Finite time tracking control of higher order nonlinear multi agent systems with actuator saturation

Distributed robust adaptive control of high order nonlinear multi agent systems

Distributed finite-time attitude containment control for multiple rigid bodies

Distributed finite-time containment control for multiple Lagrangian systems is addressed by introducing fractional-order powers in the control laws properly. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the states of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors' information. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the states of the followers converge to the dynamic convex hulls formed by those of the leaders in finite time. We also explicitly show the finite settling time.

International audience

In this article, the distributed adaptive finite-time containment control problem is investigated for nonlinear multi-agent systems with unknown input saturations. Since the leaders are only available to partial subsystems, a distributed estimator is designed to estimate the local reference signals. The saturated function is converted to the combination of a linear part and a nonlinear part, thus overcomes the difficulties caused by unknown saturated bounds. By utilising the command filtered and backstepping control techniques, a two-step method is adopted to construct the controller, under which the effect of unknown input saturations can be compensated well. It is proved that the closed-loop system is practical finite-time stable, and the output of each follower can converge to the dynamic convex hull spanned by the leaders in finite time. Finally, a group of four one-link manipulator systems is used to support the feasibility of the developed control scheme.

Several finite-time containment control issues under stationary and dynamic leadership are the main emphasis of this thesis, which is concerned with a typical class of second-order nonlinear multi-agent systems susceptible to outside intervention. According to a given network topology, the second-order super-twisting sliding mode control is a technique for distributed control that has been developed. In this paper, we mainly consider the situation that the leader moves at a uniform speed. With the proposed method, the followers update status in real time via communication with each other such that all of them are able to eventually converge to the convex hulls consisting of stationary leaders and dynamic leaders in finite time. It leads to make the followers remain stationary or keep moving within the designed region. Eventually, according to the matrix theory and finite-time stability theorem, the paper proves the stability of the finite-time on the proposed control protocol and validates its effectiveness and correctness through simulation.

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law.

Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input

In view of the marine surface vehicles are subject to unknown time-varying external disturbance and its velocities are not available for feedback, a robust finite-time output feedback control scheme is presented for multiple marine surface vehicles to achieve precise formation control in this paper. Without neglecting the first time derivative of disturbance, a novel finite-time extended state observer (FTESO) is proposed to precisely estimate the external disturbance and velocity information in finite time. Based on the outputs of FTESO, the distributed formation controller is designed to guarantee that a group of marine surface vehicles can track the time-varying virtual leader in finite time with precise tracking performance. The errors of the proposed FTESO and formation controller can be guaranteed to converge to zero in finite time by using the homogeneous method and the Lyapunov theory. Numerical simulations are presented to illustrate the effectiveness of the proposed finite-time output feedback formation control scheme.

This paper presents a novel leader-follower consensus control method for a special class of nonlinear multi-agent mechanical systems in the presence of control input saturation and external disturbances, and this class includes robot system dynamics with a wide range of potential applications in industry. In the innovative technique, one of the agents is selected as the leader and the other agents are guided in such a way that the entire states of the system can reach a consensus within the transient limits of the determined performance. Due to the presence of disturbance in most practical systems, the effect of limited disturbance has been evaluated in the consensus control method and actuator saturation is included in the design process of the control technique. Finally, a terminal sliding mode control method is adapted to ensure the stability of the overall system and fast finite-time leader-follower consensus control. The simulation results of the multi-agent nonlinear robot system in the MATLAB environment, in different scenarios by simultaneously considering the actuator saturation and external disturbance, show the effectiveness of the proposed control method.

Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration

Distributed containment control for multiple ocean bottom flying nodes with velocity error constraint and input saturation

A generalized performance evaluation method is presented for extended Kalman filter based state estimation of first order nonlinear dynamic systems. The first order nonlinear dynamic systems are placed in three categorizes in terms of the upper bound of the absolute values of the derivatives of the nonlinear functions. According to the proposed theoretical analysis, it is shown that different state estimation performances are achieved by applying the extended Kalman filter to the first order nonlinear systems in these three categorizes. The steady state mean square error performance of the filter is presented explicitly in terms of the bounds on the nonlinearity and noise variance. The advantage of this performance evaluation method is that the convergence property of estimation error variance can be easily concluded from the system nonlinearity before its implementation. This provides insight into what is going to happen in applications, e.g. for dynamic systems used in chaotic synchronization. The simulation of several different nonlinear dynamic systems shows the effectiveness of the proposed performance evaluation criteria.

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

This paper addresses the leader–follower consensus control problem for a nonlinear multi-agent robot system with control input constraint and external disturbances. Robot system is one of the most important practical systems in the industry. Due to the presence of disturbances in most practical systems, this paper considers the issue of finite-time leader–follower consensus control of the nonlinear multi-agent robot system along with actuator saturation and bounded disturbance. The modified terminal sliding mode control method is suggested for the system which is able to guarantee the stability of the overall system and fast finite-time leader–follower consensus control. For two different scenarios, the simulation of multi-agent robot system has been performed. The results show the effectiveness of the proposed control method.