Fuzzy Adaptive Predefined Time and Precision Control for Nonlinear Systems with Unknown Control Direction

Asymptotic containment control of uncertain multi-agent systems with partially unknown non-identical control directions

Consensus control of higher-order nonlinear multi-agent systems with unknown control directions

Distributed control of higher-order nonlinear multi-agent systems with unknown non-identical control directions under general directed graphs

In this article, under directed graphs, an adaptive consensus tracking control scheme is proposed for a class of nonlinear multiagent systems with completely unknown control coefficients. Unlike the existing results, here, each agent is allowed to have multiple unknown nonidentical control directions, and continuous communication between neighboring agents is not needed. For each agent, we design a group of novel Nussbaum functions and construct a monotonously increasing sequence in which the effects of our Nussbaum functions reinforce rather than counteract each other. With these efforts, the obstacle caused by the unknown control directions is successfully circumvented. Moreover, an event-triggering mechanism is introduced to determine the time instants for communication, which considerably reduces the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors can converge to an arbitrarily small residual set. Simulation results illustrate the effectiveness of the proposed scheme.

The problem of adaptive consensus is addressed for a class of second‐order nonlinear multi‐agent systems with aperiodically time‐varying parameters and unknown control directions. Firstly, a new adaptive control approach, so‐called congelation of variables method, is adopted to deal with aperiodically time‐varying parameters which are fast‐varying in an unknown compact set with only their radii known a priori. Secondly, a novel Nussbaum‐type function approach is utilized to address the problem of unknown control directions. It is noteworthy that the control directions investigated in this paper are allowed to be completely unknown and nonidentical, whereas the unknown control directions in the most existing works are assumed to be identical. Thirdly, the unknown nonlinear function in each follower's dynamics is approximated by radial basis function neural network approximation technique. The approximation error, external disturbance in the follower's dynamics, as well as the leader's unknown acceleration dynamics are suppressed as an adaptive robust term, which can alleviate the online computational burden. Then, by designing time‐varying control gains updated adaptively with only local information, a fully distributed adaptive consensus control scheme is designed to guarantee that the multi‐agent systems achieve consensus asymptotically in the presence of unknown aperiodically time‐varying parameters, unknown nonidentical control directions, unknown nonlinearities, and external disturbances. Two simulation examples are provided to validate the effectiveness of the proposed consensus protocol.

An iterative learning control (ILC) scheme is designed for a class of nonlinear discrete-time dynamical systems with unknown iteration-varying parameters and control direction. The iteration-varying parameters are described by a high-order internal model (HOIM) such that the unknown parameters in the current iteration are a linear combination of the counterparts in the previous certain iterations. Under the framework of ILC, the learning convergence condition is derived through rigorous analysis. It is shown that the adaptive ILC law can achieve perfect tracking of system state in presence of iteration-varying parameters and unknown control direction. The effectiveness of the proposed control scheme is verified by simulations.

The leaderless consensus problem over strict-feedback nonlinear multiagent systems (MASs) with unknown model parameters and control directions is investigated. The main idea of the existing consensus strategies for strict-feedback nonlinear MASs with unknown control directions is leading agents toward predefined global leaders/exosystems. However, in several missions, agents need to reach autonomous agreement on an a priori unknown quantity for a desired state, and hence the existing results are not applicable in these missions. The main contribution of this article is designing an adaptive leaderless consensus control scheme for strict-feedback nonlinear MASs when agents' control directions are unknown and unidentical. First, we introduce decentralized local error surfaces designed based on each agent position and neighboring agents' positions. We show that as the error surfaces remain bounded and converge to zero, the boundedness of the agents' positions and achieving leaderless consensus in the MAS can be guaranteed. Then, based on the properties of the Nussbaum-type functions, a decentralized backstepping adaptive control law is proposed under which the local error surfaces remain bounded and converge to zero. Finally, the design is more clarified and evaluated via an example.

In this paper, robust adaptive control is proposed for a class of time delay nonlinear systems with unknown constant control gain and control direction. The design is based on the principle of sliding mode control and the use of Nussbaum-type function in solving the problem of the completely unknown control gain. The unknown function and the upper bound of the unknown time delay term are assumed to be in the form of nonlinear functions with unknown coefficients. The uncertain time delay terms are compensated for using appropriate Lyapunov- Krasovskii functional and Young's inequality in the design. The closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.

Observer-based adaptive fuzzy controller for nonlinear systems with unknown control directions and input saturation

This paper proposes a novel two-layer distributed control scheme for global cooperative output regulation for a class of nonlinear multi-agent systems. The concerned systems are (i) heterogeneous and uncertain, (ii) with unknown local control directions, and (iii) under a directed communication graph. To cope with the problem, a two-layer control structure is first configured and distributed and decentralized laws are developed for the layers respectively. Then we demonstrate that combination of the control laws may lead to an effective solution to the cooperative output regulation problem. Finally, an illustrative example is given to show the effectiveness of the proposed control algorithm.

This paper investigates the problem of unknown virtual control directions in a state-quantized adaptive recursive control design for a class of arbitrarily switched uncertain pure-feedback nonlinear systems in a band-limited network. State quantization is considered for state feedback control in a band-limited network. The primary contribution of this study is to provide a quantized state feedback adaptive control strategy to address the unknown control direction and arbitrarily switched nonaffine nonlinearities. Herein, a coupling problem between Nussbaum functions and quantization errors caused by quantized state feedback control laws is considered in the Lyapunov-based design and stability analysis. A state-quantized adaptive recursive control scheme using the function approximation is constructed without a priori knowledge of the signs of the control gain functions, where the estimated parameters and Nussbaum-type functions are adaptively updated via quantized states. Theoretical lemmas are derived to show that the adaptive parameters and quantization errors of the closed-loop signals are bounded using the proposed control scheme. The boundedness of the closed-loop signals and the convergence of tracking error to a neighborhood of the origin are proved using the common Lyapunov function approach. Two simulation examples are shown to illustrate the effectiveness of the proposed theoretical result.

This chapter presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent function. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function’s characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

A decentralized approximation-free control design approach is proposed for interconnected nonlinear time-delay systems with unknown nonaffine pure-feedback nonlinearities. The signs of control coefficient functions derived from the mean value theorem are assumed to be unknown. Control errors are integrated with a priori designable performance functions denoting the bounds of transient and steady-state performance. Based on these integrated errors, a local controller for each subsystem is derived from the recursive design procedure, without the use of function approximators and the repeated differentiations of virtual control laws, where Nussbaum functions are employed to deal with unknown control directions. Compared with the previous multiple approximator-based control results for large-scale systems with unknown nonlinearities, the proposed local approximation-free controller for each subsystem has a simple structure consisting of the integrated errors and the design parameters. All signals in the total closed-loop systems are uniformly ultimately bounded, and the predefined transient and steady-state performance of the tracking error for each subsystem is achieved in the Lyapunov sense.

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.