The state feedback control problem is addressed for a class of nonlinear time-delay systems. The time delays appear in all state variables of the nonlinear system, which brings a challenging issue ...for controller design. With an introduced new Lyapunov-Krasovskii functional, we develop a novel control strategy. With the help of a backstepping method, we design a memoryless state feedback controller, which does not need the precise knowledge of time delays. It is rigorously proved that the closed-loop system is asymptotically stable. Chemical reactor plants are typical nonlinear systems with time delays. We apply the developed method to the control design of a two-stage chemical reactor with delayed recycle streams, and the simulation results verify the effectiveness of the main results.
The decentralized control problem is considered for a class of nonlinear time-varying interconnected systems. Each subsystem is with the dead-zone input and unmodeled dynamics. The interconnections ...are bounded by time-varying nonlinear functions, which relaxes the commonly used linear condition or time-invariant condition. Based on the recursive method, we design a new decentralized finite-time controller such that all the state variables reach zero in finite time. The reaching time is based on the design parameters and initial value of system state. Furthermore, the fixed time stability conditions are given and the constructed controller can guarantee the fixed-time stabilization of the system, in which the reaching time only depends the control design parameters. Finally, simulation results are presented to illustrate the effectiveness of proposed method.
The master-slave control design problem is considered for the networked teleoperation system with friction and external disturbances. A new finite-time synchronization control method is proposed with ...the help of adaptive fuzzy approximation. We develop a new nonsingular fast terminal sliding mode (NFTSM) to provide faster convergence and higher precision than the linear hyperplane-sliding mode and the classic terminal-sliding mode (TSM). Then, the adaptive fuzzy-logic system is employed to approximate the system uncertainties, and the corresponding adaptive fuzzy NFTSM controller is designed. By constructing Lyapunov function, the stability and finite-time synchronization performance are proved with the new controller in the presence of system uncertainties and external disturbances. Compared with the traditional teleoperation design method, the new control scheme achieves better transient-state performance and steady-state performance. Finally, the simulations are performed and the comparisons are shown among the proposed method, the P+d method, the PD+d method, the DFF method, and the classic TSM FTSM. The simulation results further demonstrate the effectiveness of the proposed method.
This paper studies the dynamic output feedback tracking control problem for stochastic interconnected time-delay systems with the prescribed performance. The subsystems are in the form of triangular ...structure. First, we design a reduced-order observer independent of time delay to estimate the unmeasured state variables online instead of the traditional full-order observer. Then, a new state transformation is proposed in consideration of the prescribed performance requirement. Using neural network to approximate the composite unknown nonlinear function, the corresponding decentralized output tracking controller is designed. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of uniformly ultimately boundedness and that both transient-state and steady-state performances are preserved. Finally, a simulation example is given, and the result shows the effectiveness of the proposed control design method.
This brief presents a novel control scheme for some problems on tracking and obstacle avoidance of a wheeled mobile robot with nonholonomic constraint. An extended state observer is introduced to ...estimate the unknown disturbances and velocity information of the wheeled mobile robot. A nonlinear controller is designed to achieve tracking target and obstacle avoidance in complex environments. Note that tracking errors converge to a residual set outside the obstacle detection region. Moreover, the obstacle avoidance is also guaranteed inside the obstacle detection region. Simulation results are given to verify the effectiveness and robustness of the proposed design scheme.
This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed ...graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.
This brief is concerned with the problem of asymptotic stability of neural networks with time-varying delays. The activation functions are monotone nondecreasing with known lower and upper bounds. ...Novel stability criteria are derived by employing new Lyapunov-Krasovskii functional and the integral inequality. The developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities. New and less conservative solutions to the global stability problem are provided in terms of feasibility testing. Numerical examples are finally given to demonstrate the effectiveness of the proposed method.
The asymptotical synchronization problem is investigated for two identical chaotic Lur'e systems with time delays. The sampled-data control method is employed for the system design. A new ...synchronization condition is proposed in the form of linear matrix inequalities. The error system is shown to be asymptotically stable with the constructed new piecewise differentiable Lyapunov-Krasovskii functional (LKF). Different from the existing work, the new LKF makes full use of the information in the nonlinear part of the system. The obtained stability condition is less conservative than some of the existing ones. A longer sampling period is achieved with the new method. The numerical examples are given and the simulations are performed on Chua's circuit. The results show the superiorities and effectiveness of the proposed control method.
The output-feedback based controller design problem is investigated for the networked teleoperation system in this paper. A new control scheme is proposed to guarantee the global asymptotic stability ...of the bilateral teleoperation system with time-varying delays and bounded inputs. First, a new fast terminal sliding-mode velocity observer is proposed to estimate the unknown velocity signals for the teleoperation system. Then, by considering the unknown gravity term, an adaptive SP+Sd-type (saturated proportion plus saturated damping) controller is designed based on the estimated velocity. In the new controllers, the specific sigmoidal function is not used, and any one on a set of saturation functions can be applied. Furthermore, by choosing Lypunov-Krasovskii functional, we show that the master-slave teleoperation system is stable under specific linear matrix inequality conditions. With the given controller design parameters and the upper bound of the input, the allowable maximal transmission delay can be computed by using the proposed stability criteria. Finally, both simulations and experiments are performed to show the effectiveness of the proposed methods.
In this paper, dynamic formation problem of three-dimensional (3D) robotic vehicle systems with nonholonomic constraint and dynamics model is investigated. The control objectives are to achieve ...formation acquisition (i.e., vehicles form a predefined geometric shape) and formation maneuvering (vehicles move as a whole following predefined velocity). For the first objective, the nonlinear model is transformed into a dynamic model similar as the Euler-Lagrangian system with uncertain parameters. Then, we propose a rigid graph based adaptive dynamic formation control law, which enables the robotic vehicle system to converge to the target formation. Meanwhile, collision avoidance between vehicles can be achieved because the rigid graph theory naturally ensures the distance constraint. Then, formation maneuvering problem is investigated, on the basis of formation acquisition, a predefined velocity signal is added to the proposed adaptive formation control law such that robotic vehicles move as a whole following the predefined velocity. Compared with the existing results, the proposed rigid graph based formation control method can effectively reduce the appearance of non-desired equilibrium points of traditional distance based methods, moreover, the distance between robot vehicles can be time-varying, and the formation shape or size can be time-varying. Simulation results confirm the effectiveness of the dynamic formation control law.
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