Unknown Nonlinearities Research Articles

RBF Neural Network Sliding Mode Control for Passification of Nonlinear Time-Varying Delay Systems with Application to Offshore Cranes.

This paper is devoted to studying the passivity-based sliding mode control for nonlinear systems and its application to dock cranes through an adaptive neural network approach, where the system suffers from time-varying delay, external disturbance and unknown nonlinearity. First, relying on the generalized Lagrange formula, the mathematical model for the crane system is established. Second, by virtue of an integral-type sliding surface function and the equivalent control theory, a sliding mode dynamic system can be obtained with a satisfactory dynamic property. Third, based on the RBF neural network approach, an adaptive control law is designed to ensure the finite-time existence of sliding motion in the face of unknown nonlinearity. Fourth, feasible easy-checking linear matrix inequality conditions are developed to analyze passification performance of the resulting sliding motion. Finally, a simulation study is provided to confirm the validity of the proposed method.

Adaptive dynamic surface output feedback control for a class of quadrotor aircraft with actuator faults

PurposeThe purpose of this study is to propose an adaptive fault-tolerant control approach based on output feedback for a class of quadrotor unmanned aerial vehicles system. In the event of a controlled actuator failure, a stable flying of the aircraft can be achieved by selecting an appropriate sliding mode surface.Design/methodology/approachAiming at the actuator failure of quadrotor aircraft during flight in the controllable range, a dynamic surface sliding mode passive fault-tolerant controller based on output feedback is designed based on the strong robustness of sliding mode method. Due to the unknown nonlinearity dynamics and parameter uncertainties in the system, a nonlinear observer is used to estimate them online.FindingsThe stability of the suggested algorithm is established using appropriate Lyapunov functions, and the performance of the proposed control approach is demonstrated using hardware-in-the-loop simulation.Originality/valueAn error performance function is introduced into the controller to ensure the convergence speed and accuracy of errors are within the predetermined range. By using the norm estimation method, there is only one parameter that needs to be updated in each step of the control process, which considerably minimizes the calculation burden. Finally, the validity of the proposed control scheme is verified on the hardware-in-the-loop simulation, and the results show that the proposed control method has achieved the desired results.

Distributed Control Design for Uncertain Multiagent Systems with Heterogenous High Powers

In this paper, a distributed asymptotic tracking control strategy is investigated by establishing filters and barrier function-based consensus control scheme to address the control of heterogenous power-chained multiagent systems (MASs) under a directed graph subject to the unknown input deadzone nonlinearities and unknown control coefficients. First, to generate estimation information from the leader, a two-order filter is exploited for every agent which solves the difficultly of the time-varying control coefficients in multiagent systems with a directed topology. Then, based on the two-order filters, prescribed performance method and barrier functions are utilized to establish the distributed tracking protocol to handle the power-chained deadzone input nonlinearities, such that the MAS can reach the global consensus while guaranteeing the prescribed tracking error performance. Using the Lyapunov stability theorem, the proof of the convergence is accomplished rigorously. Ultimately, the efficacy and advantage of the devised method are validated by two simulation examples.

Event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems

This paper is concerned with event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems. The approach of fuzzy logic systems (FLSs) approximation is extended to high-order stochastic nonlinear systems to deal with the unknown nonlinear uncertainties. A novel high-order adaptive fuzzy tracking controller is firstly presented via a backstepping approach and event-triggering mechanism which can mitigate the unnecessary waste of computation and communication resources. Based on the above techniques, frequently-used growth assumptions imposed on unknown system nonlinearities are removed and the influence for the high order is handled. The proposed high-order adaptive fuzzy tracking control method not only deals with the influence of high order, but also ensures that the tracking error converges to a small neighborhood of the origin in probability. Finally, the effectiveness of the proposed control method is illustrated by a numerical example.

Distributed Adaptive Finite-Time Consensus for High-Order Multi-Agent Systems with Intermittent Communications under Switching Topologies

In this paper, a distributed adaptive finite-time consensus (FTC) control protocol for a high-order multi-agent system (MAS) with intermittent communications under switching topologies is proposed. Meanwhile, considering the problem of heterogeneous unknown nonlinearities and other uncertain disturbances, the adaptive neural network and the sliding mode control method are used to compensate the nonlinearity of each agent separately. The agents are homogeneous, so the system has symmetry. The switching topologies considered in this paper are asymmetric. Compared with consensus protocol for asymptotic convergence, simulation results show that the proposed method can effectively solve the presence of the nonlinear and accelerate the convergence speed of the system so that an FTC can be reached.

