Class Of Nonlinear Systems Research Articles

Emotional Intelligent Finite-Time Tracking Control for a Class of Nonlinear Systems

Emotional Intelligent Finite-Time Tracking Control for a Class of Nonlinear Systems

Recurrent Neural Network Inspired Finite-Time Control Design

Dear Editor, This letter is concerned with the role of recurrent neural networks (RNNs) on the controller design for a class of nonlinear systems. Inspired by the architectures of RNNs, the system states are stacked according to the dynamic along with time while the controller is represented as the neural network output. To build the bridge between RNNs and finite-time controller, a novel activation function is imposed on RNNs to drive the convergence of states at finite-time and propel the overall control process smoother. Rigorous stability proof is briefly provided for the convergence of the proposed finite-time controller. At last, a numerical simulation example is presented to illustrate the efficiency of the proposed strategy.

Least squares adaptive control for uncertain system based on modified predictive model

AbstractThis research addresses the tracking problem of least squares adaptive control for a class of nonlinear system with mismatched uncertainties. Different from most of existing solutions, modified predictive model is integrated into the proposed least squares adaptive control architecture. The significant role of modified predictive model in the adaptive control architecture is to achieve smooth transient by filtering out the high‐frequency oscillations, which cannot be canceled out by use of the hypothetical parameterized uncertainty models. Meanwhile, in order to guarantee tracking performance, a generalized restricted potential function (GRPF) is designed to constrain the weighted Euclidean norm of the predictive error of the modified predictive model to be less than a predefined scalar worst‐case bound. Finally, comparative simulations via the generic transport model (GTM) are conducted to examine the effectiveness of the proposed method. The results show that the transient performance and tracking performance of the controlled system can be improved simultaneously by the proposed method.

Asymptotic adaptive output-feedback stabilisation of nonlinear systems with unknown growth rate and sensor uncertainty

For a class of nonlinear systems with sensor uncertainty, the problem of adaptive output feedback stabilisation is investigated in this paper. It is assumed that only the output is available for feedback control, which suffers from sensor uncertainty. At the same time, the nonlinear function in the system model has an unknown growth rate. To solve this problem, a set of state observers is designed to estimate the unknown system states based on the uncertain output, and an adaptive output-feedback control is designed based on this. By using the corollary of Barbalet's Lemma, it is shown that the equilibrium of the closed-loop system is asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme

Neural network-based prescribed performance tracking control for a class of nonlinear systems with mismatched disturbances

This paper addresses the prescribed performance tracking control problem for a class of nonlinear systems subject to mismatched uncertainties. A novel disturbance observer-based control (DOBC) scheme is proposed through combining radial basis function neural network (RBFNN) and prescribed performance function (PPF). In contrast to traditional DOBC, the proposed approach employs RBFNN technology to approximate unknown nonlinear functions in the system, instead of treating them as part of lumped disturbances. A novel disturbance observer is developed to estimate disturbances characterised by a nonlinear exogenous system. To enhance control performance, a PPF that characterises both transient and steady-state behaviour is used for the transformation of tracking errors. It can be proved that all the states of the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB), and that the tracking error evolves within the prespecified boundaries. Theoretical results are validated and supported by two simulation examples.

Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics

This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.

An improved Bayesian filter for nonlinear systems under multistep randomly delayed and lost measurements

AbstractThis article addresses the Bayesian filtering problem for a class of nonlinear systems under multistep randomly delayed and lost measurements. A new measurement model is established that can characterize the random delay and loss of measurement data. First, an augmented Gaussian mixture filter framework is developed in the case of random delay of measurement data; the posterior probability density function after state augmentation is calculated by marginalizing over delay variables to extract accurate information from delayed measurements. The implementation of the filter is transformed into the computation of nonlinear numerical integrals. Second, under the proposed framework, novel expressions of the mean and covariance are generated by propagating the measurement taken at the previous moment in the event of no new measurement being received. Finally, we present two simulation examples for estimating system states, and the results demonstrate the effectiveness and superiority of our proposed filter.

Exponential-form predefined-time convergent controller and its applications to Van-der-Pol system and 2-DOF helicopter

This paper proposes a predefined-time convergent stabilization controller for a class of nonlinear systems. First, a controller is introduced for linear systems where the convergent time is selected in advance, independent of initial conditions, and can be assigned as a parameter of a control input. The corresponding result is then obtained for a multidimensional system consisting of [Formula: see text] nonlinear differential equations. The block control technique is employed to consequently stabilize each state component by a virtual control until the real control appears. Finally, the presented result is applied to a multivariable nonlinear system to design a predefined-time convergent robust controller. To show effectiveness of the proposed convergent controller, numerical simulations have been carried out for a Van-der-Pol system and a 2-degree-of-freedom (2-DOF) helicopter model.

