Distributed Control of Multi-agent Systems with Unknown Time-varying Gains: A Novel Indirect Framework for Prescribed Performance

In this paper, a new yet indirect performance guaranteed framework is established to address the distributed tracking control problem for networked uncertain nonlinear strict-feedback systems with unknown time-varying gains under a directed interaction topology. The proposed framework involves two steps: In the first one, a fully distributed robust filter is constructed to estimate the desired trajectory for each agent with guaranteed observation performance that allows the directions among the agents to be non-identical. In the second one, by establishing a novel lemma regarding Nussbaum function, a new adaptive control protocol is developed for each agent based on backstepping technique, which not only steers the output to asymptotically track the corresponding estimated signal with arbitrarily prescribed transient performance, but also largely extends the scope of application since the unknown control gains are allowed to be time-varying and even state-dependent. In such an indirect way, the underlying problem is tackled with the output tracking error converging into an arbitrarily pre-assigned residual set exhibiting an arbitrarily pre-defined convergence rate. Besides, all the internal signals are ensured to be semi-globally ultimately uniformly bounded (SGUUB). Finally, simulation results are provided to illustrate the effectiveness of the co-designed scheme

Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems with Less Conservative Controllability Conditions

For uncertain multiple inputs multi-outputs (MIMO) nonlinear systems, it is nontrivial to achieve asymptotic tracking, and most existing methods normally demand certain controllability conditions that are rather restrictive or even impractical if unexpected actuator faults are involved. In this note, we present a method capable of achieving zero-error steady-state tracking with less conservative (more practical) controllability condition. By incorporating a novel Nussbaum gain technique and some positive integrable function into the control design, we develop a robust adaptive asymptotic tracking control scheme for the system with time-varying control gain being unknown its magnitude and direction. By resorting to the existence of some feasible auxiliary matrix, the current state-of-art controllability condition is further relaxed, which enlarges the class of systems that can be considered in the proposed control scheme. All the closed-loop signals are ensured to be globally ultimately uniformly bounded. Moreover, such control methodology is further extended to the case involving intermittent actuator faults, with application to robotic systems. Finally, simulation studies are carried out to demonstrate the effectiveness and flexibility of this method

An adaptive extended fuzzy function state-observer based control with unknown control direction

In this paper, a novel adaptive extended fuzzy function state observer based controller is proposed to control a class of unknown or uncertain nonlinear systems. The controller uses Nussbaum-gain technique from literature to prevent controller singularity with unknown control direction and the controller degree of freedom is increased. A state observer which employs the adaptive extended fuzzy function system to approximate a nonlinear system dynamics and estimates the unmeasurable state. The stability of closed-loop control system are shown using Lyapunov stability criterion and Nussbaum function property. The proposed and conventional fuzzy system based controllers are designed to control an inverted pendulum in simulation and a flexible-joint manipulator in real-time experiment. The integral of absoulte error (IAE) of tracking, integral of squared error (ISE) of tracking and integral of required absolute control signal (IA U) performances are compared in applications. The aim of the paper is not only to improve the tracking performances, but also to implement the adaptive extended fuzzy function based controller to a real-time system and conduct the tracking with unknown control direction

Research on Tracking and Synchronization of Uncertain Chaotic Systems

The tracking and synchronization problem of uncertain chaotic system, which is considered to be applied in secure communication in the future by many researchers, is considered in this paper. A double integral sliding mode controller is adopted to cope with the uncertainties of the chaotic system. Adaptive and robust strategies, such as Nussbaum gain method, are used to solve the unmodeled dynamic problem and unknown control direction problem. Meanwhile, the stability of the whole system is guaranteed by constructing of a big Lyapunov function for the whole system. Finally, a four dimension super-chaotic system is used as an example to do the numerical simulation and it testifies the rightness and effectiveness of the proposed method

An Adaptive Dynamic Surface Controller for Ultralow Altitude Airdrop Flight Path Angle with Actuator Input Nonlinearity

In the process of ultralow altitude airdrop, many factors such as actuator input dead-zone, backlash, uncertain external atmospheric disturbance, and model unknown nonlinearity affect the precision of trajectory tracking. In response, a robust adaptive neural network dynamic surface controller is developed. As a result, the aircraft longitudinal dynamics with actuator input nonlinearity is derived; the unknown nonlinear model functions are approximated by means of the RBF neural network. Also, an adaption strategy is used to achieve robustness against model uncertainties. Finally, it has been proved that all the signals in the closed-loop system are bounded and the tracking error converges to a small residual set asymptotically. Simulation results demonstrate the perfect tracking performance and strong robustness of the proposed method, which is not only applicable to the actuator with input dead-zone but also suitable for the backlash nonlinearity. At the same time, it can effectively overcome the effects of dead-zone and the atmospheric disturbance on the system and ensure the fast track of the desired flight path angle instruction, which overthrows the assumption that system functions must be known