Unknown Nonlinear Terms Research Articles

Adaptive Resilient Neural Control of Uncertain Time-Delay Nonlinear CPSs with Full-State Constraints under Deception Attacks.

This paper focuses on the adaptive control problem of a class of uncertain time-delay nonlinear cyber-physical systems (CPSs) with both unknown time-varying deception attacks and full-state constraints. Since the sensors are disturbed by external deception attacks making the system state variables unknown, this paper first establishes a new backstepping control strategy based on compromised variables and uses dynamic surface techniques to solve the disadvantages of the huge computational effort of the backstepping technique, and then establishes attack compensators to mitigate the impact of unknown attack signals on the control performance. Second, the barrier Lyapunov function (BLF) is introduced to restrict the state variables. In addition, the unknown nonlinear terms of the system are approximated using radial basis function (RBF) neural networks, and the Lyapunov-Krasovskii function (LKF) is introduced to eliminate the influence of the unknown time-delay terms. Finally, an adaptive resilient controller is designed to ensure that the system state variables converge and satisfy the predefined state constraints, all signals of the closed-loop system are semi-globally uniformly ultimately bounded under the premise that the error variables converge to an adjustable neighborhood of origin. The numerical simulation experiments verify the validity of the theoretical results.

NNs-observer-based fully distributed consensus control for MASs under deception attacks

This paper proposes a novel resilient intrusion-tolerance control scheme to solve the consensus control problem of multi-agent systems (MASs) under deception attacks. Consider the state unavailability of MASs with unknown nonlinear terms, the unmeasurable state is estimated by designing the neural-networks(NNs)-based observer. Then, a fully distributed intrusion-tolerant adaptive protocol is developed to implement the consensus control task. The designed control strategy only involves the agent states that interact with the neighboring agent and does not relate to the whole communication topology information. The designed controller can ensure that the consensus error of the nonlinear MASs is eventually ultimately bounded under deception attacks. Finally, a numerical simulation is provided to verify the feasibility of the designed scheme.

Secure Cooperative Path Following of Autonomous Surface Vehicles Under Cyber and Physical Attacks

This paper is concerned with the networked cooperative path following (CPF) problem for multiple autonomous surface vehicles (ASVs) subject to simultaneous cyber and physical attacks. First, to compensate the adverse effects of the physical-attack-induced bias injections, an extended state observer is designed to provide real-time estimates of the unmeasured velocities and unknown nonlinear terms. Next, to identify and handle various cyber attacks, a novel secure data transmission mechanism, featuring a secure transmitter and a secure receiver, is developed for each ASV. Then, a secure CPF control scheme, consisting of a networked cooperative kinematic control law and a networked kinetic control law, is presented. Furthermore, the observer error dynamics and networked CPF error dynamics are derived to account for the simultaneous network-induced delays, packet dropouts, physical attacks, and cyber attacks. The proposed control scheme is capable to preserve satisfactory secure tracking performance of the resulting CPF control system under a desired reference path even in the presence of external environmental disturbances, delays, packet dropouts, and malicious attacks. Finally, several case studies are provided to substantiate the effectiveness of the secure CPF control scheme.

DSC‐based finite‐time adaptive resilient control for a class of nonstrict‐feedback switched nonlinear systems with deception attacks

AbstractIn this paper, the finite‐time adaptive resilient control problem for a class of switched nonlinear systems with deception attacks by using the dynamic surface control (DSC) strategy is addressed. A more general class of uncertain nonstrict‐feedback switched nonlinear systems with the sensor and actuator deception attacks are considered. Deception attacks can damage sensor, control and switching data, which results in the switching signal and the finite‐time control gains unknown, meanwhile the conventional dynamic surface errors inacessible. To overcome the difficulty, first, the approximation technique of neural networks (NNs) is used to deal with the unknown nonlinear terms and compensate the sensor and actuator deception attacks. Secondly, a new coordinate transformation and a novel switched adaptive finite‐time filter are designed to mitigate the effects caused by the sensor attacks and avoid the problem of “explosion of complexity”. Thirdly, Nussbaum technology is exploited to handle the unknown finite‐time control gains problem caused by deception attacks. Then, by the proposed control strategy, the practical finite‐time stability analysis is presented. Finally, a simulation example is provided to validate the feasibility of the proposed control method.

Finite-Time Adaptive Fuzzy Control for Unmodeled Dynamical Systems with Actuator Faults

This article concentrates upon the issue of finite-time tracking control for a category of nonlinear systems in pure-feedback form with actuator faults and unmodeled dynamics, where the loss of effectiveness and bias fault are considered. Meanwhile, the function approximation method utilizing fuzzy logic systems and dynamic surface control approach with first-order filter are implemented to model the unknown nonlinear terms induced from the proposed controller procedure and tackle the “explosion of complexity” issue of the classic backstepping method. The use of the maximal norm of the weight vector estimation method and adaptive approach reduces the computation load induced by fuzzy logic systems. Within the framework of backstepping control, a finite-time adaptive fuzzy fault-tolerant control protocol is derived to guarantee the boundedness of all signals and tracking error of the controlled system within a finite-time. Simulation studies are offered to show the validity of the derived theoretical results of the finite-time control protocol.

