Uncertain Nonlinearities Research Articles

Neural Predictor-Based Dynamic Surface Parallel Control for MIMO Uncertain Nonlinear Strict-Feedback Systems

We propose a neural predictor-based dynamic surface parallel control method for a class of uncertain nonlinear systems in this brief. The dynamics of the physical system is in the strict-feedback form and subject to multi-input, multi-output, and uncertain nonlinearities. The parallel control method is developed based on an ACP methodology, including three steps. Firstly, an artificial system to the physical system is developed using an echo state network-based neural predictor structure. Next, a high-order tuner-based computational experiment is developed to achieve online adaptive training of the echo state network. Finally, parallel execution is developed by using a second-order linear tracking differentiator-based dynamic surface control approach. The total closed-loop system can be proved to be input-to-state stable. The effectiveness of the proposed theoretical results is demonstrated by a simulation of trajectory tracking of an autonomous surface vehicle.

Homogeneous Domination Approach to Global Stabilization of Stochastic Continuous Nonlinear Time-Delay Systems With SISS-Like Conditions

This article aims to investigate the global stabilization for a class of stochastic continuous time-delay nonlinear systems involved with unknown control coefficients and stochastic-input-to-state-stable-like conditions. Without involving the traditional adaptive compensation approach, a dominate gain is adopted to deal with uncertain nonlinearities, which not only include unmeasurable state but also involve input and state delays. On account of homogeneous domination manner and stochastic stability theory, a delay-independent controller is developed to guarantee that the closed-loop system is globally asymptotically stable in probability. Finally, a simulation example is supplied to show the virtue of the devised strategy.

Virtual angle‐based adaptive control for trajectory tracking and balancing of ball‐balancing robots without velocity measurements

SummaryThis article proposes a virtual angle‐based adaptive control method for trajectory tracking and balancing of ball‐balancing robots without velocity measurements. The trajectory tracking and balancing control of ball‐balancing robots is challenging due to underactuation and uncertain nonlinearities. The hierarchical control strategy, which designs the control system using a linear combination of trajectory tracking and balancing errors, can be a solution. However, it has a local minimum problem where the convergence of tracking and balancing errors is not guaranteed even though the linear combination error is zero. Therefore, a virtual angle‐based control method is presented, which can solve the underactuation problem without the local minimum issue. In addition, a neural network‐based observer is developed to estimate the velocity information of ball‐balancing robots with uncertainties, and the input saturation problem is considered. It is proven that all tracking and balancing errors are bounded and can be made arbitrarily small in the Lyapunov sense. Finally, simulation results are provided to verify the effectiveness of the proposed control system.

Fuzzy observer-based adaptive fixed-time leader-following control for high-order nonlinear multiagent systems

Most current research on fixed-time leader-following control of high-order nonlinear multiagent systems requires prior knowledge of the system dynamics or that each follower has state information about the leader. To release the above restriction, this article presents a fixed-time fuzzy observer for high-order multiagent systems with uncertain nonlinearities. Based on adaptive fuzzy control, we achieve consensus control of fixed-time pre-described accuracy for uncertain high-order nonlinear multiagent systems and overcome the difficulty of having information gaps between leaders and followers. According to the proposed observer and stability criterion, not only can the leader’s state be estimated in fixed time, but the consensus tracking error can also converge to the pre-described interval within a fixed time. The proposed control protocol guarantees the following properties:1.The proposed observer can estimate the leader’s state in a fixed time.2.Boundedness is satisfied for all closed-loop signals.3.Each follower can achieve fixed-time and predefined accuracy tracking for the leader.

Neural Network Trajectory Tracking Control on Electromagnetic Suspension Systems

A new adaptive-like neural control strategy for motion reference trajectory tracking for a nonlinear electromagnetic suspension dynamic system is introduced. Artificial neural networks, differential flatness and sliding modes are strategically integrated in the presented adaptive neural network control design approach. The robustness and efficiency of the magnetic suspension control system on desired smooth position reference profile tracking can be improved in this fashion. A single levitation control parameter is tuned on-line from a neural adaptive perspective by using information of the reference trajectory tracking error signal only. The sliding mode discontinuous control action is approximated by a neural network-based adaptive continuous control function. Control design is firstly developed from theoretical modelling of the nonlinear physical system. Next, dependency on theoretical modelling of the nonlinear dynamic system is substantially reduced by integrating B-spline neural networks and sliding modes in the electromagnetic levitation control technique. On-line accurate estimation of uncertainty, unmeasured external disturbances and uncertain nonlinearities are conveniently evaded. The effective performance of the robust trajectory tracking levitation control approach is depicted for multiple simulation operating scenarios. The capability of active disturbance suppression is furthermore evidenced. The presented B-spline neural network trajectory tracking control design approach based on sliding modes and differential flatness can be extended to other controllable complex uncertain nonlinear dynamic systems where internal and external disturbances represent a relevant issue. Computer simulations and analytical results demonstrate the effective performance of the new adaptive neural control method.

