This paper is concerned with the distributed coordination problem for the nonlinear multi-agent system (MAS) over a general digraph, where each agent is a multi-input multi-output system. The existing solutions are limited to the system without inputs coupling and with known, global Lipschitz, or linearly growing nonlinearities. To remove these requirements, we propose an integrated sub-optimal and control strategy for the more general nonlinear MAS. It consists of a fully distributed adaptive gradient optimization algorithm and a set of model-free prescribed performance controllers. Our approach ensures that the outputs of the MAS converge to the arbitrarily small neighborhoods of the optimal outputs; in particular, the reference-tracking performance is allowed to be freely predefined. Besides, the proposed control strategy is notably simple compared to the existing approaches, which typically employ function approximation, parameter identification, or derivative calculation. Finally, the simulation results illustrate the effectiveness and superiority of the proposed approach.

This paper is concerned with the problem of prescribed performance tracking control for strict-feedback systems with parametric uncertainties and unmatched disturbances. An adaptive command-filtered control approach with performance guarantees is put forward to address the problem. By means of a new-type self-adjustable performance function and a barrier function, it is capable of achieving the practical prescribed time tracking and enhancing the reliability of control implementation simultaneously, without yet the requirement for the specific initial condition. In the control design, a class of finite-time command filters is adopted to solve the “explosion of complexity” problem, and the error compensation mechanism with practical finite-time stability is introduced to remove the impact of filtered errors. Moreover, considering that the overshoot of the tracking error fails to be quantified by the majority of performance functions with infinite initial values, a pair of asymmetric performance functions is constructed such that the trajectory tracking with the predefined overshoot, settling time, and accuracy is achieved, while preserving the capability of relaxing the initial condition. It turns out that the proposed approach warrants the performance-related constraint satisfaction and the boundedness of all the closed-loop signals. Three simulation studies are carried out to demonstrate the theoretical findings.Note to Practitioners—This paper is motivated by the potential fragility problem exhibited in the traditional constraint-handling methods in the presence of paroxysmal factors such as suddenly strong disturbances or highly fluctuating target trajectories. For practical applications (e.g., satellite docking, automobile production, target interception, and network congestion control) suffering from the above scenario, it might be favorable to widen prescribed performance boundaries in a proactive way from the perspective of the safe and reliable operation of the controlled system. On this basis, a novel command filter-based adaptive tracking control solution with self-adjustable performance guarantees is proposed. It not only achieves trajectory tracking with the preassigned overshoot, settling time, and accuracy in the context of raising the reliability of control implementation but also possesses the attributes of inexpensive computation burden and easy acceptability in practical applications.

This paper is concentrated on the problem of decentralized output-feedback control of interconnected strict-feedback systems with actuator failures. It is focused on the cases where the virtual control coefficients of the plant are unknown; the global boundedness, matching conditions or global Lipschitz conditions of the interconnections are not assumed; the control algorithm is as simple as possible. They render the existing decentralized output-feedback fault-tolerant control designs infeasible. To address the problem, a low-complexity decentralized robust prescribed performance control approach based on a linear state transformation and an input-driven filter is put forward in this paper. It achieves the system outputs to track the corresponding references with the preassigned speed and accuracy. It is also inherently robust against the unknown system dynamics, the actuator failures, and the disturbances, thus without parameter estimation, function approximation, derivative computation, command filtering, fault detection, fault isolation or fault estimation. Finally, a comparative simulation on two inverted pendulums linked by a spring is conducted to demonstrate the developed control design. Note to Practitioners—Many complex systems, such as power systems, aerospace systems, and chemical systems, can be modeled as interconnected systems. Moreover, due to the increasing scale and complexity of engineering systems, actuator failures are becoming more likely to occur during system operation. On the other hand, both the transient and steady-state tracking performance of the systems are required to be preassigned in practical scenarios, e.g., missile interception. Existing approaches to compensate for the actuator failures guarantee only the boundedness of the tracking error under nonparametric uncertainties in the system model. This paper presents a decentralized robust prescribed performance control approach. It is inherently robust to the system nonlinearities, the actuator failures, and the disturbances. It exhibits lower costs in computation, higher efficiency in design, and is more user-friendly in implementation. It achieves trajectory tracking with preassigned rate and accuracy, despite the actuator failures. Extension of the approach to multi-agent systems with actuator failures is an interesting topic for future investigations.

