Predictive control of discrete-time high-order fully actuated systems with application to air-bearing spacecraft simulator

This paper addresses an output tracking problem for discrete-time high-order fully actuated (DHOFA) systems and its application in the control of air-bearing spacecraft (ABS) simulator. A HOFA system model, as a novel system representation, is applied to establish the dynamics of discrete-time control systems. Accordingly, a HOFA predictive control scheme is presented to deal with this problem, which is composed of a HOFA feedback for stabilization and a HOFA predictive control for tracking. In this scheme, a Diophantine equation is exploited to construct an incremental HOFA (IHOFA) prediction model to substitute a reduced-order prediction model, and then a cost function involving tracking performance is minimized by using multi-step output predictions. A sufficient and necessary condition is proposed to discuss the stability and tracking performance of the closed-loop DHOFA systems, it is simple to utilize in system analysis and extend in practice. Two experiments of the control of ABS simulator are shown to illustrate the feasibility of the presented HOFA predictive control scheme.     

High-order command filtered adaptive backstepping control for second- and high-order fully actuated strict-feedback systems

In this paper, a high-order command filtered adaptive backstepping (HOCFAB)-based approach is proposed in order to track a given reference signal for the second- and high-order strict-feedback systems (SFSs) with parametric uncertainties, where both their subsystems hold a common full-actuation structure, namely, high-order fully actuated (HOFA) SFSs. Unlike the prevailing traditional first-order state-space backstepping approach which suffers from the problem of “explosion of terms”, the proposed HOCFAB approach circumvents the complexity arising owing to differentiating the virtual controllers repeatedly, and does not need to convert the high-order systems into first-order forms which is easier to carry out and demands fewer steps. Meanwhile, an error-compensating mechanism is constructed to reduce filtering errors. A critical analysis is theoretically proven which indicates that in both cases the entire system states are uniformly ultimately bounded under the proposed high-order controller, and the tracking error could be made arbitrarily small with predesigned parameters. Finally, the effectiveness of the proposed scheme is verified by a benchmark application in the robotic manipulator.     

Event-triggered fuzzy control for nonlinear time-delay system with full-state constraints and unknown hysteresis

This article considers the nonlinear time-delay system with full-state constrains and actuator hysteresis. Compared with the previous research on input hysteresis phenomenon, all states in the system are required to be constrained in a bounded compact set and the direction of hysteresis is unknown. Thus, the system is difficult to be stabilized and get perfect error tracking performance, and the design procedure is more complicated. By combining barrier Lyapunov functions (BLFs) and Nussbaum functions, a new virtual controller is designed, which combines the properties of Nussbaum function with fuzzy logic systems (FLSs). Furthermore, considering that the rate-dependent characteristic of actuator hysteresis will adversely affect the stability of networked control systems (NCSs), a first-order filter is used to solve the problem, but it brings challenges to the design of Lyapunov–Krasovskii functions (KLFs). Thus, a new LKFs is constructed to compensate for the adverse effects of state delay on the nonlinear system. What’s more, this article propose event-triggered technique to solve the coupling effect of the system communication resource constrains. The proposed adaptive control strategy ensures the boundedness of all signals and does not violate the state constraints, and the controller avoids Zeno behavior, and the tracking error fluctuates around zero in a predetermined compression range. Finally, two simulations results verify the effectiveness of the adaptive control strategy.     

Adaptive robust fault-tolerant control for a two-slider synchronization system with a flexible beam

In this paper a novel adaptive robust fault-tolerant sync control method is proposed for a two-slider system where two sliders are constrained by a flexible beam. At first the dynamic models of sync motion system subject to external disturbances and actuator faults are derived. In order to avoid the shortcomings of truncated model, the model of flexible beam is described by using infinite dimensional equation. Then based on the models a novel disturbance observer and an adaptive fault-tolerant control law are designed. The disturbance observer is used to estimate and cancel external disturbances. The adaptive fault-tolerant control is used to deal with the partial loss of effectiveness faults. Lyapunov functional approach is used to prove that the closed-loop system with the proposed control laws is uniformly bounded stable. Finally, some simulation results display that the proposed control laws can obtain excellent sync performance in the present of external disturbances and actuator partial loss of effectiveness faults.     

