Unknown Nonlinearities Research Articles

Backstepping Control for a Class of Nonlinear Discrete-Time Systems Subject to Multisource Disturbances and Actuator Saturation.

In this article, the backstepping control scheme is designed for a class of systems with multisource disturbances, actuator saturation, and nonlinearities in the domain of discrete time. To address the multisource disturbances, we put forward a novel discrete-time hybrid observer, which can deal with both modeled and unmodeled disturbances. In virtue of the radial basis function neural networks, the unknown nonlinearities are approximated. In addition, the anti-windup technique is adopted to cope with the actuator saturation phenomenon, which is pervasive in engineering practice. Bearing all the adopted mechanisms in mind, the composite control strategy is designed in a backstepping manner. Sufficient conditions are established to guarantee that the states of the system ultimately converge to a small range with linear matrix inequalities. Finally, the effectiveness of the presented methodology is verified for the spacecraft attitude system.

Approximate Output Regulation of Discrete-Time Stochastic Multiagent Systems Subject to Heterogeneous and Unknown Dynamics

The output regulation approach has been extensively applied for the cooperative control of heterogeneous multiagent systems (MASs) with known dynamics, but rarely for MASs subject to stochastic and unknown dynamics. One challenging problem is that it is still unclear how to construct the regulator equations of stochastic MASs with unknown dynamics for dynamic exosystem compensation. Toward this end, this article develops a novel distributed control scheme for the approximate output regulation of discrete-time stochastic MASs subject to heterogeneous and unknown nonlinear dynamics. A distributed observer is designed for the exosystem-state estimation of agents, based upon which nonlinear regulator equations are constructed for the feedforward control design, thereby achieving distributed exosystem compensation. A high-order neural network is deployed to approximately solve the nonlinear regulator equations with unknown nonlinearity, and an adaptive control law is developed for the approximate output regulation of discrete-time stochastic MASs. Stability analysis shows that the closed-loop system is semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness and efficiency of the proposed control law.

Global Stabilization for Stochastic Continuous Cascade Nonlinear Systems Subject to SISS Inverse Dynamics and Time-Delay: A Dynamic Gain Approach

This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system.

Impact angle constrained fuzzy adaptive fault tolerant IGC method for Ski-to-Turn missiles with unsteady aerodynamics and multiple disturbances

An impact angle constrained fuzzy adaptive fault tolerant integrated guidance and control method for Ski-to-Turn (STT) missiles subject to unsteady aerodynamics and multiple disturbances is proposed. Unsteady aerodynamics appears when flight vehicles are in a transonic state or confronted with unstable airflow. Meanwhile, actuator failures and multisource model uncertainties are introduced. However, the boundaries of these multisource uncertainties are assumed unknown. The target is assumed to execute high maneuver movement which is unknown to the missile. Furthermore, impact angle constraint puts forward higher requirements for the interception accuracy of the integrated guidance and control (IGC) method. The impact angle constraint and the precise interception are established as the object of the IGC method. Then, the boundaries of the lumped disturbances are estimated, and several fuzzy logic systems are introduced to compensate the unknown nonlinearities and uncertainties. Next, a series of adaptive laws are developed so that the undesirable effects arising from unsteady aerodynamics, actuator failures and unknown uncertainties could be suppressed. Consequently, an impact angle constrained fuzzy adaptive fault tolerant IGC method with three loops is constructed and a perfect hit-to-kill interception with specified impact angle can be implemented. Eventually, the numerical simulations are conducted to verify the effectiveness and superiority of the proposed method.

State estimation and fuzzy sliding mode control of nonlinear Markovian jump systems via adaptive neural network

This paper deals with the problem of Takagi-Sugeno fuzzy model-based state estimation and sliding mode control for nonlinear systems through an adaptive neural network, in which the system parameters follow the Markovian switching rules. In order to deal with the unknown local nonlinearity, a multi-layer neural network is used for the nonlinear function approximation. First, a Lebesgue fuzzy observer with adaptive compensator is designed based on state-dependent fuzzy rules. Second, an integral sliding surface is proposed, based on which the obtained sliding mode dynamics has good property of sliding mode manifold. Third, an H∞ performance with stochastic stability of the sliding mode dynamics and error dynamics are developed in the form of linear matrix inequality. Moreover, reachability of sliding surface in finite-time and maintenance of sliding motion are realized by constructing a fuzzy sliding mode controller. Finally, a simulation study is added to show the validity of the proposed results on the robot manipulator model.