Generalized Super-Twisting Backstepping Sliding Mode Control for Electro-Hydraulic Servo Systems Considering the Coexistence of Matched and Mismatched Uncertainties

Aiming at the problem of the coexistence of matching and mismatching uncertainties in electro-hydraulic servo systems, disturbance observers and a backstepping sliding mode controller based on the generalized super-twisting algorithm (GSTA) are proposed in this paper. First, in order to compensate for the uncertainty in the controller, two generalized super-twisting disturbance observers (GSTDOs) are constructed to effectively reduce the discontinuous gain of the controller. Then, the GSTA is introduced to optimize the backstepping sliding mode controller to obtain a better control effect. Finally, the proposed control strategy is compared and simulated on the electro-hydraulic servo system. The experimental results verify that the proposed control strategy has better tracking performance. The effect of asymptotic tracking in the presence of parameter uncertainties and disturbances is achieved, while transient tracking performance and final tracking accuracy are guaranteed in the presence of time-varying uncertain nonlinearities.

Frequency Regulation Strategy of Two-Area Microgrid System with Electric Vehicle Support Using Novel Fuzzy-Based Dual-Stage Controller and Modified Dragonfly Algorithm

Energy in microgrids (MGs) can now be generated from a variety of renewable sources, but their effective and sustainable use is dependent on electrical energy storage (EES) systems. Consequently, the expansion of MGs is greatly reliant on EES systems. The high infiltration of electric vehicles (EVs) causes some problems for the smooth functioning of the electric power system. However, EVs are also able to offer ancillary services, such as energy storage, to power systems. The research presented in this paper aims to develop a novel frequency regulation (FR) approach for biogas diesel engines (wind), the organic Rankine cycle (ORC), and solar-based two-area islanded microgrids with EVs in both areas. This article discusses the introduction of a fuzzy logic controller (FLC) for FR with scaled factors configured as proportional integral (PI) and proportional derivative with filter (PDF), i.e., a FLC-SF-PI-PDF controller. A recently created modified dragonfly algorithm is used to determine the best values for the controller parameters. To justify the effectiveness of the proposed controller with the presence of EVs, the execution of the proposed controller is associated with and without the presence of EVs. This research also looks at the different uncertain conditions, non-linearities, and eigenvalue stability analysis to validate the supremacy of the proposed approach.

A composite adaptive robust control for nonlinear systems with model uncertainties

AbstractThis article is concerned with a composite adaptive robust control (CARC) for non‐strict feedback nonlinear systems with model uncertainties including parametric uncertainties and uncertain nonlinearities. It is assumed that the model uncertainties of the nonlinear system are bounded but unknown. Firstly, prescribed tracking performance is achieved by the CARC control law even the unknown parameters are time‐varying. This is accomplished firstly by designing a discontinuous projection that confines the unknown parameters in an estimated region. Then the robustness of the closed‐loop system is guaranteed by leveraging the deterministic robust control philosophy. Also, a command filter has been designed to avoid computing complex derivatives of virtual control law in the backstepping procedure. Secondly, a composite adaptation law that intelligently integrates information of both tracking error and prediction error is constructed for improving the performance of controllers. The high adaptation gain of CARC leads to higher parameter convergence speed and smaller tracking errors. Moreover, if the actual parameters are within the design range, asymptotic stability can be achieved in presence of parametric uncertainties only. In addition, exponential convergence of tracking errors and parameters can be shown under certain conditions. Finally, numerical examples are made to validate the superiority and effectiveness of the proposed control scheme.

Neural network-based secure event-triggered control of uncertain industrial cyber-physical systems against deception attacks

This paper addresses the problem of secure event-triggered control is to guarantee the stability and security of a general class of industrial cyber-physical systems (CPSs) under limited resource budget and deception attacks. Note that the coupled data and the complicated structure of the CPS make it hard for the traditional control algorithms to fulfill the stability and security requirements. To this end, a neural network learning-based approximation algorithm is first proposed to separate the coupling influence, and then estimate the lumped uncertain nonlinearities. This is done by using the separated data as the input of the neural networks. Second, Nussbaum-type functions are presented to settle the unknown sign of the time-varying attack injection signal. Third, an event triggering mechanism is developed to reduce the communication load. Under the developed secure control laws, all the signals of the resulted closed-loop CPS are bounded. Finally, to validate the effectiveness of the proposed secure event-triggered control method, a benchmark control example for the one-link manipulator actuated by a DC motor is exploited.