This paper is concerned with the problem of fault-tolerant prescribed performance attitude stabilization for space-craft under model uncertainties and actuator failures. In most of the existing control designs for spacecraft described by the unit quaternion, the possible singularity issue of the virtual control coefficient matrix is neglected such that the controllability of the attitude subsystem cannot be warranted throughout. On the other hand, the related works depend on complex algorithms of approximation, estimation or diagnosis to deal with unknown system dynamics. In this paper, a singularity-free low-complexity fault-tolerant prescribed performance control (PPC) strategy is put forward. To exclude the singularity issue, an initialization principle of the performance envelop is devised. On this basis, a static PPC law is developed, without parameter identification, function approximation, disturbance estimation, failure detection, failure isolation, failure estimation. In place of the classical Lyapunov stability theory, a unified performance analysis framework based on proof by contradiction and the barrier Lyapunov function is constructed. It not only turns out attitude stabilization with the preassigned settling time and accuracy whenever the actuator failures happen, but also discloses the intrinsic robustness of the control system versus actuator failures and model uncertainties. A comparative study on a rigid spacecraft is performed to demonstrate the validity and advantage of our approach.

This paper is dealt with the tracking control problem for the multi-input multi-output (MIMO) block-triangular nonlinear systems with output constraints under discontinuous references. It is focused on the case where the system exhibits inherent nonlinearities, e.g., radically unbounded nonlinearities, and totally unknown dynamics. This renders the existing solutions infeasible. To surmount this challenge, a novel hybrid tracking control strategy composed of a robust decoupling constrained controller and a proportional controller is devised in this paper. It guarantees that the system outputs evolve within the prescribed constraint bands and track the discontinuous references with the tunable settling time and accuracy. Moreover, the controller shows a significant simplicity. No attempt is made for parameter identification, function approximation, disturbance estimation, derivative calculation or command filtering, despite the unknown system dynamics and the recursive control design. The theoretical findings are validated by a comparative experiment on a 2-DOF serial flexible link (2DSFL) robot.

This paper is dealt with the problem of reference tracking for the robotic manipulators with unknown dynamics and subject to multiplicative and additive sensor faults. The resulting dynamics of the closed-loop system is both unknown and structurally variable, for which the widely adopted approximation tools are not effective straightforward. Moreover, the multiplicative sensor faults result in the loss of strong controllability of the closed-loop system, which renders the conventional fault-tolerant control methods infeasible. To overcome these obstacles, an innovative fault-tolerant funnel control strategy based on a mixed-gain adaption technique is put forward in this paper. The controller involves information of neither the plant model nor the sensor faults, but does not invoke the tools for parameter identification, function approximation, data driving, iterative learning, disturbance estimation, fault estimation or fault diagnosis. It achieves reference tracking of the robotic arms with the predefined settling time and accuracy against the sensor faults. A comparative experiment on a 2-DoF serial flexible link robot is conducted to illustrate the effectiveness and advantages of the proposed approach.Note to Practitioners—This paper was motivated by the problem of fault-tolerant control (FTC) of robotic manipulators but also applies to other MIMO nonlinear plants with inputs coupling, e.g., permanent magnet synchronous motors and dynamic positioning operated vessels. The existing FTC methods work for the case where sensor faults do not alter the strong controllability of the closed-loop system. Instead, the non-strongly controllable faulty plants are considered in this paper to develop the FTC approaches to further enhance the fault tolerance of robotic manipulators. On the other hand, the involvement of sensor faults results in irregular dynamics of the closed-loop system, which cannot be addressed by the conventional approximation techniques, e.g., neural networks or fuzzy logic systems. Therefore, FTC of robotic manipulators against sensor faults that cause loss of strong controllability of control systems is challenging but significant in both academia and industry. To this end, this paper suggests a novel fault-tolerant funnel control approach based on a mixed-gain adaption technique. It is independent of the model information or the fault information, thus with a high universal property. Even so, no effort is paid for model identification or fault diagnosis, and thus the controller is simple and easy for implementation. It achieves fast accurate tracking control with prescribed settling time and accuracy, which is significant for improving efficiency and quality. The feasibility of the proposed approach is validated by a 2-DoF serial flexible link robot.