Adaptive extreme learning machine‐based event‐triggered control for perturbed Euler–Lagrange systems

ABSTRACTThe problem of event‐triggered finite‐time trajectory tracking control of perturbed Euler–Lagrange systems with nonlinear dynamics and disturbances is addressed in this article. Extreme learning machine (ELM) framework is employed to formulate unknown nonlinearities, and adaptive technique is adopted to adjust output weights of the ELM networks and remedy the negative impacts of disturbances, nonlinearities, and residual errors. Then to ensure the system follows the desired position trajectory within a finite‐time, an adaptive ELM‐based sliding mode control strategy is developed. Moreover, event‐triggered control technique is proposed to regulate control outputs on the basis of the developed control strategy for reducing actuator actions and saving communication resources. Lyapunov stability theorem is utilized to confirm bounded trajectory tracking results and finite‐time convergence of the Euler–Lagrange system. Finally, the effectiveness of the developed adaptive ELM‐based event‐triggered sliding‐mode control strategies is substantiated by simulations in a robotic manipulator system.

Adaptive neural-network-based distributed fault estimation for heterogeneous multi-agent systems

This contribution addresses the issue of distributed fault estimation for heterogeneous multi-agent systems which are composed of unmanned ground vehicles and unmanned aerial vehicles in the presence of actuator faults, completely unknown nonlinearities and external disturbances. Given that these two types of agents have different state dimensions and the motion of unmanned aerial vehicles in the XOY plane and Z-axis is relatively independent, the heterogeneous multi-agent systems can be divided into the XOY plane of all agents’ position subsystem and the Z-axis of unmanned aerial vehicles’ position subsystem. Then, combining the influences of completely unknown nonlinearities and external disturbances, an adaptive neural-network-based distributed fault estimation scheme is proposed to effectively estimate unknown actuation effectiveness parameters and can be applied to XOY plane and Z-axis of heterogeneous multi-agent systems separately. During the design of the observer, the neural network methodology is adopted to approximate completely unknown nonlinearities and a proper adaptive update law to estimate the 2-norm upper bound of disturbances and compensate for the influences of disturbances is designed. With output from a local agent and its neighbors, the proposed observer can be built on this agent, realizing simultaneous estimation of possible faults occurring in both the selected agent and its neighbor agents, which presents a new distributed framework. At last, simulation results are shown to illustrate the feasibility and effectiveness of the presented fault estimation algorithm.

Event-triggered adaptive neural finite-time tracking control for non-strict feedback stochastic nonlinear systems with unknown time-varying control directions and input nonlinearities

This paper focuses on dynamic-surface-based event-triggered adaptive neural finite-time tracking control for a category of non-strict feedback stochastic nonlinear system subject to unknown time-varying control directions, and input nonlinearities. Firstly, an improved event-triggered mechanism is presented, which simultaneously considers tracking error variables and compensating for event errors in threshold value. Secondly, a novel Lemma is provided to address concurrently the issues of Nussbaum terms in stability analysis and stochastic system finite-time stability. Thirdly, neural networks are utilized to cope with unknown functions. In addition, the Nussbaum functions are applied to identify time-varying unknown control directions and input nonlinearities. Moreover, the errors of the dynamic surface technique are compensated successfully by error compensation signals. By combining the proposed Lemma 1 and event-triggered adaptive neural finite-time control scheme, finite-time stability of considered systems in probability can be guaranteed, the tracking error can drive to a small neighborhood of the origin in finite time, and the Zeno behavior can be excluded. Finally, the effectiveness of the designed control scheme has been demonstrated through a second-order numerical system and a mass-spring-damper example.

Distributed containment control of networked uncertain MIMO pure‐feedback nonlinear systems via quantized state feedback and communication

AbstractThis article presents a distributed adaptive containment control strategy using quantized state feedback and communication for uncertain multiple‐input‐multiple‐output pure‐feedback nonlinear multi‐agent systems with state quantization. It is assumed that quantized state variables of multiple followers and quantized outputs of multiple dynamic leaders are only available for constructing local adaptive feedback controllers of followers under a directed network. Compared with existing containment control approaches, the primary contribution of this study is dealing with discontinuously quantized state feedback and communication problems for containment control design in the presence of unknown nonaffine nonlinearities. Based on quantized state and communication information, local adaptive neural network trackers of followers and their adaptive tuning laws are developed to guarantee that the trajectories of all followers converge to the dynamic convex hull spanned by the multiple leaders regardless of unknown pure‐feedback nonlinearities. By analyzing the stability of the local quantization errors between quantized signals and original signals, we prove the boundedness of all closed‐loop signals and the convergence of the containment errors to a sufficiently small domain around the origin. Simulation examples involving flexible‐joint manipulators are presented to validate the proposed quantized feedback scheme.

