Class Of Unknown Nonlinear Systems Research Articles

Adaptive fuzzy output feedback control for a class of uncertain nonlinear systems in the presence of sensor attacks

In this paper, an adaptive fuzzy output feedback control scheme is proposed for a class of unknown nonlinear systems with sensor attacks. The fuzzy logic systems are employed to approximate the uncertain nonlinearities, and the backstepping technique is implemented to construct controllers. The unknown output feedback coefficient is handled by using a Nussbaum function in the first step of backstepping design, eventually developing an adaptive controller to accommodate sensor attacks. Compared to the current control schemes for nonlinear systems under sensor attacks, the benefit of the proposed adaptive controller is that it can apply to nonlinear systems with both uncertainty and unmeasurable states. Finally, two examples validate the efficacy of the proposed control scheme.

Disturbance observer-based control with adaptive neural network for unknown nonlinear system

This paper presents an adaptive neural network controller based on a disturbance observer to compensate the disturbance caused by neural network approximation for a class of unknown nonlinear systems. The proposed adaptive neural network control with an updated parameters mechanism is not subject to the restriction of compact set assumption for satisfying the universal approximation property. The neural network approximation error can be compensated online through the proposed disturbance observer. The proposed method eliminates the need to obtain an exact system model before applying the ideal controller. The effectiveness of the proposed method is validated by numerical simulations.

Resilient iterative learning control for a class of discrete‐time nonlinear systems under hybrid attacks

AbstractThe security control problem for a class of unknown nonlinear systems is considered in this paper. For the nonlinear system running in the network environment, the measurement channel is subjected to hybrid attacks. Intermittent denial of service attacks and false data injection attacks are modeled as the hybrid attacks. According to the characteristics of the repetitive system, a resilient iterative learning control (ILC) algorithm under hybrid attacks is devised. Subsequently, the stability of the system is proved by mathematical derivation and theoretical analysis in the sense of mathematical expectation. The theoretical analysis results indicate that the resilient ILC algorithm can ensure the stability of the system, and the tracking error converges with the increased number of iterations. Finally, the validity of the algorithm is illustrated by numerical simulation and mobile robot simulation.

Resilient Model-Free Adaptive Iterative Learning Control for Nonlinear Systems Under Periodic DoS Attacks via a Fading Channel

This article studies the resilient control problem for a class of unknown nonlinear systems with fading measurements under malicious denial-of-service (DoS) attacks. The system output is assumed to be transmitted through a fading channel, where the fading phenomenon is described by a Rice fading model. The strategy of the attacker is to periodically interfere with the networked channels to reduce the success rate of data transmissions. First, a dynamic linearization method along the iteration domain is introduced to convert the nonlinear system into an equivalent data-related model. Then, a model-free adaptive iterative learning control (MFAILC) scheme is presented, which is independent of model information. The convergence of the MFAILC scheme is deduced theoretically and the influence of DoS attacks and stochastic fading phenomenon on system stability are also analyzed. Finally, the effectiveness of the design is verified by a numerical simulation and a trajectory tracking example of wheeled mobile robots (WMRs).

Adaptive neural finite-time control of nonlinear systems subject to sensor hysteresis

In this paper, an adaptive neural control scheme is proposed for a class of unknown nonlinear systems with unknown sensor hysteresis. The radial basis function neural networks are employed to approximate the unknown nonlinearities and the backstepping technique is implemented to construct controllers. The difficulty of the control design lies in that the genuine states of the system are not available for feedback, which is caused by sensor hysteresis. The proposed control scheme eventually ensures the practical finite-time stability of the closed-loop system, which is proved by the Lyapunov theory. A numerical simulation example is included to verify the effectiveness of the developed approach.

