Adaptive fault-tolerant control for high-order fully actuated system with full-state constraints

This paper studies the adaptive tracking control problem for a class of uncertain high-order fully actuated (HOFA) systems with actuator faults and full-state constraints. Firstly, we design a novel nonlinear transformation function (NTF) only related to state and constraint boundaries and capable of handling asymmetric time-varying constraints. With the designed function, we obtain an equivalent totally unconstrained HOFA model which is generally simpler to design controllers than first-order state-space model. Then, the adaptive fault-tolerant controller is constructed with the help of the HOFA approach. By applying the Lyapunov stability theory, it is rigorously proved that the output tracking error converges to zero asymptotically, other signals of the resulting closed-loop systems are bounded, and full-state constraints are not violated for all time. Finally, the simulation results verify the efficiency of the proposed control design method.     

Cascade design for formation control of nonholonomic systems in chained form

This paper presents a constructive method to design a cooperative state and output feedback to steer a group of nonholonomic mobile robots in chained form to form a desired geometric formation shape. The control methodology divides the resulting tracking error dynamics into a cascaded of linear and time-varying subsystems. A basic consensus algorithm is first applied to the linear subsystem which makes the states synchronize exponentially to zero. Once this first linear subsystem has converged, the second cascade can be treated as a linear time-varying subsystem perturbed by a vanishing term from its cascade. A dynamic state and output feedback is constructed to achieve synchronization of the rest of the states. The proof of stability is given using a result from cascade systems. Since time delay appears in many interconnection networks and particularly in cooperative control, its effect on the stability of the closed-loop system is analyzed using Razumikhim theorem. It is shown that the established cooperative controller work well even in the presence of time delay. Numerical simulations are performed on models of car-like mobile robots to show the effectiveness of the proposed cooperative state and output-feedback controllers.     

Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.     

MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback

In practice, many controlled plants are equipped with MIMO non-affine nonlinear systems. The existing methods for tracking control of time-varying nonlinear systems mostly target the systems with special structures or focus only on the control based on neural networks which are unsuitable for real-time control due to their computation complexity. It is thus necessary to find a new approach to real-time tracking control of time-varying nonlinear systems. In this paper, a control scheme based on multi-dimensional Taylor network (MTN) is proposed to achieve the real-time output feedback tracking control of multi-input multi-output (MIMO) non-affine nonlinear time-varying discrete systems relative to the given reference signals with online training. A set of ideal output signals are selected by the given reference signals, the optimal control laws of the system relative to the selected ideal output signals are set by the minimum principle, and the corresponding optimal outputs are taken as the desired output signals. Then, the MTN controller (MTNC) is generated automatically to fit the optimal control laws, and the conjugate gradient (CG) method is employed to train the network parameters offline to obtain the initial parameters of MTNC for online learning. Addressing the time-varying characteristics of the system, the back-propagation (BP) algorithm is implemented to adjust the weight parameters of MTNC for its desired real-time output tracking control by the given reference signals, and the sufficient condition for the stability of the system is identified. Simulation results show that the proposed control scheme is effective and the actual output of the system tracks the given reference signals satisfactorily.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

Connectivity-preserving approximation-free design for synchronized tracking of uncertain networked nonaffine nonlinear multi-agent systems

This paper presents a connectivity-preserving approximation-free design strategy for the distributed synchronized tracking of uncertain nonlinear multi-agent systems with limited communication ranges. All nonaffine nonlinearities in pure-feedback form are assumed to be unknown. The main contribution of this paper is to achieve approximation-free synchronized tracking while preserving the initial interaction patterns among agents. To this end, each synchronization error term is individually transformed to a nonlinear error function with a predefined time-varying function. The local tracking laws using only the relative output information among agents are designed via these nonlinear error terms. The connectivity preservation and preassigned tracking performance of the proposed synchronized tracking system are recursively analyzed in the Lyapunov sense, without employing any function approximators and potential functions. Finally, the effectiveness and robustness of the proposed strategy are demonstrated through simulation examples.     

Robust time-varying output formation tracking for heterogeneous multi-agent systems with adaptive event-triggered mechanism

This paper investigates the time-varying output formation tracking problem of heterogeneous multi-agent systems subjected to model uncertainties and external disturbances via adaptive event-triggered mechanism. Firstly, an adaptive distributed event-triggered observer is constructed to acquire the leader’s state and a time-varying formation output tracking controller utilizing sliding mode method is proposed to deal with the model uncertainties and external disturbances can be addressed. Secondly, an algorithm is given to claim the design procedures of the event-triggered based controller and asymptotic convergence of the controller is proved based on Lyapunov theory. Thirdly, Zeno-behavior is proved to be excluded strictly. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.     

Output tracking control with L1-gain performance for positive switched systems

This paper concentrates on the output tracking control problem with L₁-gain performance of positive switched systems. We adopt the multiple co-positive Lyapunov functions technique and conduct the dual design of the controller and the switching signal. Through introducing a new state variable, which is not the output error, the output tracking control problem of the original system is transformed into the stabilization problem of the dynamics system of this new state. The proposed approach is still effective even the output tracking control problem of any subsystem is unsolvable. According to the state being available or not, we establish the solvability conditions of the output tracking control problem for positive switched systems, respectively. In the end, a number example demonstrates the validity of the presented results.     