Finite-Time Adaptive Neural Control Scheme for Uncertain High-Order Systems with Input Nonlinearities and Unmodeled Dynamics

This paper proposes a novel finite-time adaptive neural control method for a class of high-order nonlinear systems with high powers in the presence of dead zone input nonlinearities and unmodeled dynamics. By utilizing prescribed performance functions and radial basis function neural networks, the tracking error and state errors are limited within the preassigned range in a finite time, which can be specified by the designer in advance according to the chosen the parameters of the novel prescribed performance functions. Nonlinear transformed error surfaces are designed to counteract the effects of dead zone input nonlinearities in nonlinear high-order systems with unknown system nonlinearities and unmodeled dynamics. Based on the Lyapunov theorem, the tracking errors are proven to converge into a preassigned set in a finite time previously specified by the novel prescribed performance function. Finally, simulation results demonstrate the effectiveness of the proposed method.

Distributed Optimal Cooperation for Multiple High-Order Nonlinear Systems With Lipschitz-Type Gradients: Static and Adaptive State-Dependent Designs

This article investigates the distributed optimal cooperation problems for multiple high-order systems, in which the dynamics of each agent is allowed to be subject to unknown nonlinearities. To eliminate the effect caused by unknown nonlinearities, a nonlinearity estimator is developed based on agents’ states, which successfully reconstructs the nonlinear dynamics if the unknown nonlinearities are bounded. And to minimize the sum of multiple local nonlinear cost functions with Lipschitz-type gradients, a couple of static and adaptive state-dependent algorithms are designed, respectively, where each agent may only have access to its own local cost function. It is challenging to solve such an optimal cooperation problem as the performance of the whole multiagent network is evaluated by the sum of all local performance functions. In order to fulfill the goal of cooperative optimization, a state-dependent distributed optimal cooperation algorithm is proposed first. By utilizing tools from the Lyapunov stability theory and convex optimization analysis, it is proven that the considered distributed optimal cooperation problem for high-order nonlinear systems can be solved by the proposed optimal cooperation algorithm if the state-dependent parameters are suitably selected. It is noted that the selections of the state-dependent parameters depend on some global information of the multiagent systems. Furthermore, by incorporating the proposed optimal cooperation algorithm with adaptive parameters strategy, the optimal cooperation problem is solved in a fully distributed manner. Finally, a numerical simulation is shown to verify the effectiveness of the proposed algorithms.

Event-Triggered Adaptive Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems With Actuator Faults.

In this article, an adaptive event-triggered fault-tolerant asymptotic tracking control problem guaranteeing prescribed performance is addressed for a class of block-triangular multi-input and multioutput uncertain nonlinear systems with unknown nonlinearities, unknown control directions, and actuator faults. Through a systematic co-design of the adaptive control law and the event-triggered mechanism, including fixed and relative threshold strategies, a control scheme with low structure and calculation complexity is designed to conserve system communication and computation resources. In this design, the output asymptotic tracking is achieved. The Nussbaum gain technique is incorporated to overcome unknown control directions with a new adaptive law, and a type of barrier Lyapunov function is adopted to handle the prescribed performance control problem, which contributes to a novel control law with strong robustness. The robust controller can address the uncertainties and couplings derived from the system structure, actuator faults, and event-triggered rules, without using approximating structures or compensators. Besides, the explosion of complexity is avoided. It is proved that all signals of the closed-loop system remain bounded, and system tracking errors asymptotically approach 0 with the prescribed performance, while the Zeno behavior is prevented. Finally, the effectiveness of the proposed control scheme is evaluated via an application example of the half-car active suspension system.

ADP-Based Remote Secure Control for Networked Control Systems Under Unknown Nonlinear Attacks in Sensors and Actuators

In this article, we concentrate on a class of networked control systems (NCSs) under the unknown nonlinear attacks, which target the sensors and actuators with remote communication channels. To attenuate the attacks remotely, the remote secure control scheme based on the adaptive dynamic programming (ADP) is proposed. First, the dynamic process of NCSs with nonlinear sensors and actuators attacks is analyzed and an adaptive remote estimator is designed to obtain the state information of the NCSs from a long distance, which is the key to achieve the purpose of remote control. Moreover, to compensate for the unknown nonlinear attacks, the adaptive law of the remote estimator is presented based on recursive least square. Furthermore, we consider the influence of the estimation errors, the minimax control theory is applied to improve the design of the policy iteration algorithm, and the ADP-based remote secure control strategy is proposed to rely on the remote estimation information. Then, the neural networks are built to implement the online algorithm. Finally, results’ analysis illustrates on two networked power systems the effectiveness of the proposed method.

Adaptive Sliding Mode Controller for Robotic Manipulator Tracking Control with Fuzzy Design

This paper introduces an adaptive sliding mode controller design based on fuzzy compensation for efficient robotic manipulator tracking control. This work introduces design of Adaptive Fuzzy Controller based on sliding control principles for Robotic Manipulators. In the work, an adaptive fuzzy sliding mode control algorithm is proposed for tracking control of robot manipulators. The fuzzy system uses a set of fuzzy rules, the parameters of which are modified in real-time by adaptive laws, to approximate unknown nonlinearities. This makes it easier to direct the nonlinear system's output to follow a specific trajectory. An adaptive control algorithm based on the adaptive fuzzy model is created using the Lyapunov approach. Both the chattering and the stable performance are assured.