Neural‐network‐based constrained optimal coordination for heterogeneous uncertain nonlinear multi‐agent systems

AbstractIn this article, we investigate a constrained optimal coordination problem for a class of heterogeneous nonlinear multi‐agent systems described by high‐order dynamics subject to both unknown nonlinearities and external disturbances. Each agent has a private objective function and a steady‐state constraint about its output. We develop a composite distributed controller for each agent by a combination of internal model and neural network techniques. All agent outputs are proven to reach the constrained minimal point of the aggregate objective function with bounded residual errors irrespective of the unknown nonlinearities and external disturbances. Two examples are finally given to demonstrate the effectiveness of the algorithm.

Adaptive Fuzzy Control With Global Stability Guarantees for Unknown Strict-Feedback Systems Using Novel Integral Barrier Lyapunov Functions

In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">particular emphasis on global stability</i> . The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determine <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> the compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the “explosion of complexity” issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

Expansive Errors-Based Fuzzy Adaptive Prescribed Performance Control by Residual Approximation

This article is concerned with an expansive errors (EE)-based fuzzy adaptive prescribed performance control of a class of multiple-input and multiple-output nonlinear systems in the presence of unknown interconnection nonlinearities using fuzzy residual approximation technique. Based on an newly defined expansive error, residual nonlinearities&#x2019; fuzzy approximation scheme is proposed. The merits of designed control can be presented as twofold: 1) by incorporating an EE-based technique into pioneering prescribed performance control methodology, the defined intermediate and output tracking errors are kept within the regions represented by preassigned functions and control parameters simultaneously and 2) expansive errors-related residual nonlinearity is approximated by fuzzy logic systems, which further ameliorates the output tracking performance by compensating the affects raised by composite inner and interconnection nonlinearities among subsystems. With the designed expansive errors-based fuzzy adaptive prescribed performance control, all the closed-loop signals are kept bounded in the sense of Lyapunov stability theorem. Comparative simulation studies are presented to verify the effectiveness and advantages of theoretical findings.

Practical fixed-time bipartite consensus control for nonlinear multi-agent systems: A barrier Lyapunov function-based approach

This paper develops a practical fixed-time bipartite consensus control framework for the uncertain nonlinear multi-agent systems (MASs) via using a barrier Lyapunov function (BLF)-based approach. Distinguish from the most existing results, the unknown nonlinearities of MASs in this paper are tackled by utilizing the robustness of BLF instead of applying fuzzy logic systems/neural networks approximating. In order to avoid feasibility verification in the traditional BLF method, a piecewise and differentiable function named the shift function is skillfully inserted into the coordination transformation of the controller design process, allowing not only the initial value of MASs states to be chosen arbitrarily, but also the settling time of bipartite consensus errors can be pre-designated. According to the backstepping framework, an approximated-free control algorithm is developed by combining the shift function with BLF, which guarantees that for any initial state of MASs, the outputs of all the agents can achieve the practical fixed-time bipartite consensus tracking, and all the signals in closed-loop systems are bounded. Especially, the settling time and the tracking error accuracy can be appointed by the designer. Finally, simulation results are given to show the effectiveness of the proposed control method.

A Scalable Adaptive Approach to Multi-Vehicle Formation Control with Obstacle Avoidance

This paper deals with the problem of distributed formation tracking control and obstacle avoidance of multi-vehicle systems (MVSs) in complex obstacle-laden environments. The MVS under consideration consists of a leader vehicle with an unknown control input and a group of follower vehicles, connected via a directed interaction topology, subject to simultaneous unknown heterogeneous nonlinearities and external disturbances. The central aim is to achieve effective and collision-free formation tracking control for the nonlinear and uncertain MVS with obstacles encountered in formation maneuvering, while not demanding global information of the interaction topology. Toward this goal, a radial basis function neural network is used to model the unknown nonlinearity of vehicle dynamics in each vehicle and repulsive potentials are employed for obstacle avoidance. Furthermore, a scalable distributed adaptive formation tracking control protocol with a built-in obstacle avoidance mechanism is developed. It is proved that, with the proposed protocol, the resulting formation tracking errors are uniformly ultimately bounded and obstacle collision avoidance is guaranteed. Comprehensive simulation results are elaborated to substantiate the effectiveness and the promising collision avoidance performance of the proposed scalable adaptive formation control approach.