Global regulation of feedforward nonlinear systems with unknown time-varying control coefficients and growth rate

In this paper, we consider a regulation problem for a class of feedforward nonlinear systems with unknown control coefficients and unknown growth rate. More specifically, the unknown control coefficients are assumed to be time-varying and belong to ranges with unknown upper and lower bounds. Due to the described control coefficients with uncertain feedfoward nonlinearities, our considered system is the natural extension of the related existing results. In solving our control problem, a new adaptive controller is derived by constructing a Lyapunov function in backstepping-like procedure and utilizing appropriate parameters based on the gain scaling technique and Nussbaum function. The uniquely designed exponents of a dynamic gain overcome the difficulties caused from the unknown sign and unknown ranges of the control coefficients and uncertain nonlinearities and thus play a key role in system regulation. We give the rigorous system analysis and simulation results of the numerical example to certify our control method.

Observer-based event-triggered adaptive neural control for time-delay nonlinear systems with input saturation and external disturbances

In this article, the issue of adaptive event-triggered tracking control is investigated for time-delay nonlinear systems with input saturation and external disturbances. In the whole process of control design, the radial basis function neural networks are utilized to approximate uncertain nonlinearities. To estimate the unknown states, a neural network-based observer is constructed. Pade approximation method is adopted to eliminate the effect of input delay. A smooth non-affine function is introduced to replace input saturation, and an auxiliary variable is employed to obtain the actual control input. An event-triggered strategy is designed to reduce the utilization of communication and computation resources. Moreover, the command filtering technique is applied to handle the issue of “explosion of complexity” in the conventional backstepping method. The designed controller can assure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Therefore, the proposed event-triggered neural control scheme can not only save network resources, but also improve the robustness of the system by dealing with input constraints and external disturbances. Finally, two simulation examples are given to verify the availability and feasibility of the designed controller.

Stability and Stabilization of Fractional-Order Uncertain Nonlinear Systems With Multiorder

Fractional-order (FO) commensurate systems have been widely studied in recent years, including their stability and control. However, for incommensurate FO systems these problems are still challenging and further research is needed. In this brief, the stability and stabilization of incommensurate FO nonlinear systems with time-varying bounded uncertainties are investigated. A new stability criterion in the form of linear matrix inequality is formulated by employing the FO comparison principle of multi-order FO systems. Then, a state feedback controller for system stabilization is derived based on the stability criteria proposed. Numerical simulations demonstrate the effectiveness of the theoretical formulation.

Global output feedback control for large‐scale time‐delay systems with inherent nonlinearities and measurement uncertainty

AbstractThis paper investigates the problem of global state regulation by output feedback for a class of large‐scale nonlinear time‐delay systems with inherent nonlinearities and unknown measurement sensitivity. The uncertain nonlinearities are bounded by nonlinear growth of lower triangular unmeasurable (delayed) states multiplied by the unknown constant, polynomial‐of‐output and polynomial‐of‐input. Different from closely related works, the simultaneous existence of complicated nonlinearities and unknown measurement sensitivity makes the problem more involved and complex. Based on the dynamic gain scaling technique, we design a set of new adaptive output feedback controllers with a simpler structure by constructing two Lyapunov–Krasovskii functionals appropriately, which can globally regulate all states of the large‐scale systems. An illustrative example is proposed to demonstrate the validity of the presented control scheme.

Adaptive Robust Servo Control for Vertical Electric Stabilization System of Tank and Experimental Validation

A tracking stability control problem for the vertical electric stabilization system of moving tank based on adaptive robust servo control is addressed. This paper mainly focuses on two types of possibly fast time-varying but bounded uncertainty within the vertical electric stabilization system: model parameter uncertainty and uncertain nonlinearity. First, the vertical electric stabilization system is constructed as an uncertain nonlinear dynamic system that can reflect the practical mechanics transfer process of the system. Second, the dynamical equation in the form of state space is established by designing the angular tracking error. Third, the comprehensive parameter of system uncertainty is designed to estimate the most conservative effects of uncertainty. Finally, an adaptive robust servo control which can effectively handle the combined effects of complex nonlinearity and uncertainty is proposed. The feasibility of the proposed control strategy under the practical physical condition is validated through the tests on the experimental platform. This paper pioneers the introduction of the internal nonlinearity and uncertainty of the vertical electric stabilization system into the settlement of the tracking stability control problem, and validates the advanced servo control strategy through experiment for the first time.

