Containment control of general linear multi-agent systems with multiple dynamic leaders: A fast sliding mode based approach

A Global Fast Terminal Sliding Mode Controller (GFTSMC) is proposed for n-link robotic manipulators by employing the Fast Terminal Sliding Mode (FTSM) control concept in both the reaching phase and the sliding phase. Under the control, the system states will reach FTSM in desired finite time and then converge to the origin along the FTSM in specified finite time, resulting in a reduced steady tracking error in comparison with the conventional sliding mode controller. The proposed controller is continuous and therefore chattering-free. An example is presented to demonstrate its effectiveness.

Robust finite-time containment control of general linear multi-agent systems under directed communication graphs

In this paper, we address the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a directed graph. A distributed adaptive control algorithm with an adaptive gain design using both relative position and velocity feedback is proposed based on the approximation capability of neural networks. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph with unknown nonlinearities and external disturbances, in which the systems achieve consensus asymptotically. We then propose a distributed containment control algorithm without using neighbors' velocity information.

Distributed containment control for uncertain nonlinear multi-agent systems in non-affine pure-feedback form under switching topologies

The paper presents a method of synthesizing the Variable Structure Controller (VSC) based on the Fast Terminal Sliding Mode (FTSM) control for an optoelectronic observatory to eliminate the effects of the vibration and the change of vehicle’s direction. An improved fast terminal sliding surface and a fuzzy saturation function have been proposed to develop the improved fast terminal sliding mode variable structure controller (IFTSM-VSC). Based on the theory of Lyapunov stability, the article has proved that the IFTSM-VSC controller ensures the Line of Sight (LOS) stabilization of the observation devices and ensures the tracking errors converge to zero in finite time. The simulation uses data about the vibration and navigation of the vehicle recorded on some streets and roads. Simulation results in Matlab/Simulink show the effectiveness of the IFTSM-VSC controller.

This paper investigates the distributed containment control problem for a class of general second-order multiagent systems with switched dynamics, which is composed of a continuous-time (CT) subsystem and a discrete-time (DT) subsystem. For this switched multiagent system under fixed directed topology, a distributed containment control protocol is proposed for each follower based on the relative local measurements of neighboring followers and leaders. Some necessary and sufficient conditions are derived under the condition that the network topology contains a directed spanning forest, and these conditions ensure that the general second-order containment control problem can be solved under arbitrary CT-DT switching. If the general second-order system is reduced to the double integrator system, some simpler containment conditions are presented. Furthermore, the similar results are also obtained under switching directed topology. Finally, some simulation examples are presented to show the efficiency of the theoretical results.

Distributed containment control for asynchronous discrete-time second-order multi-agent systems with switching topologies

This paper investigates the distributed containment control problem for multi-agent systems with general linear dynamics under a directed graph. A new observer based on the relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of the observer and the controller gains. Then a sufficient condition on the existence of the observer-based controllers is presented in terms of strict linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design method.

Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input

When a permanent magnet synchronous motor runs at low speed, the inverter will output discontinuous current and generate torque ripple; when the motor is runs at high speed, a large amount of stator harmonic current generates, which affects its speed following ability and torque stability. To ensure the fast and smooth switching of a permanent magnet synchronous motor in the full speed domain, this paper proposes the nonsingular terminal sliding mode control of PMSM speed control based on the improved exponential reaching law. Firstly, the improved exponential reaching law is composed of the state variables and power terms of the sliding mode surface functions. The reaching law function is designed in sections to balance the fast dynamic response of the system and chattering control. Secondly, an improved exponential reaching law based on the sliding mode control strategy of the PMSM speed loop is proposed. By designing the initial value of the integral term in the nonsingular terminal sliding mode surface function, the initial state of the system is located on the sliding mode surface. The integral sliding mode surface is used to reduce the system steady-state error, while the proposed sliding mode reaching law is used to increase the arrival speed and suppress system chattering, ultimately affecting modeling error problems, complex working conditions, and uncertainty factors. This paper proposes a sliding mode observer based on an improved exponential reaching law to compensate for the disturbances. Lyapunov stability theory can prove that this system can make the speed tracking error converge to zero in finite time. Hardware-in-the-loop experiments were used to validate the effectiveness of the proposed method.

This article proposes an adaptive nonsingular fast terminal sliding mode control scheme with piecewise fast multi-power reaching law for tracking control of underactuated autonomous underwater vehicles under model uncertainties, ocean disturbances, and measurement noise. This control approach enhances the robustness and guarantees faster convergence of state error to zero in finite time while reducing the chattering effect. Utilizing the benefit of adaption law prevents overestimating control parameters, and it eliminates the need for the upper bound value of disturbances. The overall stability of the system is analyzed using the Lyapunov criterion. The results of the proposed approach are compared with adaptive nonsingular terminal sliding mode control and adaptive sliding mode control. The performance of the proposed control approach is evaluated by using the performance indices root mean square error and chattering indicator. The simulation results confirm the efficiency of the proposed approach.

In this paper, an adaptive fast terminal sliding mode control technique combined with a global sliding mode control scheme is investigated for the tracking problem of uncertain nonlinear third-order systems. The proposed robust tracking controller is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Under the uncertainty and nonlinearity effects, the reaching phase is removed and the chattering phenomenon is eliminated. This scheme guarantees robustness against nonlinear functions, parameter uncertainties and external disturbances. The derivative of the state variable is replaced by a delay term in the form of an Euler approximation of the derivative function. Furthermore, the knowledge of upper bounds of the system uncertainties is not required, which is more flexible in the real implementations. Simulation results are presented to show the effectiveness of the suggested method.

This paper introduces a variable structure to regulate speed of PMSM system by a global fast terminal sliding mode control (GFTSMC) technique optimizing speed tracking performance of permanent magnet synchronous motor (PMSM) servo system. Firstly, a global fast terminal sliding mode control strategy is introduced. Compared with common sliding mode control strategy, this strategy eliminates the chattering phenomenon in that it does not contain switching terms. Also, it can make the output speed reach the reference value in finite time, along with a shorter convergence time and a better tracking precision. Due to the complexity of control equations, S-function in MATLAB is adopted to design the GFTSMC. The effectiveness and robustness of the proposed scheme are verified by MATLAB simulations.

In this paper, a chatter free sliding mode control (SMC) strategy for chaos control is introduced to the nonlinear uncertain chaotic systems in the presence of unknown bounded uncertainties and external disturbances. The sliding mode surface with differential operators is proposed to divert the discontinuous gian function swith term into only one control input, and the control input is smooth and differentiable with respect to time. Based on the Lyapunov stability theory, SMC stability analysis is performed and a theorem serving as designing a chatter free sliding mode control input is also introduced. Finally, numerical simulations are presented to verify the usefulness of the proposed control strategy.

Aiming at the distributed containment control problem for multi-agent robotic system with stationary leaders, a position-sensorless control strategy is proposed based on binocular visual servo and feedback dissipative Hamilton theory. Firstly, the topological relationship among the robots is built by using directed graph, which makes each follower determine its neighbour robots. Secondly, a binocular visual servo model is established, so as to describe the dynamic information of the tracking target point for each follower through the neighbour robots' image information. Thirdly, the distributed containment controllers are designed based on the pre-feedback control strategy and feedback dissipative Hamilton theory; furthermore, in the case that each follower is not equipped with internal position sensor, the full-order state observers are developed by using the 'expansion + feedback' method, and then realise the position-sensorless control. Finally, a simulation is carried out on multiple two degrees-of-freedom (DOF) robots, and results show the validity of the proposed control strategy.