Space-Decomposition-Based Spectral Modeling for Distributed Battery Thermal Dynamics

The thermal behavior has sustainable impacts on the safety performance and cycle life of lithium-ion batteries. This article proposes a physics/data hybrid modeling framework for the thermal process of the pouch cell. Since the thermal effects of the tab area have different dynamic characteristics from other parts of the battery, a space decomposition strategy is designed to generate a more effective multiphysics-based model. To capture the battery thermal dynamics in real time, a reduced-order model is derived using the eigenfunction-based spectral expansion. All the unknown nonlinearities and other disturbances are further compensated through data-based learning. Simulation studies and experiments demonstrate the effectiveness of the proposed modeling methodology.

PI-generalizing saturated repetitive learning control for a class of nonlinear uncertain systems: Robustness w.r.t. relative degree zero or one

The class of single-input, single-output, nonlinear, time-invariant systems with unknown output-dependent nonlinearities, unknown parameters and relative degree ρ ∈ { 0 , 1 } is considered. A priori knowledge of the system includes globally Lipschitz nature of the nonlinearities and positive sign of the high-frequency gain, besides the minimum-phase property. Single-input, single-output, observable, minimum phase, linear, time-invariant systems are included as a very special case. The aim is to track, via the output error feedback only, periodic output reference signals with known period. Here we originally show that the same saturated repetitive learning control that constitutes the most natural generalization of the PI (Proportional–Integral) control, concurrently ensures the following properties for any initial condition of the system: asymptotic convergence to zero of the output tracking error is guaranteed if ρ = 1 ; exponential convergence to zero is achieved for both the output and the input tracking errors if ρ = 0 .

Neural Network Adaptive Output-Feedback Optimal Control for Active Suspension Systems

The adaptive neural network (NN) output-feedback optimal control issue has been investigated for a quarter-car active electric suspension systems, where the suspension stiffness is unknown and partial state variables are unavailable for measurement. NNs are utilized to identify unknown nonlinearities, and an NN state observer is devised to estimate the unmeasurable states. For each backstepping step, via reinforcement learning (RL), a critic–actor architecture is designed to get the approximation solution of Hamilton–Jacobi–Bellman (HJB) equations and actual and virtual optimization controllers are designed, in which the input saturation constraint and road interference are considered. It is analytically proved that all controlled system signals remain bounded, while the power of the control input signal, as well as the amplitude of the vertical displacement, has been minimized. A comparative simulation is eventually given to elaborate the feasibility of the developed control algorithm.

Novel Neural Network Fractional-Order Sliding-Mode Control With Application to Active Power Filter

In this article, a fractional-order sliding-mode control scheme based on a two-hidden-layer recurrent neural network (THLRNN) is proposed for a single-phase shunt active power filter. Considering the shortcomings of traditional neural networks (NNs) that the approximation accuracy is not high and weight and center vector of NNs are unchangeable, a new THLRNN structure which contains two hidden layers to make the network have more powerful fitting ability, is designed to approximate the unknown nonlinearities. A fractional-order term is added to a sliding-mode controller to have more adjustable space and better optimization space. Simulation and experimental studies prove that the proposed THLRNN strategy can accomplish the current compensation well with acceptable current tracking error, and have satisfactory compensation property and robustness compared with a traditional neural sliding controller.

Composite event-triggered disturbance-observer-based control and passive control for semi-Markovian jump nonlinear systems with actuator saturation

In this paper, the composite control problem of continuous time semi-Markovian jump system with actuator saturation, multiple disturbances and unknown nonlinearity is investigated. A stochastic stability condition and a lower bound of the time between two consecutive events are derived to avoid Zeno behaviour, based on the combination of disturbance-observer-based control and event-triggered control. In addition, the passive control of the system based on the disturbance observer is studied. Finally, numerical simulation proves that the designed composite controller can effectively save communication resources, and can maintain the system to meet the passive performance indicators of the obtained closed-loop system under the influence of multiple disturbances and actuator saturation.

A receptance-based vibration control with dead-zone compensation for systems with input delay

This paper presents a novel compensation approach for receptance-based second-order systems with long input delay and unknown dead-zone input nonlinearity. The approach is based on a filtered Smith predictor for systems with long input delay based on the receptance model. An innovative discrete-time adaptive strategy approach for dealing with unknown input dead-zone is also based on a receptance model realization. The receptance-based second-order model is used on several fundamental applications, including active control vibration of mechanical vibrating systems. In the proposed approach, a filtered prediction error that considers the effects of time delay can be applied to pursue state feedback design for active vibration control purposes. The dead-zone compensation is treated by a discrete-time state observer, which is based on displacement, velocity, and control effort signals to estimate the unknown parameters to be used on an adaptive algorithm. The main contribution of this work is to combine unknown dead-zone adaptive mechanism and a receptance-based time delay compensation in a unified design. Some numerical examples illustrate the effectiveness of the innovative proposed approach.