Prescribed Performance Tracking of Uncertain MIMO Nonlinear Systems in the Presence of Delays

In this article, we design a low-complexity state-feedback controller for uncertain multi-input and multi-output (MIMO) nonlinear systems, capable of imposing prespecified performance attributes (in terms of maximum steady-state error and minimum convergence rate) on the output tracking errors, in the presence of time-varying delays both in the state measurement and control input signals. The state measurement delay is considered known and the control input delay unknown though bounded by some known constant. The control design does not incorporate any knowledge regarding the controlled system nonlinearities and does not require derivatives of the desired trajectories. We verify the theoretical results by simulation studies performed on a two-link robotic manipulator.

An Adaptive Inverse Model Control Method of Vehicle Yaw Stability with Active Front Steering Based on Adaptive RBF Neural Networks

In order to enhance vehicle yaw stability, this paper proposes a novel adaptive inverse model control (AIMC) method for active front steering (AFS) design based on adaptive radial basis function (RBF) neural networks. To approximate the uncertain nonlinearity and modeling errors in vehicle dynamics, an adaptive RBF neural network (ARBFNN) controller is firstly designed. For smaller tracking errors and better robustness, a RBF networks-based AIMC system is further established. Apart from the ARBFNN control law, another two RBF neural networks are utilized, which work as model identifier and inverse model controller, respectively. After being trained offline, both of them are updated by using online learning algorithms. For faster learning and stability, adaptive learning rates are developed. Consequently, the inverse model controller is able to generate required steering wheel angle. Finally, the comparative studies are carried out and the simulation results illustrate the robustness and effectiveness of proposed control strategy.

Event-triggered adaptive NN practical finite-time control with its application to MPCVD reactors

The practical finite-time control problem of uncertain nonlinear systems is investigated in this paper. To address the uncertain nonlinearities of the system, neural networks are introduced to approximate the lumped nonlinearities containing the system unknown functions. On the other hand, to alleviate the signal transmission pressure of the system, an improved event-triggered mechanism is presented to reduce the controller update frequency without degrading the control performance of the system. By using practical finite-time stability, it is obtained that the system tracking errors are practical finite-time stable without Zeno behavior. Finally, the effectiveness of the proposed method is verified by the simulation results of its application to a microwave plasma chemical vapor deposition (MPCVD) reactor system.

FLS-based AHOSM control for driverless vehicle steering system with parameter uncertainty

This paper aims to address the tracking control problem for the steer-by-wire (SbW) system with uncertain nonlinearity and parameter uncertainty. First, the adaptive fuzzy logic system (FLS) is constructed to realize the intelligent modeling of the SbW system. In addition, an adaptive higher-order sliding mode (AHOSM) control with dynamic gain is designed to overcome the lumped uncertainties including inaccurate model-parameter and fuzzy logic system approximation error, and has the advantage of eliminating the gain-overestimation phenomenon effectively without the prior knowledge about the bounds of approximation error and parameter uncertainty. Furthermore, theoretical analysis based on Lyapunov stability theory is provided to verify that the real sliding mode can be established. Finally, simulations and vehicle experiments are given to evaluate the effectiveness and superiority of the proposed methods.

Adaptive finite‐time control of multi‐agent systems with partial state constraints and input saturation via event‐triggered strategy

AbstractThis paper focuses on the finite‐time control problem of multi‐agent systems with input saturation, unknown nonlinear dynamics, external disturbances and partial state constraints via output feedback. Fuzzy logic system and fuzzy state observer are introduced to approximate the uncertain nonlinearities and estimate the unmeasurable states, respectively. The partial state constraints are dealt with by using the barrier Lyapunov function, so that all states of the system do not exceed the preset boundary values. In order to reduce the computational complexity of the virtual controller and save communication resources, a first‐order filter and an event‐triggered mechanism are introduced, respectively. It is proved that the Zeno behavior does not occur via the proposed event‐triggered controller. By stability analysis, the finite‐time convergence of tracking error to a small neighborhood of the origin is proven. The effectiveness of the theoretical results is verified by examples.

Compound Adaptive Fuzzy Synchronization Controller Design for Uncertain Fractional-Order Chaotic Systems

In this paper, the synchronization of two fractional-order chaotic systems with uncertainties and external disturbances is considered. A fuzzy logic system is utilized to estimate uncertain nonlinearity, and its estimation accuracy is improved by constructing a series-parallel model. A disturbance observer is implemented to estimate bounded disturbance. To solve the “explosion of complexity” problem in the backstepping scheme, fractional-order command filters are employed to estimate virtual control inputs and their derivatives, and error compensation signals are devised to reduce filtering errors. Based on the fractional-order Lyapurov criterion, the proposed compound adaptive fuzzy backstepping control strategy can guarantee that the synchronization error converges to a small neighborhood of the origin. At last, the validity of the proposed control strategy is verified via a numerical simulation.