Event-triggered adaptive NN tracking control with dynamic gain for a class of unknown nonlinear systems

An event-triggered tracking control problem is investigated for a class of unknown nonlinear systems in this paper. First, to approximate the unknown function, the radial basis function neural network is used. Then, we propose an event-triggered adaptive neural network control scheme with dynamic gain. Both the event-triggered mechanism in the controller-to-actuator channel and the dynamic gain in the sensor-to-controller channel are considered to reduce the communication load between the controller and the actuator and in the meantime to alleviate the burden of parameter adjustment as well. This scheme makes full use of the advantage that the dynamic gain is driven by the tracking error to ensure that the system output signal can track the reference signal within a prespecified accuracy without adjusting the parameters in use. Moreover, a detailed theoretical proof is given to illustrate that Zeno behavior can be excluded under the designed event-triggered controller. Finally, a simulation example is provided to show the effectiveness of our control scheme.

Adaptive backstepping quantized control for a class of unknown nonlinear systems

In this paper, the stability problem for a class of nonlinear systems in the form of strict-feedback with applying input quantization has been addressed. By considering a sector-bounded hysteresis quantizer, signal quantization has been achieved. The employed quantizer can reduce the potential chattering which can occur in some approaches. By using a common Lyapunov function (CLF) and the backstepping method, a control scheme has been introduced to stabilize the uncertain nonlinear system. Compared with the recent papers, in order to handle the quantization error, one of the sector-bounding features has been utilized straightly instead of decomposing the quantized input into linear and nonlinear parts, in this case, the possible disturbance-like term has been ignored. The designed control scheme does not need the global Lipschitz assumption over the system mismatched nonlinearities. Besides, the asymptotic stability of system trajectories to the origin is guaranteed and the imposed restrictions over quantization design parameters such as quantization density have been eliminated. Finally, in the simulation results, the accuracy and efficiency of the this control scheme are shown.

Data-driven adaptive control of wide-area non-linear systems with input and output saturation: A power system application

In this paper, a Data-Driven Adaptive Controller is proposed for wide-area Multi-Input and Multi-Output (MIMO) non-linear systems featuring input–output saturations. Complexity has always been a major concern in the modeling and control of real-world industrial processes. Traditionally, researchers look for simplified and enough precise models of these systems. However, with the significant advancement in sensor and communication technologies, a considerable amount of data is available from the process which may compensate for the lack of precise models. The emerging data-driven control systems perform both identification and control actions based on data collected from the process, making the system less dependent on a pre-identified model. In this context, an efficient MIMO Data-Driven Adaptive Control (MIMO-DDAC) is designed in this paper for stabilizing a class of unknown non-linear systems. A recursive modeling/control process is proposed for the MIMO systems in the presence of saturation in sensors and actuators, and its stability and performance are mathematically proved. This approach is applied to the load frequency control problem in an interconnected multi-area power grid in the presence of governor saturation, load and parametric uncertainties. Simulation results reveal the effectiveness of the proposed method.

Bank of High-Gain Observers in Output Feedback Control: Robustness Analysis Against Measurement Noise

This paper analyzes output feedback control of a class of unknown nonlinear systems in the presence of measurement noise using multiple high-gain observers (MHGO). It is well-known that single high-gain observers (HGO) are not able to provide satisfactory performance when the system output is contaminated by noise. More specifically, there is a trade-off between the convergence speed of state estimation and the bound of steady estimation error in HGO when the output measurement is contaminated by noise. In the presented scheme, the output feedback controller utilizes the state estimation obtained from an appropriate combination of information provided by a bank of HGOs. The proposed strategy is capable of mitigating the destructive effects of measurement noise and speeding up the convergence process, and it does that because it introduces an extra design parameter. The performance recovery capabilities of MHGO-based controllers and the stability of the closed-loop system are discussed. Simulations are performed on an underwater vehicle system and a mechanical system to evaluate the performance of the MHGO-based controller. Furthermore, a detailed comparison between the MHGO-based controller and controllers based on conventional HGO, HGO with switching gain, and multi-observer approach is provided, which shows the superiority of the MHG-based controller over the other methods.

