Intelligent Tracking Control for a Class of Uncertain High-Order Nonlinear Systems

Adaptive Iterative Learning Fault-Tolerant Control for State Constrained Nonlinear Systems With Randomly Varying Iteration Lengths

This article presents an adaptive iterative learning fault-tolerant control algorithm for state constrained nonlinear systems with randomly varying iteration lengths subjected to actuator faults. First, the modified parameters updating laws are designed through a new defined tracking error to handle the randomly varying iteration lengths. Second, the radial basis function neural network method is used to deal with the time-iteration-dependent unknown nonlinearity, and a barrier Lyapunov function is given to cope with the state constraint. Finally, a new barrier composite energy function is used to achieve the tracking error convergence of the presented control algorithm along the iteration axis with the state constraint and then followed with the extension to the high-order case. A simulation for a single-link manipulator is given to illustrate the effectiveness of the theoretical studies.

Event-triggered tracking control of uncertain p-normal nonlinear systems with full-state constraints

This paper investigates the tracking control problem of uncertain p-normal nonlinear systems with full-state constraints via event-triggered mechanism. By skillful constructing an adaptive dynamic gain and a time-varying event-triggered strategy, a state-feedback controller is proposed to achieve practical tracking. The adaptive dynamic gain is incorporated to deal with the system uncertainties and eliminate the bad effect of the sampling error. A rigorous Lyapunov stability analysis method is put forward to verify that all the closed-loop signals are uniformly bounded and the tracking error converges into a prescribed arbitrary accuracy, and full-state constraints are not violated. Compared with the existing event-triggered strategies, the proposed time-varying event-triggered strategy is low-complexity without designing the hyperbolic tangent function.

Adaptive composite dynamic surface neural control for nonlinear fractional-order systems subject to delayed input

In the article, the adaptive composite dynamic surface neural controller design problem for nonlinear fractional-order systems (NFOSs) subject to delayed input is discussed. A fractional-order auxiliary system is first designed to solve the input-delay problem. By using the developed novel estimation models, the defined prediction errors and the states of error system can decide the weights of radial basis function neural networks (RBFNNs). During the dynamic surface controller design process, the developed fractional-order filters are designed to handle the complexity explosion problem when the classical backstepping control technique is utilized. It is shown that the designed adaptive composite neural controller ensures that all the system state variables are bounded and the tracking error of the considered system finally tends to a small neighborhood of zero. Finally, the results of the simulation explain the feasibility of the developed controller. In addition, the developed controller can also be applied to single input and single output(SISO) nonlinear systems subject to a unitary input function.

Fixed-Time Tracking Control for Nonlinear Cascade Systems with Unknown High Powers

This paper investigates the global fixed-time tracking control problem of nonlinear cascade systems with unknown high powers. In the process of control design, a upper bound and a lower bound of high powers are introduced to compensate the unknown system powers, and a state feedback controller is designed under any initial system conditions. Based on the Lyapunov stability analysis method and the fixed-time stability theory, it is verified that the proposed method can regulate the output tracking error to a disc region of the origin within a fixed-time and all the closed-loop signals are bounded. At last, the effectiveness of the proposed scheme is verified by some simulation results.

A Separation-Based Methodology to Consensus Tracking of Switched High-Order Nonlinear Multiagent Systems

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. Even the adding-one-power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the power of the virtual and actual control laws increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.

Novel deep learning architectures for haemodialysis time series classification

Classifying haemodialysis sessions, on the basis of the evolution of specific clinical variables over time, allows the physician to identify patients that are being treated inefficiently, and that may need additional monitoring or corrective interventions. In this paper, we propose a deep learning approach to clinical time series classification, in the haemodialysis domain. In particular, we have defined two novel architectures, able to take advantage of the strengths of Convolutional Neural Networks and of Recurrent Networks. The novel architectures we introduced and tested outperformed classical mathematical classification techniques, as well as simpler deep learning approaches. In particular, combining Recurrent Networks with convolutional structures in different ways, allowed us to obtain accuracies above 81%, coupled with high values of the Matthews Correlation Coefficient (MCC), a parameter particularly suitable to assess the quality of classification when dealing with unbalanced classes-as it was our case. In the future we will test an extension of the approach to additional monitoring time series, aiming at an overall optimization of patient care.