Fixed-time self-structuring neural network fault-tolerant tracking control of underactuated surface vessels with state constraints

In this paper, a fixed-time fault-tolerant control strategy is proposed for trajectory tracking of underactuated surface vessels (USVs) with input saturation. A predefined region boundary function is proposed, which has all predefined fixed-time convergence properties and provides predefined specifications for tracking errors. To achieve the predetermined tracking performance, a fixed-time adaptive neural network state constrained fault-tolerant controller is proposed based on dynamic surface control technology, a back-stepping program, and an asymmetric time-varying tangent barrier Lyapunov function (ATVTBLF). The unknown external environment disturbances and complex continuous unknown nonlinear terms are approximated by a self-structuring neural network (SSNN), which can improve the robustness of the control system to unknown parameters and guarantee the tracking performance of the control system. The number of neurons of the SSNN can be adjusted online according to the approximation efficiency, which can reduce the amount of calculation of the control system. Based on Lyapunov stability theory, it is proven that the closed-loop system is bounded and stable in a fixed time, and the tracking error is always kept within the constraint range. The simulation results show that the underactuated surface vessel control system has good tracking performance.

Leader–follower consensus for nonlinear multi-agent systems with unknown measurement sensitivities

In this paper, the leader–follower consensus problem is investigated for a class of lower-triangular nonlinear multi-agent systems with unknown measurement sensitivities. By developing a dual-domination gain method, a distributed compensator is proposed for each follower by utilising the output information of the follower and its neighbour agents. Based on the compensator, an output feedback control law is designed to achieve consensus. These two gains are used to deal with the unknown measurement noises and nonlinear terms, respectively. Then the consensus problem is transformed into a stability problem by introducing an appropriate state transformation. Based on the Lyapunov stability theory, it is proved that the states of the leader and followers can achieve consensus asymptotically. In the end, numerical simulations are provided to verify the correctness of the proposed consensus algorithm.

Integral Sliding Mode-Based Fault-Tolerant Control for Dynamic Positioning of Unmanned Marine Vehicles Based on a T-S Fuzzy Model

This paper investigates a fault-tolerant control problem for the dynamic positioning of unmanned marine vehicles based on a Takagi–Sugeno (T-S) fuzzy model using an integral sliding mode scheme. First, the T-S fuzzy model of an unmanned marine vehicle is established by taking the yaw angle variable range into account. An integral sliding mode control scheme combined with the H∞ performance index is then developed to attenuate the initial influence of thruster faults and ocean disturbances. The unknown nonlinear function is approximated using a fuzzy logic system based on a representation of marine data, which provides a good tradeoff between resolution of the unknown nonlinear term approximation and computational complexity for marine engineering by adjusting the number of fuzzy logic system rules. In addition, the fault estimation information is utilized to design the sliding mode surface on the basis of an adaptive mechanism and a matrix full rank decomposition technique, which reduces conservatism. The validity of the proposed approach is finally demonstrated by an analysis of simulation results using a typical floating production vessel model.

Dynamic event-triggered-based human-in-the-loop formation control for stochastic nonlinear MASs

The dynamic event-triggered (DET) formation control problem of a class of stochastic nonlinear multi-agent systems (MASs) with full state constraints is investigated in this article. Supposing that the human operator sends commands to the leader as control input signals, all followers keep formation through network topology communication. Under the command-filter-based backstepping technique, the radial basis function neural networks (RBF NNs) and the barrier Lyapunov function (BLF) are utilized to resolve the problems of unknown nonlinear terms and full state constraints, respectively. Furthermore, a DET control mechanism is proposed to reduce the occupation of communication bandwidth. The presented distributed formation control strategy guarantees that all signals of the MASs are semi-globally uniformly ultimately bounded (SGUUB) in probability. Finally, the feasibility of the theoretical research result is demonstrated by a simulation example.

Distributed Bearing-Only Formation Control for Heterogeneous Nonlinear Multi-Robot Systems

This paper addresses the bearing-only formation tracking problem for heterogeneous nonlinear multi-robot systems. In contrast to position and distance-based formation algorithms, the robots can only measure the bearing information from their neighbors to achieve cooperation while the state information is unavailable. This characteristic is able to be implemented in the hardware to reduce the requirements of the sensors. We construct a compensation function in the proposed controller to eliminate the effect of the unknown nonlinear terms in the system. This compensation function is also based on bearing measurements, which guarantees that the overall controller is bearing-only. The stability of the proposed formation tracking strategy can be ensured by Lyapunov techniques. Moreover, we analyze the performance of the protocol for moving leaders, where the formation tracking error can be restricted in a bounded set. Finally, the simulation results are presented to validate the feasibility of the proposed algorithm for both fixed and moving leaders.