High-order fully actuated system approaches: Model predictive control with applications to under-actuated systems

The main results of this paper are concentrated on the nonlinear model predictive control (MPC) tracking optimization based on high-order fully actuated (HOFA) system approaches. The proposed HOFA MPC strategy makes full use of full-actuation property to eliminate the nonlinear dynamics of the system, and then the nonlinear optimization problem is equivalently transformed into a series of easy-solve linear convex optimization problems. Different from general nonlinear MPC methods and the current optimal control of the HOFA system approach, an analytical controller with smooth and less energy is obtained by the moving horizon optimization. And it is proven that the proposed controller can stabilize the corresponding tracking error closed-loop system. Finally, not limited to FA systems, as examples, a nonlinear numerical under-actuated model in the mathematical sense and a benchmark nonlinear under-actuated mechanical system are transformed into corresponding equivalent HOFA systems, the simulation results are given to verify the effectiveness of the proposed strategy.     

Switching fault-tolerant control of a moving vehicle-mounted flexible manipulator system with state constraints

In this brief, a switching fault-tolerant control (FTC) scheme is presented for a moving vehicle-mounted flexible manipulator subject to state constraints. The dynamic characteristics of the system are represented by coupled ordinary differential equations and partial differential equations (ODEs–PDEs). When actuators are healthy, vibration control and position regulations can be realized without violation of the given constraints based on a Barrier Lyapunov Function (BLF). Moreover, a switching strategy is introduced to prevent the transgression of constraints even under actuator failure by detecting actuator faults as-assisted by the proposed monitoring functions. The closed-loop states are kept within the given bounds under FTC laws. By extending LaSalle's Invariance Principle to an infinite dimension, the asymptotic stability of the fault-free closed-loop system is strictly verified. Simulation results demonstrate the effectiveness of the proposed approach.     

Neuroadaptive deferred full-state constraints control without feasibility conditions for uncertain nonlinear EASSs

This article studies the neuroadaptive full-state constraints control problem for a class of electromagnetic active suspension systems (EASSs). First, the original constraint system with arbitrary initial values is transformed into a new constraint system with zero initial values by using the shift function method. Then, a new kind of cotangent-type nonlinear state-dependent transition function is constructed to solve the asymmetric time-varying full-state constraints control problem, which eliminates the limitation that the virtual controller needs to satisfy the feasibility conditions in the previous full-state constraints control based on Barrier Lyapunov Function (BLF) and Integral BLF. Furthermore, the neural networks (NNs) are used as nonlinear function approximators to deal with the unknown nonlinear dynamics of EASSs, a neuroadaptive full-state constraints control design method is proposed under the Backstepping recursive design framework. Finally, the effectiveness of the proposed method is verified by a simulation of EASSs with road disturbances.     

Adaptive dynamic surface tracking control for uncertain full-state constrained nonlinear systems with disturbance compensation

In this paper, an asymptotic adaptive dynamic surface tracking control strategy is investigated for uncertain full-state constrained nonlinear systems subject to parametric uncertainties and external disturbances. A novel disturbance estimator (DE) is firstly used to compensate for external disturbances. The parametric uncertainties are accordingly handled via a synthesized adaptive law. Then, by using the barrier Lyapunov function (BLF) and dynamic surface control (DSC), an appropriate backstepping design framework employing a novel adaptive-gain nonlinear filter is given, which avoids the “explosion of complexity” and relieves the conservatism of filter gain selection. The theoretical analysis reveals the asymptotic tracking performance is assured with the proposed controller. In the end, some simulation cases demonstrate the validity of the proposed controller.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Robust fault-tolerant control for four-wheel individually actuated electric vehicle considering driver steering characteristics

A robust fault-tolerant control scheme for distributed actuated electric vehicles is proposed to maintain vehicle stability suffering actuator faults while considering the driver personality differences. The proposed scheme integrates the cooperative game and terminal sliding mode control into the framework of the feedback linearization method (FLM). Firstly, the nonlinearities of the driver-vehicle system are treated by the knowledge of Lie derivative, and then a set of controllable virtual subsystems is obtained through diffeomorphism. To achieve multi-objective cooperation, the interaction framework of virtual subsystems is modeled based on cooperative game theory, which provides a basic feedback control scheme (BFCS). Finally, a terminal sliding mode technology-based active compensation control scheme is integrated into BFCS to handle the systemic disturbances caused by actuator faults. An implementation of hardware-in-the-loop verifies that the stability of the vehicle under the control of the developed approach can be guaranteed for different drivers and different fault types.     