Finite-time fault-tolerant control of a spacecraft using composite learning in the presence of moment of inertia uncertainty and external disturbances

In this paper, a neuro-adaptive finite-time fault-tolerant control for a class of nonlinear systems is proposed based on the backstepping method, considering model uncertainties and external disturbances. To compensate for model uncertainties, a neural network is employed, while external disturbances and the estimation error of the neural network are handled using a disturbance observer. Additionally, actuator faults are estimated and compensated for distinctly using two adaptive elements in the proposed control system. Moreover, to enhance the learning of the neural network, disturbance observer, and other adaptive elements, particularly in the lack of persistently exciting signals, a composite learning approach is utilized. To this end, a state-observer is introduced, and its estimation error along with the tracking error is used in the updating rules of all the adaptive elements in the design. Additionally, to prevent the explosion of terms in the backstepping method, a command filter with practical finite-time stable auxiliary variables is incorporated into the proposed controller. Finite-time convergence of the tracking error to zero is rigorously proved using the Lyapunov method. To demonstrate the effectiveness of the proposed control method, the problem of attitude control of a rigid spacecraft with moment of inertia uncertainty, external disturbances, and multiple actuator faults is considered since precise attitude control of a spacecraft is of great importance in different maneuvers. The results show that using the introduced control system, the spacecraft is able to track the desired trajectory under different types of uncertain dynamics.

Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Mismatched Disturbances

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

Attack-Resilient Distributed Nash Equilibrium Seeking of Uncertain Multiagent Systems Over Unreliable Communication Networks.

This article investigates the distributed Nash equilibrium (NE) seeking problem of uncertain multiagent systems in unreliable communication networks. In this problem, the action of each agent is subject to a class of nonlinear systems with uncertain dynamics, and the communication network among agents will be affected by the nonperiodic denial of service (DoS) attacks. Note that, in this insecure network environment, the existence of DoS attacks will directly destroy the connectivity of the network, which leads to performance degradation or even failure of the most existing distributed NE seeking algorithms. To address this problem, we propose a two-stage distributed NE seeking strategy, including the attack-resilient distributed NE estimator and the neuroadaptive tracking controller. The estimator based on the projection subgradient method and the consensus protocol can converge exponentially to virtual NE against DoS attacks. Then, the neuroadaptive tracking controller is designed for uncertain multiagent systems with the output of the estimator as the reference signal such that the actual action of all agents can reach NE. Based on the Lyapunov stability theory and improved average dwell time automaton, the stability of the estimator and the controller is proven, and all signals in the closed-loop system are uniformly bounded. Numerical examples are presented to verify the effectiveness of the proposed strategy.

Sliding Mode Fuzzy Control of Stochastic Nonlinear Systems Under Cyber-Attacks.

In this article, the problem of integral sliding mode control (ISMC) for a class of nonlinear systems with stochastic characteristics under cyber-attack is investigated. The control system and the cyber-attack are modeled as an Itô-type stochastic differential equation. The stochastic nonlinear systems are approached by the Takagi-Sugeno fuzzy model. A dynamic ISMC scheme is applied and the states and control input are analyzed within a universal dynamic model. It is demonstrated that trajectory of the system can be confined to the integral sliding surface within finite time, and the stability of closed-loop system under cyber-attack will be guaranteed by using a set of linear matrix inequalities. Following a standard procedure of universal fuzzy ISMC, it is shown that all signals in the closed-loop system will be guaranteed bounded, and the states are asymptotic stochastic stable if some conditions are met. An inverted pendulum is applied to show the effectiveness of our control scheme.

Dynamic output feedback control of uncertain nonlinear systems based on co-design adaptive event-triggered scheme

This paper presents a framework to design a robust dynamic output feedback (DOF) controller for a class of nonlinear systems, based on the adaptive event-triggered control (AETC) method. The considered system contains parametric uncertainty and to design the event-triggered mechanism (ETM) Finite-gain L2 stability criteria are used. In this paper, a robust adaptive event-triggered mechanism (AETM) is first designed using a pre-designed controller. Then, in a co-design approach, the AETM and the DOF controller are designed together to increase the closed-loop performance. Indeed, the matrices of the DOF controller and the sufficient conditions for the AETM are obtained simultaneously. These conditions are represented as linear matrix inequalities (LMIs) and lead to a significant increase in the update interval. Moreover, the proposed design method guarantees the stability of the closed-loop system in the presence of the proposed triggering event. Finally, to illustrate the performance of the controller three examples are simulated.

Practical Prescribed-Time Stabilization of a Class of Nonlinear Systems by Event-Triggered and Self-Triggered Control

Practical Prescribed-Time Stabilization of a Class of Nonlinear Systems by Event-Triggered and Self-Triggered Control

Generalization of Direct Adaptive Control Using Fractional Calculus Applied to Nonlinear Systems

This paper presents a new direct adaptive control (DAC) technique using Caputo’s definition of the fractional-order derivative. This is the first time a fractional-order adaptive law is introduced to work together with an integer-order stable manifold for approximating the uncertainty of a class of nonlinear systems. The DAC approach uses universal function approximators such as multi-layer perceptrons with one hidden layer or fuzzy systems to approximate the controller. This paper presents a new lemma, which elucidates and clarifies the link between the Caputo and the Riemann–Liouville definitions. The introduced lemma is useful in developing a Lyapunov candidate to prove the stability of using the proposed fractional-order adaptive law. This is further explained by a numerical example, which is provided to elucidate the practicality of using the fractional-order derivative for updating the approximator parameters. The main novelty of the results in this paper is a rigorous stability proof of the fractional DAC approach for a class of nonlinear systems that is subjected to unstructured uncertainty and deals with the adaptation mechanism using a traditional integer-order stable manifold. This makes the control scheme easier to implement in practice. The fractional-order adaptation law provides greater degrees of freedom and a potentially larger functional control structure than the conventional adaptive control. Finally, the paper demonstrates that traditional integer-order DAC is a special case of the more general fractional-order DAC scheme introduced here.