Adaptive event-triggered fuzzy control for hot strip finishing mill via a disturbance observer-based method

In this paper, a disturbance observer-based adaptive event-triggered control scheme is proposed for hot strip finishing mill against the problem brought by the interstand tension and the looper angle. Firstly, a standard backstepping method is adopted to the design of control scheme with the consideration that the interstand looper possesses particular structure of the dynamic model. Then, via selecting a suitable gain function, the unknown disturbance can be estimated well by the disturbance observer. Meanwhile, it is noted that the looper current control has very fast dynamics when generating the looper torque. Therefore, the actuator torque can be viewed as directly related to the control signal. In addition, since the strip tension fluctuation has an effect on width and thickness, it will be dampened until larger than looper angle fluctuation. Furthermore, unknown nonlinear terms generated by the process of finishing mills can be approximated by linear functions integrated by fuzzy logic systems. The proposed event-triggered control scheme is used to guarantee the Lyapunov stability and performance requirements of the overall system. The effectiveness of the proposed controller is illustrated in simulation results and application.

Highly Accurate Wavelet Solution for Bending and Free Vibration of Circular Plates Over Extra-Wide Ranges of Deflections

Abstract The wavelet multiresolution interpolation Galerkin method in which both the unknown functions and nonlinear terms are approximated by their respective projections onto the same wavelet space is utilized to implement the spatial discretization of the highly coupled and nonlinear Von Karman equation for thin circular plates with various types of boundary conditions and external loads. Newton’s method and the assumption of a single harmonic response are then used for solving the static bending and free vibration problems, respectively. Highly accurate wavelet solutions for an extremely wide range of deflections are finally obtained by the proposed method. These results for moderately large deflections are in good agreement with existing solutions. Meanwhile, the other results for larger deflections are rarely achieved by using other methods. Comparative studies also demonstrate that the present wavelet method has higher accuracy and lower computational cost than many existing methods for solving geometrically nonlinear problems of thin circular plates. Moreover, the solutions for large deflection problems with concentrated load support the satisfactory capacity for handling singularity of the proposed wavelet method. In addition, a trivial initial guess, such as zero, can always lead to a convergent solution in very few iterations, even when the deflection is as large as over 46 times thickness of plate, showing an excellent convergence and stability of the present wavelet method in solving highly nonlinear problems.

Reinforcement-learning-based fixed-time attitude consensus control for multiple spacecraft systems with model uncertainties

In this study, the problem of fixed-time attitude consensus control was investigated for multiple spacecraft systems with model uncertainties. First, a distributed fixed-time adaptive observer is proposed for estimating the states of the leader. Subsequently, on the basis of the observation errors, transformed error dynamics are described and they are used to combine the unknown nonlinear terms of a spacecraft system. By using the non-singular fast terminal sliding mode technique and a reinforcement learning optimization algorithm, we implemented a neural-network-based fixed-time control strategy to achieve optimal attitude consensus control. The stability of the system and the fixed-time convergence of the tracking error are demonstrated by using the Lyapunov theory. Furthermore, the effectiveness and superiority of the control strategy are shown through numerical simulations.

Model‐free adaptive and iterative learning composite control for subway train under actuator faults

AbstractIn this article, the model‐free adaptive and iterative learning composite control (CMFAC‐ILC) is proposed to ensure the speed and position tracking for the subway train system subjected to the iteration‐time‐varying actuator faults. First, a nonlinear subway train system is transformed into a faults‐related full‐form dynamic linearization data model (FFDLDM), which relies on the input, output, and faults data of the subway train system. The actuator faults and unknown nonlinear terms of the subway train system are estimated by the projection algorithm. Then, in the time domain, the model‐free adaptive control (MFAC) algorithm is utilized and unknown controller parameters are estimated by the RBFNN algorithm. In the iteration domain, a feedforward D‐type iterative learning control (ILC) algorithm is added to the outer loop of the MFAC algorithm. Finally, the theoretical analysis proves that the speed and position tracking errors of the subway train are bounded, the simulations demonstrate the effectiveness of the proposed composite control scheme of the subway train.

Cooperative Adaptive Model-Free Control With Model-Free Estimation and Online Gain Tuning.