This article is concerned with the high-performance leader-following problem for the heterogeneous nonlinear multiagent systems. It is focused on the cases where the underlying communication graph is directed and switching; the model information of each agent is unknown; only the relative output measurement is available for the local controller design. They render the existing distributed high-performance control solutions infeasible. In this article, a distributed robust output-feedback prescribed performance control strategy is put forward to conquer this obstacle. First, the resulting control is off-line designed, regardless of the initial condition or the switching condition. Second, it automatically adjusts the neighborhood errors and the intermediate errors online, against the topology switching. Besides, it is inherently robust to the unknown system dynamics, without parameter identification, function approximation, disturbance estimation, or derivative calculation or estimation. It turns out that global fast accurate output synchronization is achieved by our approach in the sense that the follower outputs track the leader output with the preassigned settling time and accuracy after the topology switching. A comparative simulation is conducted to substantiate the above theoretical findings.

The problem of prescribed performance control (PPC) for the multi-input multi-output block-triangular nonlinear systems under output constraints is investigated in this article. It is focused on the scenario where the references are not known in advance. This renders the related solutions infeasible and becomes more challenging under the totally unknown and inherently nonlinear dynamics of the system. To overcome this challenge, a novel robust decoupling PPC strategy is developed in this article, in which an online boundary generation scheme and a smoothly constraint switching rule are devised and introduced. The resulting controller ensures that the system outputs evolve within their respective constraint bands and track the references with the predetermined overshoot, settling time and accuracy. Moreover, it is independent of function approximation, parameter identification, or disturbance estimation, despite the unbounded nonlinearities, unmatched disturbances and unknown dynamics. A comparative experiment on a 2-DOF serial flexible link robot is conducted to show the efficacy and superiority of our low-complexity high-performance control approach.

The problem of high-performance tracking control for the nonlinear systems with nonparametric uncertainties as well as time-varying disturbances is investigated in this paper. In place of the methods of sliding-mode control, variable structure control, and robust integral of the sign of the error control, an output- feedback fuzzy prescribed performance control approach is put forward. It consists of a fuzzy state observer, a proportional- integral (PI) constraint-handling scheme, and an adaptive fuzzy backstepping PI control unit. The developed approach achieves output tracking with the predefined settling time and accuracy. Moreover, it actively restrains the oscillations of both the tracking error and the intermediate errors. On the other hand, the compact set condition for fuzzy approximation is rigorously warranted. Besides, the chattering phenomenon and the requirement for differentiable disturbances by the existing methods are excluded. A pair of comparative simulations is performed to demonstrate the efficacy and advantage of our approach.

This article is focused on the problem of prescribed performance control (PPC) for the strict-feedback systems under actuator failures with dynamic redundancies and deferred actuator replacement. It is concentrated on the cases where both the multiplicative nonlinearities and the additive nonlinearities of the plant are unknown and the fault-tolerant control (FTC) algorithm is as simple as possible. They render the existing solutions infeasible. In this article, we develop a low-complexity fault-tolerant PPC (FTPPC) approach, which is made up of a nominal controller, a fault detection module, and a reconfigurable controller. It ensures reference tracking with the predetermined speed and accuracy during the fault-free case and recovers the predefined performance after the deferred actuator replacement. The controller does not rely on the specific knowledge about the system dynamics, the disturbances, or the time profile and bound of the actuator failures. Moreover, it obviates the needs for parameter identification, function approximation, command filtering, and disturbance estimation. A comparative simulation on a jet engine compressor is carried out to demonstrate the above theoretical findings.