Adaptive fault-tolerant control for continuous-time Markovian jump systems with signal quantization

This paper investigates the adaptive fault-tolerant control problem for a class of continuous-time Markovian jump systems with digital communication constraints, parameter uncertainty, disturbance and actuator faults. In this study, the exact information for actuator fault, disturbance and the unparametrisable time-varying stuck fault are totally unknown. The dynamical uniform quantizer is utilized to perform the design work and the mismatched initializations at the coder and decoder sides are also considered. In this paper, a novel quantized adaptive fault-tolerant control design method is proposed to eliminate the effects of actuator fault, parameter uncertainty and disturbance. Moreover, it can be proved that the solutions of the overall closed-loop system are uniformly bounded, which is asymptotically stable almost surely. Finally, numerical examples are provided to verify the effectiveness of the new methodology.     

Adaptive stabilization control for high-order nonlinear time-delay systems with its application

This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.     

Distributed fixed-time control of high-order multi-agent systems with non-holonomic constraints

In this paper, a protocol is proposed for fixed-time consensus of the high-order chained-form multi-agent systems subject to non-holonomic constraints. By employing the backstepping structure and a power integrator, the distributed fixed-time protocol is designed to guarantee that system states reach consensus before a fixed time. The fixed settling time can be calculated explicitly, and it is independent of initial conditions. The proposed protocol is applied to multi-agent wheeled mobile robots to support the theoretical result.     

Distributed fault-tolerant consensus tracking control for multiple Lagrangian systems with preset error bound constraints

Actuator faults often occur in physical systems, which seriously affect the transient performance and control accuracy of the system. For the finite-time consensus tracking problem of multiple Lagrangian systems with actuator faults and preset error constraints, a novel distributed fault-tolerant controller is proposed in this paper. The proposed controller is developed based on the barrier Lyapunov function method and the adding a power integrator technique, which can not only guarantee the steady-state performance of the system but also its transient performance. Due to its strong sensitivity to the variation of system errors, the proposed controller can quickly eliminate the system initial errors and the error perturbations caused by actuator faults. That is, the controller can guarantee that the consensus error converges to zero in a finite time and is always constrained within the preset error bound. Finally, the effectiveness of the developed controller is verified by simulation of a multi-manipulator system.     

Adaptive fault-tolerant shape control for nonlinear Lipschitz stochastic distribution systems

This paper addresses the problem of adaptive fault estimation and fault-tolerant control for a class of nonlinear non-Gaussian stochastic systems subject to time-varying loss of control effectiveness faults. In this work, time-varying faults, Lipschitz nonlinear property and general stochastic characteristics are taken into consideration in a unified framework. Instead of using the system output signal, the output distribution is adopted for shape control. Both the states and faults are simultaneously estimated by an adaptive observer. Then, a fault tolerant shape controller is designed to compensate for the faults and realize stochastic output distribution tracking. Both the fault estimation and the fault tolerant control schemes are designed based on linear matrix inequality (LMI) technique. Satisfactory performance has been obtained for a numerical simulation example. Furthermore the proposed scheme is successfully tested in a case study of particle size distribution control for an emulsion polymerization reactor.     

Adaptive fault-tolerant control for a class of nonlinear multi-agent systems with actuator faults

This paper considers the distributed adaptive fault-tolerant control problem for linear multi-agent systems with matched unknown nonlinear functions and actuator bias faults. By using fuzzy logic systems to approximate the unknown nonlinear function and constructing a local observer to estimate the states, an effective distributed adaptive fault-tolerant controller is developed. Furthermore, different from the traditional method to estimate the weight matrix, only the weight vector needs to be estimated by exchanging the order of weight vectors and fuzzy basis functions in the fuzzy logic systems. In contrast to the existing results, the assumption that the dimensions of input vector and output vector are equal is removed. In addition, it is proved that the proposed control protocol guarantees all signals in the closed-loop systems are bounded and all agents converge to the leader with bounded residual errors. Finally, simulation examples are given to illustrate the effectiveness of the proposed method.     