A distributed FDI cyber-attack detection in discrete-time nonlinear multi-agent systems using neural networks

This paper proposes a distributed, false data injection (FDI) cyber-attack detection method in communication channels for a class of discrete-time, nonlinear, heterogeneous, multi-agent systems controlled by our formation-based controller. A distributed neural network (NN)-based observer is proposed that generates the residual signal which is used in detection of FDI attacks on agents’ sensors, actuators, and neighboring communication channels in a multi-agent formation control setting. A radial basis function neural network (RBFNN) is used to approximate the unknown nonlinearity in the dynamics. A Lyapunov stability theory is used to prove that the attack detection residual and the multi-agent formation error are uniformly ultimately bounded (UUB), and to explicitly derive the NN weights tuning law and the attack detectability threshold. The proposed method’s attack detectability properties are analyzed, and simulation results are provided to demonstrate performance of the detection methodology.

Adaptive control for manipulators with unknown virtual control coefficients and input nonlinearities

This paper addresses the adaptive control problem for a one-link manipulator system driven by a motor with uncertain virtual control coefficients (VCCs) and nonlinearities. The unknown VCCs are composed by the certain and uncertain items, where the first part is decided by the moment of inertia of the manipulator and another is generated by that of the load. An auxiliary variable and the Nussbaum gain technique are invoked to handle the uncertainties of VCCs and input nonlinearities. Moreover, a finite-time prescribed performance function is introduced to design the adaptive control scheme for the manipulator system, which guarantees the tracking error converges to a fixed interval in a setting time and all signals in the manipulator system are bounded.

Distributed quantized state feedback strategy for ensuring predesignated formation tracking performance of networked uncertain nonholonomic multi-robot systems with quantized communication

We present a distributed quantized state feedback approach for ensuring predesignated formation tracking performance of uncertain multiple nonholonomic mobile robots under a band-limited directed network with signal quantization. Under a networked formation control environment, it is assumed that state variables and inputs of all robots are quantized by uniform-hysteretic quantizers and the quantized states of robots are communicated to neighbor robots. A distributed recursive approximation-free design methodology using nonlinear error functions is presented to construct local quantized state feedback trackers that achieve predesignated robust formation tracking performance under quantized communications among robots and unknown nonlinearities of robot dynamics. The proposed local quantized state feedback trackers require only the information of quantized relative positions among robots, without any velocity information of neighbor robots. An analysis strategy for the stability of the proposed formation tracking system is presented using the quantization errors of closed-loop signals. The effectiveness of the distributed quantized feedback design is verified based on the simulation results.

Sliding Mode Control of a 2DOF Robot Manipulator: A Simulation Study Using Artificial Neural Networks with Minimum Parameter Learning

Background: In this paper we have developed an intelligent control law for the control of mobile manipulator robots by investigating the various techniques proposed in the literature. Thus, we have adopted a hybrid approach integrating part of classical and advanced automation in order to create an efficient control structure that can cope with a certain level of complexity. Our research logic is based on the process of keeping in mind that the control system must comply with the constraints imposed during the implementation of the control architecture. Objective: This paper aims to develop a control law in order to guarantee a certain level of performance and, more precisely, during a trajectory tracking application for mobile handling missions. The developed control law guarantees robustness with respect to external disturbances and parametric uncertainties due to the modelling of the system. Methods: In this paper, a study of the basic concepts of robotics and robot modelling is presented in order to set up the dynamic model used for the elaboration of the command. A sliding-mode controller based on a radial base function neural network with minimum parameter learning is developed for the Pelican robot as a two link robot manipulator. This approach, which combines a Radial Base Function Neuronal Network (RBFNN) and a Sliding Mode Control (SMC), is presented for the tracking control of this class of systems with unknown nonlinearities. The centres and outputs weights of the RBFNN are updated via online learning in accordance with the adaptive laws, allowing the control output of the neural network to approach the equivalent control in the sliding mode in the predetermined direction. The Lyapunov function is used to develop the adaptive control algorithm based on the RBFNN model. To reduce computational load and increase real-time arm performance, an RBFNN-based on the SMC with the Minimum Parameter Learning (MPL) method is designed. Results: Neural network sliding mode control is designed to underline the effectiveness of the approach to control the manipulator. This method of control ensure the tracking trajectories. Conclusion: The results of the simulation for the manipulator arm presented demonstrates the effectiveness of the modelling strategy, the correction and the robustness of the control approach.