Finite-Time Adaptive Fuzzy Tracking Control for a Class of Nonlinear Systems With Full-State Constraints

In this article, a new command filtered backstepping based finite-time adaptive fuzzy tracking control scheme for a class of unknown nonlinear systems with full-state constraints is established. First, the proposed finite-time command filter will filtering the virtual control signal and get the intermediate control signal within finite-time, so the problem of calculating complexity will not occur in the backstepping process. Then, the fraction-power-based error compensate signal is set up, which can eliminate the influence of filtering error on the control performance. Considering that the unknown nonlinearities exist in the system, the fuzzy logic system based adaptive control technique is used to deal with them, and only one parameter needs to be estimated. It is shown that the states will not violate the prescribed constrains, all the signals in the closed-loop system are bounded in finite-time and the tracking error can converge to the desired neighborhood of the origin in finite time under the barrier Lyapunov function and fraction-power-based virtual control signals. Finally, the effectiveness of the control method is shown by the simulations.

Finite-time prescribed performance adaptive fuzzy control for unknown nonlinear systems

This paper aims at the problem of finite-time prescribed performance adaptive fuzzy control for a class of unknown nonlinear systems. An adjustable finite-time performance function with faster convergence rate is applied to the procedure of the controller design, whose parameters can be adjusted in real time on the basis of the tracking error. Furthermore, a finite-time prescribed performance adaptive fuzzy tracking controller is designed by the backstepping method, which can guarantee that all the signals in the closed-loop system are bounded. Simultaneously, the output tracking error always stays within an adjustable boundary and converges to a fixed region at finite-time settling time. Besides, the tracking performance in transient state is slightly optimized. Simulation results demonstrate the effectiveness of the proposed controller.

Neural-network-based adaptive backstepping control for a class of unknown nonlinear time-delay systems with unknown input saturation

In this paper, a neural-network-based adaptive backstepping control scheme is developed for a class of unknown nonlinear systems with unknown time-varying delayed states and unknown saturated delayed input. In the proposed method, radial basis function neural network is adopted to approximate the unknown nonlinear functions. An adaptive backstepping design is employed to compensate for the unknown time-varying delays in states. In addition, to overcome the effects of input delay, an auxiliary dynamic system is constructed. Moreover, a novel adaptive law is used for estimating unknown bounds of saturation function. Using the Lyapunov stability theorem, it is proven that the closed-loop system is semi-globally uniformly ultimately bounded and the tracking error can converge to small desired value by the proper choose of design parameters. Finally, the effectiveness of the proposed method is illustrated by applying it to a chemical reactor recycle system, one-link manipulator actuated by a DC motor and a Brusselator model.

Event-Triggered Prescribed Performance Control for a Class of Unknown Nonlinear Systems

This article is concerned with the tracking control problem for a sort of networked system with unknown nonlinear functions, unmatched disturbances, and event-triggered input. A novel prescribed performance control strategy together with an actuator update protocol is developed to form a solution. Different from the existing results, only a binary signal (either 0 or 1) needs to be sent to the actuator. In this way, the number and the bit of data transmission are both curtailed, leading to the economy of the communication cost. On the other hand, output tracking with guaranteed transient and steady-state performance is achieved regardless of unknown nonlinearities, disturbances, and measurement errors. Finally, simulation results are given to illustrate the established theoretical findings.

High Order Sliding Mode Backstepping Control for a Class of Unknown Pure Feedback Nonlinear Systems

This paper aims at addressing the problem of finite time exact tracking control for a class of unknown nonlinear systems in pure feedback form while guaranteeing the closed-loop stability. The uncertain nonlinear system considered in this paper is not only in completely non-affine form but also explicitly dependent on the time and therefore, can cover a general class of nonlinear systems. By incorporating high order sliding mode controller into backstepping design procedure, a new robust control scheme with novel integrators is proposed, which is able to steer the tracking error to zero. Moreover, the closed loop stability can be proved with the help of the constructed integrators in every design step. Two simulation examples are presented to illustrate the correctness and effectiveness of the proposed control scheme.