Robust adaptive control for uncertain nonlinear systems with odd rational powers, unmodeled dynamics, and non-triangular structure

Numerous approaches have been reported for different control problems of low-order triangular nonlinear systems. Nevertheless, it shows that the dynamic models of some practical plants are high-order nonlinear systems with odd rational powers. Besides, these systems constantly possess a non-triangular form and suffer from the impact of unmodeled dynamics. The related studies of such systems are very few and more challenging. This work concentrates on adaptive control issue of high-order nonlinear system with odd rational powers, unmodeled dynamics, and non-triangular structure. Based on the small-gain theorem, and by employing the adaptive technique, adding a power integrator method, and neural network method, we successfully construct a new adaptive controller, which greatly decreases the use of parameter estimations in the adaptive control of the considered system. An example highlights that the strategy regulates the studied systems well and performs satisfied system responses.

Fuzzy Adaptive Cooperative Consensus Tracking of High-Order Nonlinear Multiagent Networks With Guaranteed Performances

This work addresses the distributed consensus tracking problem for an extended class of high-order nonlinear multiagent networks with guaranteed performances over a directed graph. The adding one power integrator methodology is skillfully incorporated into the distributed protocol so as to tackle high powers in a distributed fashion. The distinguishing feature of the proposed design, besides guaranteeing closed-loop stability, is that some transient-state and steady-state metrics (e.g., maximum overshoot and convergence rate) can be preselected a priori by devising a novel performance function. More precisely, as opposed to conventional prescribed performance functions, a new asymmetry local tracking error-transformed variable is designed to circumvent the singularity problem and alleviate the computational burden caused by the conventional transformation function and its inverse function, and to solve the nondifferentiability issue that exists in most existing designs. Furthermore, the consensus tracking error is shown to converge to a residual set, whose size can be adjusted as small as desired through selecting proper parameters, while ensuring closed-loop stability and preassigned performances. One numerical and one practical example have been conducted to highlight the superiority of the proposed strategy.

Adaptive Neural Network Stochastic-Filter-Based Controller for Attitude Tracking With Disturbance Rejection

This article proposes a real-time neural network (NN) stochastic filter-based controller on the Lie group of the special orthogonal group [Formula: see text] as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. First, an adaptive NN-based stochastic filter is proposed, which estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely, unknown bias and noise corrupting angular velocity measurements. The closed-loop signals of the proposed NN-based stochastic filter have been shown to be semiglobally uniformly ultimately bounded (SGUUB). Second, a novel control law on [Formula: see text] coupled with the proposed estimator is presented. The control law addresses unknown disturbances. In addition, the closed-loop signals of the proposed filter-based controller have been shown to be SGUUB. The proposed approach offers robust tracking performance by supplying the required control signal given data extracted from low-cost inertial measurement units. While the filter-based controller is presented in continuous form, the discrete implementation is also presented. In addition, the unit-quaternion form of the proposed approach is given. The effectiveness and robustness of the proposed filter-based controller are demonstrated using its discrete form and considering low sampling rate, high initialization error, high level of measurement uncertainties, and unknown disturbances.

Consensus in High-Power Multiagent Systems With Mixed Unknown Control Directions via Hybrid Nussbaum-Based Control

This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.

Adaptive Approximation-Based Tracking Control for a Class of Unknown High-Order Nonlinear Systems With Unknown Powers

In this article, the problem of adaptive tracking control is tackled for a class of high-order nonlinear systems. In contrast to existing results, the considered system contains not only unknown nonlinear functions but also unknown rational powers. By utilizing the fuzzy approximation approach together with the barrier Lyapunov functions (BLFs), we present a new adaptive tracking control strategy. Remarkably, the BLFs are employed to determine a priori the compact set for maintaining the validity of fuzzy approximation. The primary advantage of this article is that the developed controller is independent of the powers and can be capable of ensuring global stability. Finally, two illustrative examples are given to verify the effectiveness of the theoretical findings.

Distributed adaptive fixed-time neural networks control for nonaffine nonlinear multiagent systems

This paper, with the adaptive backstepping technique, presents a novel fixed-time neural networks leader–follower consensus tracking control scheme for a class of nonaffine nonlinear multiagent systems. The expression of the error system is derived, based on homeomorphism mapping theory, to formulate a set of distributed adaptive backstepping neural networks controllers. The weights of the neural networks controllers are trained, by an adaptive law based on fixed-time theory, to determine the adaptive control input. The control algorithm can guarantee that the output of the follower agents of the system effectively follow the output of the leader of the system in a fixed time, while the upper bound of the settling time can be calculated without initial parameters. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed consensus tracking control approach. A step-by-step procedure for engineers and researchers interested in applications is proposed.