Adaptive finite-time fuzzy control for hybrid levitation system of maglev trains with active anti-lock constraints

The great risk of the suspension contact tremendously restricts the practical public service of hybrid maglev trains. If an operational train contacts to the guideway resulting in the “lock” state, it would cut down its lifetime or even endanger passenger safety. To address the deadlock problem of hybrid maglev trains, a novel adaptive finite-time fuzzy control with active anti-lock constraints is proposed in this paper. First, an efficient fuzzy-logic system is applied to approximate the hybrid levitation dynamics, not only precisely describing the system but also reducing computation burden. Moreover, by a novel nonlinear coordinate transformation, an anti-lock levitation controller is designed to prevent suspension contact between trains and guideways via the back-stepping technique. In the process, command filtering is utilized to circumvent the derivatives of virtual control variables and to address practical input constraints. Differing from the barrier Lyapunov function technique, the proposed nonlinear transformation helps to directly address both positive lower and upper boundaries. In addition, finite time convergence is achieved by the proposed scheme, which enjoys the characteristics of a fast and quantifiable response. Numerical simulations verify the theoretical results.     

Adaptive neural network control for flexible telerobotic systems with communication constraints

This paper investigates the synchronous control problem for a class of flexible telerobotic systems subject to system uncertainties and communication constraints. In view of the asymmetric time-varying communication delays, an adaptive time-delay estimator is designed to reduce the impacts of delays on the system. Moreover, by combining the neural networks and parameter adaptive method, the uncertainties of system dynamics are estimated and compensated. Based on these efforts, a new adaptive compensation control protocol is proposed. Additionally, input quantization in network control induced chattering phenomenon and unknown parameters is also dealt with by the adaptive compensation method. A useful characteristic of this paper is that the “complexity explosion” problem caused by the backstepping technique is circumvented effectively. Finally, sufficient conditions are derived for the synchronous control of the master-slave flexible telerobotic system under Lyapunov stability theory. A numerical example of flexible-joint robotic system is provided to illustrate the effectiveness of the proposed control schemes.     

Removing the feasibility conditions on adaptive fuzzy decentralized tracking control of large-scale nonlinear systems with full-state constraints

This work is dedicated to solving the adaptive fuzzy decentralized tracking control issue of large-scale nonlinear systems with full-state constraints. Different with barrier Lyapunov function, the main difference is that a novel nonlinear state-dependent function (NSDF) is introduced to prevent the state constraints being overstepped. Based on NSDF, the necessary feasibility conditions for virtual controllers are completely removed. Then, the prior knowledge of the unknown virtual control coefficients is no longer required since the original system is transformed via the new affine variable. Under the control strategy, three objectives on system performance are achieved: (a) all signals of the closed-loop system are bounded; (b) the subsystem output closely tracks the reference trajectory and original error is ultimately uniformly bounded; (c) the full-state constraints are not violated for all the time. At the end, two simulation examples are shown to verify the effectiveness of the control method.     

Adaptive data-driven fault-tolerant control for nonlinear systems: Koopman-based virtual actuator approach

This paper proposes an adaptive data-driven fault-tolerant control scheme using the Koopman operator for unknown dynamics subjected to nonlinearities, time-varying loss of effectiveness, and additive actuator faults. The main objective of this method is to design a virtual actuator to hide actuator faults from the view of the system’s nominal controller without having any prior knowledge about the system’s underlying dynamics. The designed virtual actuator is placed between the faulty plant and the nominal controller of the system to keep the dynamical system’s performance consistent before and after the occurrence of actuator faults. Based on the Koopman operator theory, an equivalent Koopman predictor is first obtained using the process data only, without knowing the governing equations of the underlying dynamics. Koopman operator is an infinite-dimensional, linear operator which takes the nonlinear process data into an infinite-dimensional feature space where the dynamic data correlations have linear behavior. Next, based on the approximated system’s Koopman operator, a virtual actuator is designed and implemented without knowing the system’s nominal controller. Needless to use a separate fault detection, isolation, and identification module to perform fault-tolerant control, the current method leverages the adaptive framework to keep the system’s desired performance in facing time-varying additive and loss of effectiveness actuator faults. Finally, the approach’s efficacy is demonstrated using simulation on a two-link manipulator benchmark, and a comparison study is presented.