Adaptive event-triggered tracking control for nonlinear systems with prescribed performance: A time-domain mapping approach

This paper proposed an event-triggered adaptive fuzzy prescribed time control strategy for a class of nonlinear systems with uncertain external disturbances and unknown virtual control coefficients under prescribed performance. A novel time-domain mapping technique is proposed to transform the prescribed time tracking control problem into an asymptotic convergence problem. An observer is designed to estimate for the external disturbance and fuzzy approximation error of fuzzy logic systems (FLSs). The problem of “explosion of complexity” is addressed by applying dynamic surface control (DSC) technique to backstepping. An adaptive fuzzy event-triggered strategy is designed using the Lyapunov stability theorem. This strategy ensures that, after time-domain mapping, the tracking error asymptotically converges to zero. Additionally, there is no Zeno behavior and all system signals are bounded. Finally, the effectiveness of the proposed scheme is verified through three simulation examples.

On global feedback control of unknown nonlinear systems

The construction of robust state-feedback controllers for unknown nonlinear systems is addressed through the derivation of robust bang-bang state-feedback controllers that lead to global asymptotic stabilisation. It is shown that a relatively simple testing process can provide sufficient information about an unknown system to facilitate the construction of bang-bang state-feedback controllers that guide the system toward global robust asymptotic stabilisation. The methodology presented in the paper applies to a broad class of nonlinear systems.

Adaptive control of A class of nonlinear systems with guaranteed parameter estimation: A concurrent learning based approach

AbstractRecent advances in concurrent learning based adaptive controllers have relaxed the persistency of excitation condition required to achieve exponential tracking and parameter estimation error convergence. This was made possible via the use of additional concurrent learning stacks in the parameter estimation algorithm. However, the proposed concurrent learning components, that is, the history stacks, needed to be filled with “selected” values dependent on the actual system states. Therefore, the previously proposed concurrent learning adaptive controllers required the system to be stable initially for a finite time so that the corresponding history stacks can be filled (finite excitation condition). In this work, motivated to remove the finite excitation condition, a novel desired system state based concurrent learning adaptive controller is proposed. In order to remove the system state dependencies in the controller and estimation algorithms, a filtered version of the dynamics and a novel prediction error formulation have been designed. The overall exponential stability, parameter error convergence and boundedness of the system states during closed loop operations are ensured via Lyapunov based arguments. The main advantages of the proposed method are its dependence on the desired system states and the overall stability results that paved the way in removing the need for finite excitation condition. Numerical studies performed on a two link robotic device are also presented to illustrate the feasibility of the proposed method.

Robust Combined Adaptive Passivity-Based Control for Induction Motors

The need for industrial and commercial machinery to maintain high torque while accurately following a variable angular speed is increasing. To meet this demand, induction motors (IMs) are commonly used with variable speed drives (VSDs) that employ a field-oriented control (FOC) scheme. Over the last thirty years, IMs have been replacing independent connection direct current motors due to their cost-effectiveness, reduced maintenance needs, and increased efficiency. However, IMs and VSDs exhibit nonlinear behavior, uncertainties, and disturbances. This paper proposes a robust combined adaptive passivity-based control (CAPBC) for this class of nonlinear systems that applies to angular rotor speed and stator current regulation inside an FOC scheme for IMs’ VSDs. It uses general Lyapunov-based design energy functions and adaptive laws with σ-modification to assure robustness after combining control and monitoring variables. Lyapunov’s second method and the Barbalat Lemma prove that the control and identification error tends to be zero over time. Moreover, comparative experimental results with a standard proportional–integral controller (PIC) and direct APBC show the proposed CAPBC’s effectiveness and robustness under normal and changing conditions.

Designated‐time stabilizing strategy for a class of time‐varying nonlinear systems and its application to pendulum system

AbstractIn this paper, a new scheme is proposed to stabilize a class of nonlinear systems within a designated time, mainly motivated by two unsolved problems: the singularity caused by infinity control magnitudes at the prescribed time instant and the lack of formulating/manipulating state responses after the prescribed time. Under the proposed scheme, an exquisite controller is constructed by entailing both the state scaling approach and a finite‐time stabilizing procedure. It is shown that the obtained control is well defined with bounded magnitude on the whole‐time horizon and ensures the existence of the solutions of the closed‐loop system. Superior to the existing prescribed time stabilization results, the proposed method is capable of ensuring that the states of the closed‐loop system converge to a small compact set within the designated time, stay inside it thereafter and perform finite‐time convergence eventually. Simulation examples are presented to illustrate the effectiveness of the proposed approach.