Improved Robust Adaptive Control Law for a Class of Uncertain Nonlinear Systems and Its Application to Chaotic Systems

An adaptive robust control scheme is proposed for a class of unknown nonlinear systems. For achieving this purpose, a class of uncertain nonlinear systems is firstly considered. Then, the regulation and tracking problems are solved with the well-known Lyapunov stability theory. It is shown that although the system dynamic may not be fully or partially known, some adaptive control laws can be mathematically derived by using the proposed control method. Hence, by the proposed control method, the closed-loop system would be globally stabilized in the sense of the Lyapunov stability theory. Finally, the proposed robust adaptive control law is numerically applied into the Lorenz and Van der Pol chaotic systems. The efficiency of the suggested approach is shown by numerical simulation via comparison with an existing method.

Model free adaptive iterative learning control for a class of nonlinear systems with randomly varying iteration lengths

This paper proposes a novel model free adaptive iterative learning control scheme for a class of unknown nonlinear systems with randomly varying iteration lengths. By applying the dynamic linearization technique along the iteration axis, such systems can be transformed into iteration-depended time varying linear systems. Then, an improved model free adaptive iterative learning control scheme can be constructed only using input and output data of the system. From the rigorous theoretical analysis, it is shown that the mathematical expectation of tracking errors converge to zero as iteration increases. This design does not require any dynamic information of the ILC systems and prior information of randomly varying iteration lengths. An illustrative example verifies the effectiveness of the proposed design.

Asymptotic Tracking Control for a Class of Pure-Feedback Nonlinear Systems

This paper studies the adaptive asymptotic tracking problem for a class of unknown nonlinear systems in pure-feedback form. Different from the traditional literatures which only tackle the bounded tracking problem for pure-feedback systems, this paper investigates the asymptotic tracking problem by developing a novel controller design method. Moreover, the differentiable assumption on nonaffine functions is canceled, and only a mild semi-bounded assumption is required as the controllability condition. By utilizing Lyapunov theorem, it is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the output tracking error can converge to zero asymptotically by choosing design parameters appropriately. Finally, a simulation result is presented to verify the effectiveness of the proposed control scheme.

Neural Network-Based Cooperative Identification for a Class of Unknown Nonlinear Systems via Event-Triggered Communication

In this paper, a neural network (NN)-based distributed cooperative identification strategy with event-triggered communication is studied for a group of coupled identical nonlinear systems. We develop a distributed cooperative learning law in the context of event-triggered communication, where an agent will transmit its NN weights to its neighbors only when its weight trigger error norm exceeds an exponentially decreasing threshold. It is proven that the estimated weights of all radial basis function NNs converge to a small neighborhood of their optimal values. Therefore, the unknown nonlinear function is approximated along the union of all the system trajectories. It is further proven that there exists a positive minimum interevent interval and Zeno behavior can be avoided. Finally, we give a simulation example to demonstrate these features.

Adaptive Control for Strict Feedback Systems With Actuator Aging and External Disturbance

Unknown actuator aging is inevitable in practice. However, reviewing the development of control theory, available results of handling actuator aging are still very limited. In this paper, we address such a problem by considering controlling a class of unknown nonlinear systems. In fact, unknown aging can be denoted as a nonlinear function of variable t with nonlinearly parameterized parameters which cannot be estimated by adaptive approach directly. To solve it, a new adaptive controller and update laws are proposed by linearizing aging function. Unlike the traditional approaches, a new Lyapunov function, including an integral term about estimation error of such parameter, is designed to analyze the stability of the closed-loop system. It is shown that the designed controller can ensure the stability and tracking performance of the closed-loop system.

Adaptive asymptotic stabilization of a class of unknown nonlinear systems with specified convergence rate

SummaryThis paper focuses on the asymptotic stabilization problem for a class of multivariable nonlinear systems with relative degree one, practical examples of which incorporate the liquid level control of water tanks, and the speed control of interconnected carts. The presence of the unknown (other than uncertain) additive and multiplicative nonlinearities renders asymptotic stability difficult to be achieved by the existing robust control methods. To conquer this obstacle, a novel adaptive control strategy is proposed. In the control design, the state constraint technique is newly introduced to the adaptive design to generate a proper control gain to compensate for unknown nonlinearities, instead of the use of extra approximating structures. By this means, both the prescribed transient performance regarding the convergence rate and the expected asymptotic stability are preserved. Finally, simulation results are given to illustrate the established theoretical findings.