Type-B Nussbaum function-based fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme.     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Controller design for 2-D stochastic nonlinear Roesser model: A probability-dependent gain-scheduling approach

This note is concerned with the static output feedback control problem for two-dimensional (2-D) uncertain stochastic nonlinear systems. The systems under consideration are subjected to time delays, multiplicative noises and randomly occurring missing measurements. A random variable sequence following the Bernoulli distribution with time-varying probability is employed to character the missing measurements which are assumed to occur in a random way. A new gain-scheduling method based on the time-varying probability parameter is proposed to accomplish the design task. By constructing a suitable Lyapunov functional, sufficient conditions to guarantee the systems to be mean-square asymptotically stable are established. The addressed 2-D controller design problem can be reduced to a convex optimization problem by some mathematical techniques. In the last section, a numerical example and the comparative analysis are provided to illustrate the efficiency of our proposed design approach.     

Leader-following rendezvous for uncertain Euler–Lagrange multi-agent systems by output feedback

In this paper, we investigate the problem of output feedback tracking for a class of Euler–Lagrange multi-agent systems with unmeasurable velocity and input disturbances. By proposing a novel dynamic velocity observer, an adaptive output feedback consensus algorithm is proposed such that the tracking errors of all agents can converge to an arbitrarily small neighborhood of zero by tuning the design parameters. A numerical example is presented to illustrate the effectiveness of the controller.     

Fuzzy adaptive output-feedback tracking control for nonlinear strict-feedback systems in prescribed finite time

The current paper addresses the fuzzy adaptive tracking control via output feedback for single-input single-output (SISO) nonlinear systems in strict-feedback form. Under the situation of system states being unavailable, the system output is used to set up the state observer to estimate the real system states. Furthermore, the estimation states are employed to design controller. During the control design process, fuzzy logic systems (FLSs) are used to model the unknown nonlinearities. A novel observer-based finite-time tracking control scheme is proposed via fuzzy adaptive backstepping and barrier Lyapunov function approach. The suggested fuzzy adaptive output feedback controller can force the output tracking error to meet the pre-specified accuracy in a fixed time. Meanwhile, all the closed-loop variables are bounded. Compared to some existing finite-time output feedback control schemes, the developed control strategy guarantees that the settling time and the error accuracy are independent of the uncertainties and can be specified by the designer. At last, the effectiveness and feasibility of the proposed control scheme are demonstrated by two simulation examples.     

Adaptive fuzzy output feedback fault-tolerant tracking control of switched uncertain nonlinear systems with sensor faults

This paper investigates the adaptive fuzzy output feedback fault-tolerant tracking control problem for a class of switched uncertain nonlinear systems with unknown sensor faults. In this paper, since the sensor may suffer from an unknown constant loss scaling failure, only actual output can be used for feedback design. A failure factor is employed to represent the loss of effectiveness faults. Then, an adaptive estimation coefficient is introduced to estimate the failure factor, and a state observer based on the actual output is constructed to estimate the system states. Fuzzy logic systems are used to approximate the unknown nonlinear functions. Based on the Lyapunov function method and the backstepping technique, the proposed control scheme with average dwell time constraints can guarantee that all states of the closed-loop system are bounded and the tracking error can converge to a small neighborhood of zero. Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme.     

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.     

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.     

Cooperative output regulation problem of multi-agent systems with stochastic packet dropout and time-varying communication delay

In this paper, we deal with the cooperative output regulation problem of linear multi-agent systems on a directed network topology subject to both stochastic packet dropout and time-varying communication delay. On the basis of introducing a queuing mechanism, a distributed state feedback control algorithm is proposed. Then the continuous-time multi-agent systems with piece-wise constant control are converted into discrete-time systems. Under some standard assumptions, the necessary and sufficient conditions under which the tracking errors of followers approach to the origin asymptotically are proposed for different exosystems. Finally, the proposed results are verified via two examples.     

Specified-time bearing-based formation control of multi-agent systems via a dynamic gain approach

In this paper, the specified-time bearing-based formation control problem is investigated via a dynamic gain approach. Both the leader-follower and leaderless cases for single- and double-integral multi-agent systems are considered with bearing measurement, respectively. By considering the communication graph as bearing rigid, distributed bearing-based controllers with a time-varying gain are designed. By using time transformation method and Lyapunov stability theory, the close-loop systems under the proposed protocols can achieve the target formation within the specified time. Comparing with some existing results, the proposed approaches can make multi-agent systems converge to the desired formation within any preset time without dependence on the initial conditions or system parameters. Finally, some simulations and experiments are presented to demonstrate the effectiveness of the proposed algorithms.     

Analysis of a relay-controlled plant with one negative real pole of order two

In this paper a relay-controlled plant possessing one negative real pole of order two is studied. First a regulating system is considered, in that we investigate design of the controller for simultaneous reduction of error and error derivative to zero. Through simple linear transformations, it is shown that the equation of switching curve can be made independent of any constant gain as well as the value of the repeated pole of the plant. Next, we consider the tracking problem and show the type of admissible input such that after a minimum transient time the plant output would follow this input perfectly and, as in the case of a regulating system, with at most one switching reversal of the relay.     

Adaptive output-feedback control for nonlinear time-delay systems in pure-feedback form

The main contribution of this paper is to develop an adaptive output-feedback control approach for a class of uncertain nonlinear systems with unknown time-varying delays in the pure-feedback form. Both the non-affine nonlinear functions and the unknown time-varying delayed functions related to all state variables are considered. These conditions make the controller design difficult and challenging because the output-feedback controller should be designed using only the output information. In order to overcome these conditions, we design an observer-based adaptive dynamic surface controller where the time-delay effects are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique using neural networks. A first-order filter is added to the control input to avoid the algebraic loop problem caused by the non-affine structure. It is proved that all the signals in the closed-loop system are semi-globally uniformly bounded and the tracking error converges to an adjustable neighborhood of the origin.