This article is concerned with the prescribed performance tracking control problem for the strict-feedback systems with unknown nonlinearities and unmatched disturbances. The challenge lies in the realization of a complete performance specification for trajectory tracking in the sense of quantitatively regulating the peak value, overshoot, settling time, and accuracy while ensuring that the initial condition holds naturally. To this end, an error transformation, equipped with a shifting function, is introduced and incorporated with a new-type barrier function. Then, a class of performance functions is exploited to quantify the settling times and steady-state bounds of the intermediate errors. Moreover, to improve the flexibility of formulating performance specifications for the tracking error, a pair of asymmetric performance boundaries are further designed. With their combination, a novel robust prescribed performance control (PPC) approach is proposed in this article. It not only achieves the quantitative performance guarantees but also preserves the unique simplicity of PPC, evading the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are confirmed via three simulation studies.

This article is concerned with the problem of reference tracking for the lower-triangular nonlinear systems with a chain of odd powers. Contrary to most of the related studies, this work is focused on the case where neither the odd powers nor their bounds are known. This renders the majority of the existing methods for stability analysis and control design for the odd-power systems infeasible. To surmount this challenge, a robust prescribed performance control strategy together with a constraint analysis by contradiction is put forward. Instead of the well-established adding one power integrator technique, a group of barrier functions are employed to combat the tracking error and the intermediate errors. In lieu of the Lyapunov stability theory, a constraint analysis by contradiction is carried out, which discloses the inherent robustness of the control system against the nonparametric uncertainties, the unmatched disturbances and the unknown odd powers. It is guaranteed that the tracking error enters into a preassigned neighborhood of zero after a given time, with a predefined bound on the overshoot. In addition, the proposed control exhibits a striking simplicity. Despite the severe model uncertainties and the recursive control design, no effort needs to be paid for parameter identification, function approximation, disturbance estimation, or derivative calculation. The above theoretical findings are substantiated by the comparative simulation results.

The problem of fast accurate trajectory tracking for the underactuated wheeled mobile robots (WMRs) with unknown dynamics and external disturbances is investigated in this article. A novel adaptive fuzzy prescribed performance control strategy is proposed to deal with the problem. Instead of the approach angle or the azimuth angle, a pair of heading- and orientation-related auxiliary variables is adopted to deal with the underactuation of the WMR. In place of the transverse function, the barrier function is combined with the adaptive fuzzy logic system to cope with the unknown WMR dynamics, as well as environmental disturbances. Moreover, the barrier function is used to confine the position error rather than the tracking errors. By doing so, a continuous singularity-free high-performance control scheme is derived, which ensures that the WMR tracks the reference trajectory with the predefined speed and accuracy. Finally, a couple of comparative simulation studies are carried out to illustrate the above theoretical findings.

This paper is concerned with the problem of fault-tolerant dynamic positioning (DP) for the marine surface vessels with sensor faults and unknown dynamics as well as random disturbances. It is anticipated that the requisite performance for the faulty system still holds, especially for the post-fault phrase, which remains open in the literature. In this paper, a fault-tolerant prescribed performance control approach is put forward to solve the problem. It achieves DP with the prescribed speed and accuracy in the sense that the DP errors evolve within the preselected performance envelops whenever the sensor faults happen. It is also inherently robust against the unknown vessel dynamics and ocean disturbances. Thus, the common assumptions on the partially known vessel nonlinearities and the differentiable disturbances are eliminated. On the other hand, there is no need for disturbance estimation, parameter identification, function approximation, fault detection, fault isolation or fault estimation, yielding a control simplicity. Finally, a pair of comparative simulations on Cybership II are carried out to validate the feasibility and advantage of the proposed approach.

