of time-varying references and disturbed signals, a robust integral policy is systematically developed to achieve the control aim in the uncertain equations with delay. Utilizing linear matrix inequality, a guideline is suggested for guaranteeing the boundedness of the solutions in uncertain systems with delays. Then, the gains of the control law are computed from a minimization. Although the boundedness is ultimately obtained in the perturbed case, the asymptotic stability would also be deduced for the nominal systems. The findings are numerically evaluated in some simulations. The favorability of the proposed integral method is shown in comparison to the traditional control strategies.

Appointed-time velocity-free prescribed performance control for space manipulators

This paper investigates the appointed-time velocity-free prescribed performance control for the space manipulators. A novel exponential-modified tracking differentiator is developed for estimating differential signals to address missing velocity information measurements. The original tracking problem is converted into the boundedness control, achieved through the bidirectional constraint-free mapping, which incorporates a novel performance function characterized by appointed-time convergence property. The coordinated control law is contributed with the designed velocity-free reference stable schemes. Ultimately, we achieve effective tracking of time-varying trajectories, ensuring simultaneous tracking of the desired values for the base and the manipulator. The tracking errors are constrained by the performance functions and convergence to the steady values at an appointed time. Simulation results validate the effectiveness of the proposed control scheme.

Observer-based quantised control of networked systems with round-robin protocol and transmission delay

This paper addresses the ultimate boundedness control problem for a class of networked nonlinear systems with the round-robin (RR) protocol and uniform quantisation. The communication between sensor nodes and the controller is implemented via a constrained communication channel. The quantised output of the system is transmitted to the remote controller through a communication channel subject to a transmission delay. For the purpose of alleviating possible data collision, the well-known RR communication protocol is deployed to schedule the data transmissions. On the other hand, the uniform quantisation effects of the network are characterised by a round function (i.e. the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of RR protocol and uniform quantisation effects, the closed-loop system is ultimately bounded. The controller is designed based on mean square stability analysis and Lyapunov-like method. A set of sufficient conditions for the ultimate boundedness of the closed-loop system are established and, on the basis of which, the desired controller gains are obtained by solving a set of linear matrix inequalities. The effectiveness of the proposed method is verified by numerical examples.

Distributed Finite-Time Boundedness Control for Large-Scale Networked Dynamic Systems

Distributed Finite-Time Boundedness Control for Large-Scale Networked Dynamic Systems

An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model

A fast, accurate, and stable numerical algorithm is proposed to solve the anisotropic phase-field dendritic crystal growth model. The algorithm combines the first-order direction splitting method and the linear stabilization technique, which preserve the energy stability while ensuring fast computing. The related stability analysis is shown. To obtain high accurate solution, the solution of first-order direction splitting method is extrapolated to be fourth-order, and the fourth-order difference method is applied to spatial discretization. To further improve the stability and prevent the blow-up of numerical solution, two post-processing methods, the bound preserving least-distance modification and the cut-off approach, are developed to control the boundedness of numerical solution, and their theoretical proofs are given. The proposed novel algorithm can be performed in parallel in each time step, significantly improving computing efficiency. Several numerical examples demonstrate the effectiveness of the proposed algorithm, including convergence and stability tests, the effectiveness of two post-processing techniques, and a series of 2D and 3D dendritic crystal growth simulations.

Ultimate Boundedness Control for Networked Singularly Perturbed Systems With Deception Attacks: A Markovian Communication Protocol Approach

In this study, the ultimate boundedness controlfor a type of networked singularly perturbed systems (SPSs) with communication constraints and deception attacks is explored. To improve the observer performance, the measurement outputs are quantized with the aid of a logarithmic quantizer. Meanwhile, the Markovian communication protocol (MCP) is forwarded to schedule the transmission sequence of the quantized signals. Unlike the conventional MCP, a novel nonhomogeneous MCP is proposed to further alleviate the communication bandwidth usage, whose transition probabilities are time-varying. By virtue of the hidden Markov model, the mismatches between the transmission mode over nonhomogeneous MCP and its detected ones are revealed, and an asynchronous observer-based controller is formed. Then, by establishing a novel singular-perturbation-parameter-based polytope Lyapunov-Krasovskii functional, the ultimate boundedness of the augmented networked SPS with randomly occurring deception attacks is elicited, and the local minimization of the controlled output is guaranteed. Finally, the effectiveness and applicability of the propounded control strategy are validated by two simulation examples.