Adaptive Fuzzy Event-Triggered Control for High-Order Nonlinear Systems With Prescribed Performance

This article focuses on the design of a novel adaptive fuzzy event-triggered tracking control approach for a category of high-order uncertain nonlinear systems with prescribed performance requirements, in which a high-order tan-type barrier Lyapunov function (BLF) is employed to handle and analyze the output tracking error, fuzzy systems are adopted to identify the totally unknown nonlinear functions, and only one gain function rather than parameter estimation functions is designed to cancel out all unknowns appearing in fuzzy systems. As a result, complicated calculations are avoided and a structured simple control is achieved. The proposed controller not only ensures that the tracking error is always within a predefined region but also reduces the communication burden from the controller to the actuator. Finally, comparison simulations are presented to verify the effectiveness of the proposed control schemes.

Tracking Control of Unknown and Constrained Nonlinear Systems via Neural Networks With Implicit Weight and Activation Learning

For systems with irregular (asymmetric and positively-negatively alternating) constraints being imposed/removed during system operation, there is no uniformly applicable control method. In this work, a control design framework is established for uncertain pure-feedback systems subject to the aforementioned constraints. By introducing a novel transformation function and with the help of auxiliary constraining boundaries, the original output-constrained system is augmented to unconstrained one. Unknown nonlinearity is approximated by neural networks (NNs) with not only neural weight updating but also activation online adjustment. The resultant control scheme is able to deal with constraints imposed or removed at some time moments during system operation without the need for altering control structure. When applied to high-speed trains, the developed control scheme ensures position tracking under speed constraints, simulation demands, and confirms the effectiveness of the proposed method.

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

Disturbance rejection in fuzzy systems based on two dimensional modified repetitive-control

This paper concerns with the issues of designing an improved-equivalent-input-disturbance (IEID) based robust two dimensional modified repetitive control (2D MRC) for a class of fuzzy systems in the presence of aperiodic disturbances. Specifically, IEID-estimator is implemented to the 2D MRC systems that estimates all types of disturbances and compensates them for assuring robust stability. In particular, the proposed 2D MRC system has two different type of behaviours such as continuous control and discrete learning independently. To obtain gains of the observer and the controller, an adequate set of robust stability conditions is derived in the form of a linear-matrix-inequalities. Finally, simulation results for three numerical examples are provided to depict the efficacy of the proposed control technique.

An Active Repetitive Learning Control Method for Lateral Suspension Systems of High-Speed Trains

This article presents a novel perspective to improve the ride quality of high-speed trains (HSTs), namely, by virtue of the periodicity of lateral dynamics to suppress the lateral vibration of HST. To resolve the contradiction between the complex HST model and the effective controller design, a simplified three-degrees-of-freedom (3-DOF) quarter-vehicle model is first employed for controller design, while a 17-DOF full-vehicle model is built for efficiency verification, where periodic and random track irregularities are considered, respectively. An active repetitive learning control (RLC) method is proposed to achieve the periodic tracking control, where the learning convergence is proved rigorously in a Lyapunov way. The configuration of RLC-based lateral suspensions is economical in the sense that only four actuators and six sensors are needed. It is verified by simulation that, compared with the dynamic matrix controller, the proposed RLC controller has greatly reduced the lateral vibration of a vehicle body, especially the lateral acceleration in the frequency range of (0, 3] Hz to which human body is strongly sensitive.

Adaptive Fuzzy Control With High-Order Barrier Lyapunov Functions for High-Order Uncertain Nonlinear Systems With Full-State Constraints

This paper focuses on the practical output tracking control for a category of high-order uncertain nonlinear systems with full-state constraints. A high-order tan-type barrier Lyapunov function (BLF) is constructed to handle the full-state constraints of the control systems. By the BLF and combining a backstepping design technique, an adding a power integrator, and a fuzzy control, the proposed approach can control high-order uncertain nonlinear system with full-state constraints. A novel controller is designed to ensure that the tracking errors approach to an arbitrarily small neighborhood of zero, and the constraints on system states are not violated. The numerical example demonstrates effectiveness of the proposed control method.