Adaptive neural consensus tracking control of distributed nonlinear multiagent systems with unmodeled dynamics

SummaryThis paper aims to address the adaptive consensus tracking control problem for distributed nonlinear multi‐agent systems with unmodeled dynamics. It should be emphasized that each considered follower is modeled as a nonlinear non‐strict feedback system in which the control gains are unknown functions rather than constants. By applying an inherent property of radial basis function (RBF) neural networks (NNs) and the introduced dynamics signals, the design difficulties aroused from unknown nonlinearities and unmodeled dynamics are overcome such that the control purpose can be achieved. Then, based on adaptive backstepping methods, a new consensus tracking control protocol is proposed. It is shown that the closed‐loop systems are stable and all the outputs of followers ultimately track the reference signal, that is, the output of the leader, synchronously. Finally, the effectiveness of the proposed control protocol is illustrated through the simulation results.

Distributed active disturbance rejection formation containment control for multiple autonomous underwater vehicles with prescribed performance

In this paper, a distributed formation containment control (FCC) issue is studied for multiple autonomous underwater vehicles (MAUVs) system with prescribed performance based on the active disturbance rejection control (ADRC) method in three-dimensional space. The unknown nonlinearities and external disturbances of the MAUVs system are approximated in real time by means of extended state observers (ESOs). Furthermore, tracking differentiators (TDs) are introduced for the sake of refraining from the explosion of complexity induced by the derivatives of the virtual control variables of autonomous underwater vehicles. Applying funnel variables, our designed control strategy ensures the formation tracking errors and containment errors to keep within the specified ranges, hence enhancing the control performance of the MAUVs system. Then, a FCC-ADRC scheme for MAUVs system is proposed. Compared with the traditional FCC scheme, the proposed FCC-ADRC scheme not only does not depend on the specific system configuration, but also can deal with any bounded disturbances, thus obtaining a more general, effective and robust disturbance rejection FCC strategies. Additionally, the stability of MAUVs system is verified through Lyapunov stability analysis. At last, the error curves and time-varying formation containment trajectories obtained by simulation confirm the feasibility and effectiveness of our method.

Remote State Estimation of Nonlinear Systems Over Fading Channels via Recurrent Neural Networks

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearities can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

Unknown System Dynamics Estimator for Active Vehicle Suspension Control Systems With Time-Varying Delay.

This article proposes a novel control method for vehicle active suspension systems in the presence of time-varying input delay and unknown nonlinearities. An unknown system dynamics estimator (USDE), which employs first-order low-pass filter operations and has only one tuning parameter, is constructed to deal with unknown nonlinearities. With this USDE, the widely used function approximators (e.g., neural networks and fuzzy-logic systems) are not needed, and the intermediate variables and observer used in the traditional estimators are not required. This estimator has a reduced computational burden, trivial parameter tuning and guaranteed convergence. Moreover, a predictor-based compensation strategy is developed to handle the time-varying input delay. Finally, we combine the suggested USDE and predictor to design a feedback controller to attenuate the vibrations of vehicle body and retain the required suspension performances. Theoretical analysis is carried out via the Lyapunov-Krasovkii functional to prove the stability of the closed-loop system. Simulation results based on professional vehicle simulation software Carsim are provided to show the efficiency of the proposed control scheme.

Fuzzy Adaptive Optimal Consensus Fault-Tolerant Control for Stochastic Nonlinear Multiagent Systems

This article investigates the problem of adaptive fuzzy optimal distributed consensus control for stochastic multiagent systems (MASs) with full-state constraints and nonaffine nonlinear faults. Fuzzy logic systems are employed to identify the unknown nonlinearities. To solve the problem of optimal state constraint control, a barrier Lyapunov function based optimal cost function is designed. By introducing Butterworth low-pass filter into control design, the deleterious effects raised by nonlinear fault can be compensated. By utilizing adaptive dynamic programming algorithm in critic–actor construction, a fuzzy adaptive distributed optimal consensus fault-tolerant control method is proposed, which can ensure that all signals of the controlled system are semiglobally uniformly ultimately bounded in probability, and outputs of the follower agents keep consensus with the output of leader. In addition, system states are all not exceeded their constrained bound. Finally, simulation results are provided to illustrate the feasibility of the developed control method and theorem.

Neural Adaptive Funnel Dynamic Surface Control with Disturbance-Observer for the PMSM with Time Delays.

This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the “complexity explosion” caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.