Uniformly Ultimate Boundedness Control with Decentralized Event-Triggering

Uniformly Ultimate Boundedness Control with Decentralized Event-Triggering

Ultimate Boundedness Control for Uncertain Nonlinear Impulsive Switched Systems: A Fuzzy Approach Based on a Complete Takagi–Sugeno Structure

This paper deals with the ultimate boundedness control of nonlinear impulsive switched systems, which ensures that the state trajectories ultimately converge to a sufficient small region containing the origin. Given a general model, we first propose novel stability criteria that do not need to be satisfied on the entire space and include a condition to guarantee the remaining of trajectories within the ultimate bound, even though the impulse size is not zero at the origin or is not vanishing near the origin. Applying these criteria to a closed-loop system leads to a set of matrix inequalities that may be infeasible when the subsystems are highly nonlinear. Therefore, we redevelop them for an impulsive switched system represented by Takagi–Sugeno (T–S) fuzzy structure with nonlinear consequent parts. Since this structure has fewer rules than the traditional T–S models with linear consequent parts, the number of established stabilization matrix inequalities is sharply reduced. We then derive an optimization problem with linear and bilinear constraints to achieve a fuzzy controller that guarantees convergence to the smallest ultimate bound as well as practical control issues. Finally, a numerical example and a practical-motivated example are given to demonstrate the applicability of the proposed approach.

Finite-Time Boundedness Control for Nonlinear Networked Systems with Randomly Occurring Multi-Distributed Delays and Missing Measurements

This paper investigates the stochastic finite-time H∞ boundedness problem for nonlinear discrete time networked systems with randomly occurring multi-distributed delays and missing measurements. The randomly occurring multi-distributed delays and missing measurements are described as Bernoulli distributed white noise sequence. The goal of this paper is to design a full-order output-feedback controller to guarantee that the corresponding closed-loop system is stochastic finite-time H∞ bounded and with desired H∞ performance. By constructing a new Lyapunov-Krasovskii functional, sufficient conditions for the existence of output-feedback are established. The desired full-order output-feedback controller is designed in terms of the solution to linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the designed method.

Boundedness control sets for linear systems on Lie groups

Abstract Let Σ be a linear system on a connected Lie group G and assume that the reachable set 𝓐 from the identity element e ∈ G is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing e. We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.

Ultimate Boundedness Control for Networked Systems With Try-Once-Discard Protocol and Uniform Quantization Effects

This paper is concerned with the ultimate boundedness control problem for a class of networked nonlinear systems subject to the try-once-discard (TOD) protocol scheduling and uniform quantization effects. To prevent the transmission data from collisions, the communication between sensor nodes and the controller is implemented via a constrained communication channel, where only one sensor node is permitted to transmit data at each time instant. The TOD protocol is utilized to regulate the signal transmission over the communication network under which the scheduling behavior is described by a special switching function. On the other hand, the uniform quantization effects of the network are characterized by a round function (i.e., the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of TOD protocol and uniform quantization effects, the closed-loop system is ultimately bounded and the controlled output is locally minimized. Sufficient conditions are established to guarantee the ultimate boundedness of the dynamics of the closed-loop system in mean square by applying the stochastic analysis approach. Furthermore, the desired controller gains are derived by solving a convex optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed controller design scheme.

On the role of diffusion factors in stability analysis for p-Laplace dynamical equations involved to BAM Cohen-Grossberg neural network

In the ordinary differential system, the uniqueness of its equilibrium point can be determined obviously by the global asymptotic stability of this point. However, the reaction-diffusion dynamical system is partial differential equations with respect to both time variable t and space variable x so that the uniqueness of its equilibrium point need to be proved solely. In this paper, a comprehensive application of M-Matrix technique, Lyapunov functional method, Yang inequality and variational methods demonstrates the unique existence of globally asymptotically stable trivial equilibrium solution for the fuzzy dynamical system with nonlinear p-Laplace (p>1) diffusion. Especially when p=2, it becomes the reaction-diffusion fuzzy BAM Cohen-Grossberg neural network (BAM CGNN). Or if diffusion phenomena are ignored, it degrades into the fuzzy ordinary differential BAM CGNN. Even in such a special case, the derived corollary is also novel against existing results due to not exerting the boundedness control on the amplification functions. Moreover, the effectiveness of the proposed methods is illustrated by a numerical example and a comparable table.