In this article, a distributed adaptive model-free control algorithm is proposed for consensus and formation-tracking problems in a network of agents with completely unknown nonlinear dynamic systems. The specification of the communication graph in the network is incorporated in the adaptive laws for estimation of the unknown linear and nonlinear terms, and in the online updating of the elements in the main controller gain matrix. The decentralized control signal at each agent in the network requires information about the states of the leader agent, as well as the desired formation variables of the agents in a local coordinate frame. These two sets of variables are provided at each agent by utilizing two recently proposed distributed observers. It is shown that only a spanning-tree rooted at the leader agent is enough for the convergence and stability of the proposed cooperative control and observer algorithms. Two simulation studies are provided to evaluate the performance of the proposed algorithm in comparison with two state-of-the-art distributed model-free control algorithms. With lower control effort as well as fewer offline gain tuning, the same level of consensus errors is achieved. Finally, the application of the proposed solution is studied in the formation-tracking control of a team of autonomous aerial mobile robots via simulation results.

Adaptive finite‐time event‐triggered control for uncertain nonlinearly parameterized systems with unknown control direction and actuator failures

In this article, the issue of adaptive finite-time event-triggered tracking control is investigated for nonlinearly parameterized systems with unknown faults and unknown control gain. By establishing the proper parameter adaptive laws with the intermediate variable, the problem of system instability caused by the uncertainty of the parametric system and the unknown faults of the actuator can be effectively handled. Simultaneously, the unknown nonlinear term denotes the bias fault is approximated by the fuzzy logic systems (FLSs). Accordingly, an improved event-triggered controller with a varying threshold strategy is developed to rule out the Zeno phenomenon and demonstrate that all the signals in the closed-loop system are semi-globally practically finite-time stable (SGPFS). Finally, a simulation result of the manipulator system is carried out to validate the proposed control scheme.

Event-triggered adaptive neural command-filter-based dynamic surface control for state constrained nonlinear systems

In this article, an event-triggered adaptive neural command-filter-based dynamic surface control (CFDSC) is discussed for states constrained nonstrict-feedback nonlinear systems with dynamic uncertainties. The order-reduced compensation signals are designed to compensate the tracking error of the filter in original dynamic surface control (DSC). The hyperbolic tangent function is adopted as the invertible mapping to deal with the full state constraints. An auxiliary signal is employed to estimate the dynamical uncertainties produced by the unmodeled dynamics. The unknown smooth nonlinear terms are approximated by radial basis function neural networks (RBFNNs) at recursive each step. An event-triggered input is constructed in this novel CFDSC framework. With the help of the defined compact set in the stability analysis, the semi-global uniform ultimate boundedness (SGUUB) of all the signals in the adaptive closed-loop system is proved. Moreover, each state can be strictly limited within the time-varying state conditions. Two simulation verifications are employed to verify and clarify the theoretical findings.

Cooperative MFAILC for Multiple Subway Trains With Actuator Faults and Actuator Saturation

In this paper, a cooperative model free adaptive iterative learning control (CMFAILC) scheme is proposed for multiple subway trains subjected to actuator faults and actuator saturation. The controller design includes: the dynamic linearization technique is adopted to transform the subway train system into an equivalent dynamic linearization data model along the iteration axis, the CMFAILC controller is designed by optimizing the cost function, the projection algorithm is applied to deal with the unknown nonlinear terms, the RBFNN is used to compensate the effects of unknown actuator faults, and the anti-windup compensator is introduced to tackle actuator saturation. Theoretical analysis shows that the speed tracking errors of multiple subway trains are bounded, and the distance of adjacent subway trains is stabilized in a safe range. Finally, the validity of the proposed CMFAILC scheme is verified through multiple subway train simulations.

A latent restoring force approach to nonlinear system identification

Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system which can be seen as an alternative viewpoint on restoring force surface type approaches. To achieve this identification, the contribution which is the nonlinear restoring force is modelled, initially, as a Gaussian process in time. That Gaussian process is converted into a state–space model and combined with the linear dynamic component of the system. Then, by inference of the filtering and smoothing distributions, the internal states of the system and the nonlinear restoring force can be extracted. In possession of these states a nonlinear model can be constructed. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.

Full-state time-varying asymmetric constraint control for non-strict feedback nonlinear systems based on dynamic surface method

We investigate the tracking control problem for a non-strict feedback nonlinear system with external disturbance and time-varying asymmetric full state constraints. Firstly, the unknown nonlinear term with external disturbance in the system are estimated by fuzzy logic system. The backstepping method is applied to the design of adaptive fuzzy controller. However, to prevent that the constraints are overstepped by introducing an improved log-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design. Secondly, the dynamic surface control (DSC) is introduced in the designed algorithm to solve the computational explosion problem of controller caused by the derivative of control law. The proposed control scheme can speed up the tracking speed of the system. Compared with the previous work, it is verified that the combination of DSC and TABLF can obtain good performance within the constraint range, and can ensure fast and stable tracking convergence under external disturbance. Finally, two simulation examples verify the performance of the adaptive controller.