This article is concerned with the fast and accurate trajectory tracking control problem for a sort of underactuated surface vehicle under model uncertainties and environmental disturbances. A novel neural networks (NNs)-based prescribed performance control strategy is proposed to solve the problem. In the control design, a new type of performance function is constructed which provides a way to predefine the settling time and accuracy, straightforward. Then, a pair of barrier functions are employed to combat not only the position error but also the virtual control input. This evades the possible singularity or discontinuity of the control solution. Next, an initialization technique is exploited, removing the requirement for the initial condition of the control system. Finally, two NNs are employed to deal with the unknown ship nonlinearities. The performance analysis not only demonstrates the effectiveness of the proposed approach but also reveals its robustness against disturbances and unknown reference trajectory derivatives. There is, thus, no need to acquire such knowledge or employ specialized tools to handle disturbances. The theoretical findings are illustrated by a simulation study.

This article is concerned with the problem of tracking control with discontinuous references for the strict-feedback systems with both multiplicative and additive nonlinearities as well as unmatched disturbances. In contrast with the existing studies, it is focused on the cases where the system nonlinearities are radially unbounded; the system dynamics or its bounding functions are unknown; and the reference derivatives are unavailable. They significantly challenge the existing control solutions under discontinuous references which are based on filtering, guidance, or impulsive systems. To conquer this obstruction, a novel hybrid control scheme is devised in this article, which consists of a robust constraint-handling controller and a proportional controller. It steers the system output to track the discontinuous reference with tunable setting time and accuracy, without violation of the prescribed constraint. Moreover, the controller exhibits a significant simplicity. While it is independent of the specific model information of the plant or the derivatives of the intermediate control signals, no effort is paid for parameter identification, function approximation, command filtering, or disturbance estimation. Finally, three simulation studies are conducted to substantiate the theoretical result.

Intelligent manufacturing has promoted the development of Industry 4.0 and enabled the manufacturing industry to gradually move into the stage of intelligence with the rapid development of the Internet of Things and the Industrial Internet. An intelligent manufacturing system is a manufacturing system that can automatically adapt to changing environments and varying process requirements with minimal supervision and assistance from operators. Therefore, intelligent manufacturing has become a recognized core high technology to enhance the overall competitiveness of the manufacturing industry. The goal of intelligent manufacturing is to make production resources form a circular network with the characteristics of autonomy, adjustability, and configurability, to develop production processes flexibly, and to realize the efficiency of individual customization. For example, by analyzing the factory floor data, equipment monitored data, and the enterprise manufacturing database, it could help to store, explore, and make complex decisions for the manufacturing system. To achieve this goal, modern information technologies, such as artificial intelligence, big data, cloud computing, and mobile Internet, modeling, control, and optimization need to be integrated and collaborated with the physical resources of the manufacturing process, which triggers new theory, solution algorithms, and application scenarios.

This article is concerned with the global prescribed performance tracking control problem for strict-feedback systems with quantized references, unknown nonlinearities, and unmatched disturbances. Discontinuity appears frequently in such references, for which most nonlinear control or filtering methods are not applicable straightforward. Besides, the existing approaches of predefining tracking performance work under local initial conditions, available nonlinearity knowledge, disturbance-free cases, or have complexity issues. In this article, a novel smoothing function is first designed for the online automatic generation of smooth trajectories in place of the quantized reference. Then, the tangent barrier functions are combined with a new form of performance functions (inverse proportional functions) to form a control. The strong robustness of the resulting controller against model uncertainties and disturbances evades the need for approximation, observation, etc., yielding simplicity of the control. The new performance functions relax the specific initial condition. Their combination ensures for any initial condition, the tracking error converges to a given bound. Simulation results on vehicular platoons illustrate the theoretical findings.