Finite-time boundedness control of morphing aircraft based on switched systems approach

The attitude and altitude boundedness control problem is presented for the programmed sweeping process of a conceptual morphing aircraft with variable sweepback wings. The motion characteristic within the morphing phase is complicated as it includes inertia loads and large variations in both formal parameters and aerodynamic coefficients. The longitudinal nonlinear dynamics is approximated by the uncertain switched linear system with bounded external disturbances corresponding to a series of equilibrium points along the transition trajectory. The finite-time boundedness robust control is introduced to guarantee the flight stability instead of the traditional asymptotic stability. The sufficient conditions are proposed in the form of linear matrix inequalities to ensure the finite-time boundedness and robust performance for uncertain switched linear system. Then the finite-time robust state feedback control algorithm is provided for the morphing flight control. The devised technique is applied in a particular example of sweeping flight, and the simulation is developed with the nonlinear model and switched controllers. Simulation results show that the proposed approach is effective for the morphing flight and achieves a proper tradeoff between the control performance and elevator deflections.

Finite-Time Boundedness Control of Time-Varying Descriptor Systems

This paper mainly studies a control problem of finite-time boundedness of time-varying descriptor systems. Firstly, a sufficient and necessary condition of finite-time stability is given, then a sufficient condition of finite-time boundedness for time-varying descriptor systems is given. Secondly, we analyze the finite-time boundedness control problem and design the finite-time state feedback controller; the controller is given based on LMIs for time-varying descriptor systems and time-varying uncertain descriptor systems, respectively. Finally, a numerical example is given to prove the effectiveness of the method.

Stability analysis and uniform ultimate boundedness control synthesis for a class of nonlinear switched difference systems

In this paper, we deal with stability analysis of a class of nonlinear switched discrete-time systems. Systems of the class appear in numerical simulation of continuous-time switched systems. Some linear matrix inequality type stability conditions, based on the common Lyapunov function approach, are obtained. It is shown that under these conditions the system remains stable for any switching law. The obtained results are applied to the analysis of dynamics of a discrete-time switched population model. Finally, a continuous state feedback control is proposed that guarantees the uniform ultimate boundedness of switched systems with uncertain nonlinearity and parameters.

Simulation and stability analysis of neural network based control scheme for switched linear systems

This paper proposes a new adaptive neural network based control scheme for switched linear systems with parametric uncertainty and external disturbance. A key feature of this scheme is that the prior information of the possible upper bound of the uncertainty is not required. A feedforward neural network is employed to learn this upper bound. The adaptive learning algorithm is derived from Lyapunov stability analysis so that the system response under arbitrary switching laws is guaranteed uniformly ultimately bounded. A comparative simulation study with robust controller given in [Zhang L, Lu Y, Chen Y, Mastorakis NE. Robust uniformly ultimate boundedness control for uncertain switched linear systems. Computers and Mathematics with Applications 2008; 56: 1709–14] is presented.

A Combined Hard and Soft Variable-Structure Control Scheme for a Class of Nonlinear Systems

This paper presents a novel variable-structure-based control scheme for nonlinear systems. First, a hard variable-structure control is constructed for achieving a uniform ultimate boundedness control. Then, a soft variable-structure control using fuzzy logic is incorporated to help improve dynamic responses when trajectories enter into the ultimate bound. For practical consideration, we added a genetic-algorithm-based alpha-beta filter in front of the fuzzy controller to suppress noise and obtain smooth input signals. For comparison purposes, an inverted pendulum system was first used as a simulated example to demonstrate the effectiveness of the design. Then, the performance of the control scheme was practically tested with an experimental PC-based magnetic levitation system. The simulation and experimental results strongly suggest that the newly proposed control scheme is encouraging for practical applications.

Finite-Time Control by Observer-Based Output Feedback for Linear Discrete-Time Systems

In this paper we consider finite-time stabilization and finite-time boundedness control problems for time-varying discrete-time systems. We give a set of sufficient conditions, in terms of differen...

Robust uniformly ultimate boundedness control for uncertain switched linear systems

This paper presents uniformly ultimate boundedness (UUB) control design for switched linear systems with parametric uncertainties. Only the possible bound of the uncertainty is needed. Under arbitrary switching laws, a continuous state feedback control scheme is proposed in order to guarantee uniformly ultimate boundedness of every system response within an arbitrary small neighborhood of the zero state. The design techniques are based on common Lyapunov functions and Lyapunov minimax approach.