Adaptive Neural Quantized Control for a Class of MIMO Switched Nonlinear Systems With Asymmetric Actuator Dead-Zone

This paper concentrates on the adaptive state-feedback quantized control problem for a class of multiple-input-multiple-output (MIMO) switched nonlinear systems with unknown asymmetric actuator dead-zone. In this study, we employ different quantizers for different subsystem inputs. The main challenge of this study is to deal with the coupling between the quantizers and the dead-zone nonlinearities. To solve this problem, a novel approximation model for the coupling between quantizer and dead-zone is proposed. Then, the corresponding robust adaptive law is designed to eliminate this nonlinear term asymptotically. A direct neural control scheme is employed to reduce the number of adaptive laws significantly. The backstepping-based adaptive control scheme is also presented to guarantee the system performance. Finally, two simulation examples are presented to show the effectiveness of our control scheme.

A New Approach to Stochastic Stability of Markovian Neural Networks With Generalized Transition Rates

This paper investigates the stability problem of Markovian neural networks (MNNs) with time delay. First, to reflect more realistic behaviors, more generalized transition rates are considered for MNNs, where all transition rates of some jumping modes are completely unknown. Second, a new approach, namely time-delay-dependent-matrix (TDDM) approach, is proposed for the first time. The TDDM approach is associated with both time delay and its time derivative. Thus, the TDDM approach can fully capture the information of time delay and would play a key role in deriving less conservative results. Third, based on the TDDM approach and applying Wirtinger's inequality and improved reciprocally convex inequality, stability criteria are derived. In comparison with some existing results, our results are not only less conservative but also involve lower calculation complexity. Finally, numerical examples are provided to show the effectiveness and advantages of the proposed results.

Neuroadaptive Control of Strict Feedback Systems With Full-State Constraints and Unknown Actuation Characteristics: An Inexpensive Solution

In this paper, we present a neuroadaptive control for a class of uncertain nonlinear strict-feedback systems with full-state constraints and unknown actuation characteristics where the break points of the dead-zone model are considered as time-variant. In order to deal with the modeling uncertainties and the impact of the nonsmooth actuation characteristics, neural networks are utilized at each step of the backstepping design. By using barrier Lyapunov function, together with the concept of virtual parameter, we develop a neuroadaptive control scheme ensuring tracking stability and at the same time maintaining full-state constraints. The proposed control strategy bears the structure of proportional-integral (PI) control, with the PI gains being automatically and adaptively determined, making its design less demanding and its implementation less costly. Both theoretical analysis and numerical simulation validate the benefits and the effectiveness of the proposed method.

A Novel Error-Compensation Control for a Class of High-Order Nonlinear Systems With Input Delay

A novel tracking error-compensation-based adaptive neural control scheme is proposed for a class of high-order nonlinear systems with completely unknown nonlinearities and input delay. In the tracking errors of existing papers, there exist the following difficulties: first, output curve always lags behind the desired trajectory, second, some big peak errors cause a decrease in tracking precision, and third, a big initial value of the modified tracking error can make the closed-loop system unstable. To tackle them, three corresponding error-compensation terms are constructed, including a prediction and compensation term, an auxiliary signal produced by the constructed auxiliary system, and a damping term. However, inequality amplification caused by high order will weaken the effectiveness of the proposed error-compensation scheme, and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known. To overcome aforementioned difficulties, in the derivation of the first virtual control law, the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities, a lumped control coefficient achieved by state transformation, and the dynamic of the proposed error-compensation terms and desired signal. Meanwhile, input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values. Finally, it is proven that all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed method.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems

In this paper, an adaptive neural net- works (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Control-oriented modeling and adaptive backstepping control for a nonminimum phase hypersonic vehicle

In this paper, the nonminimum phase problem of a flexible hypersonic vehicle is investigated. The main challenge of nonminimum phase is the prevention of dynamic inversion methods to nonlinear control design. To solve this problem, we make research on the relationship between nonminimum phase and backstepping control, finding that a stable nonlinear controller can be obtained by changing the control loop on the basis of backstepping control. By extending the control loop to cover the internal dynamics in it, the internal states are directly controlled by the inputs and simultaneously serve as virtual control for the external states, making it possible to guarantee output tracking as well as internal stability. Then, based on the extended control loop, a simplified control-oriented model is developed to enable the applicability of adaptive backstepping method. It simplifies the design process and releases some limitations caused by direct use of the no simplified control-oriented model. Next, under proper assumptions, asymptotic stability is proved for constant commands, while bounded stability is proved for varying commands. The proposed method is compared with approximate backstepping control and dynamic surface control and is shown to have superior tracking accuracy as well as robustness from the simulation results. This paper may also provide a beneficial guidance for control design of other complex systems.