This article is concerned with the cooperative tracking control problem for heterogeneous multiagent systems in a leader-following form under a directed graph. The dynamics of each following agent is unknown, obeying a strict-feedback form. With the help of fuzzy-logic systems, input filters, and constraint-handling schemes, a fully distributed output-feedback control algorithm is proposed to achieve output synchronization with prescribed performance and guarantee boundedness of signals in the closed-loop systems. In addition, the algorithm exhibits a simplicity control attribute in the sense that: 1) the control design utilizes only relative output measurements, and no extra information needs to be transmitted via the network and 2) the issue of explosion of complexity is addressed, without employing command filters or dynamic surface control techniques. Finally, the simulation results clarify and verify the established theoretical findings.

This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study.

This article is concerned with the fault-tolerant tracking control problem for pneumatic continuum manipulator (PCM) systems with actuator faults. Conventional control strategies applied to PCMs have difficulty addressing the tracking control issue for systems subject to actuator faults. In this article, we provide a robust fault-tolerant control strategy for solving this issue. We first present an error transformation approach that possesses potential robustness against model uncertainties and unknown actuator faults. To relax certain restrictions in the error transformation approach, we then adopt a tuning function to adjust the error variables. By doing so, global stability of the closed-loop system is ensured. Finally, the effectiveness of this control strategy is validated through experiments on a PCM.

This article is concerned with the tracking control problem for a sort of networked system with unknown nonlinear functions, unmatched disturbances, and event-triggered input. A novel prescribed performance control strategy together with an actuator update protocol is developed to form a solution. Different from the existing results, only a binary signal (either 0 or 1) needs to be sent to the actuator. In this way, the number and the bit of data transmission are both curtailed, leading to the economy of the communication cost. On the other hand, output tracking with guaranteed transient and steady-state performance is achieved regardless of unknown nonlinearities, disturbances, and measurement errors. Finally, simulation results are given to illustrate the established theoretical findings.

This paper investigates the tracking control problem for a family of strict-feedback systems with unknown nonlinear functions as well as unmatched disturbances. A low-computation adaptive fuzzy control strategy combined with a constraint-handling technique is proposed to achieve accurate trajectory tracking and boundedness of the closed-loop signals. In contrast to the existing results: first, without the expense of introducing auxiliary filters, iterative calculation of virtual control signal derivatives at each step of the backstepping design that may cause the explosion of complexity issue is obviated; second, the need for disturbance observers and robust compensators to suppress disturbances and approximation errors that require a mass of online learning parameters for estimation is evaded; and third, a small number of closed-loop signals are incorporated into the input space of fuzzy logic systems for approximation. The result from a comparative simulation further illustrates the superiority of the presented approach.

This article is concerned with the fault-tolerant control (FTC) problem for Euler-Lagrange systems subject to process faults that cause changes in the system dynamics. The possibly time-varying and discontinuous changes bring out a challenge for fuzzy approximation. To conquer this obstacle, a novel adaptive fuzzy FTC strategy is proposed in this article. First, a constraint-handling scheme is designed to ensure zero overshoot for certain signals. In this way, the resulting unknown term, composed of the signs of sliding surfaces, the bounds of faults, and model uncertainties, is both continuous and within a fixed form. Subsequently, adaptive fuzzy systems are adopted to approximate this unknown term for compensation. It is proved that the tracking performance and the boundedness of signals in the closed-loop system are guaranteed by the developed method. The simulation results further illustrate the established theoretical findings.

This paper explores the fault-tolerant control problem for a family of nonlinear systems in Brunovsky form. The presence of process and actuator faults leads to an unknown and time-varying system structure, such that neural networks or fuzzy logic systems cannot be utilized for approximation directly. To solve this problem, a new-type control strategy is proposed. A zero-overshoot error constraint technique is first introduced to keep the sign of a certain variable invariant, while ensuring the premise on a compact set. Then, a fuzzy logic system is adopted to approximate the bound of the unknown and time-varying nonlinear dynamics. Further a group of adaptive mechanisms are employed to compensate for the approximation error as well as actuator faults. It is proved that by applying the presented method, both the tracking performance and the boundedness of closed-loop signals can be guaranteed. Finally, simulation results are given to illustrate the established theoretical findings intuitively.

This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.