Control Of Nonlinear Systems Research Articles

Adaptive Control of Constrained Nonlinear Systems With Intermittent Faults: A Fixed‐Time Fault‐Tolerant Framework Based on Projection Operator

ABSTRACTThis article investigates the problem of adaptive fixed‐time fault‐tolerant control for nonlinear systems with time‐varying intermittent faults and asymmetric output constraints. For this purpose, a novel adaptive law based on the projection operator technique is developed to estimate time‐varying intermittent faults, which eliminates the problem that the estimated value increases continuously with the accumulation of fault times. Considering that the fault estimation time needs to be less than the minimum time interval of intermittent faults, the fixed‐time design methodology is introduced to ensure that the relationship between the above two can be quantitatively analyzed. Then, a novel adaptive fixed‐time fault‐tolerant control strategy is put forward for the closed‐loop system, in which a universal barrier function is adopted to remain the system output in the time‐varying asymmetric constraint condition invariably. The theoretical analysis indicates that the developed strategy can guarantee the boundedness of all signals in the closed‐loop system in a fixed‐time. Finally, two examples, one of which involves the rotary steerable drilling tool systems are provided to demonstrate the feasibility and validity of the put forward scheme.

Fixed-time neural network composite learning control for uncertain nonlinear systems

A novel fixed-time neural network composite learning control (FNNCLC) scheme is proposed for nonlinear strict-feedback systems with unknown dynamics. The neural network (NN) is employed to handle system uncertainty. By utilizing tracking errors and prediction errors to update NN weights, accurate network learning is achieved under a weaker excitation condition termed interval excitation (IE) condition, instead of the typically required strict persistent excitation (PE) condition. Moreover, for the first time, a high order term and first order term of the prediction error are introduced to design composite learning adaptive laws, achieving the convergence of NN weights within fixed time. Additionally, a smooth fixed-time (FXT) dynamic surface control scheme is constructed without potential singularity problems, which mitigates complexity explosion by avoiding fractional power terms and complex switching strategies when formulating the control law. The stability of the proposed control scheme is analyzed by using Lyapunov technique. Simulation results demonstrate the effectiveness of the proposed controller.

Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.

Event‐Triggered Impulsive Control of Nonlinear Stochastic Systems With Exogenous Disturbances

ABSTRACTIn this work, the stability problem of nonlinear stochastic systems is investigated under exogenous disturbances through event‐triggered impulsive control (ETIC). The ETIC strategy proposed in this paper incorporates three levels of events, taking into account four indicators: threshold, control‐free index, inspection interval, and waiting time for stochastic systems, which is more practically significant and can effectively eliminate the Zeno behavior. By utilizing Lyapunov stability theory, stochastic analysis techniques, and some fundamental inequalities, sufficient conditions for the moment input‐to‐state stability (‐ISS) and exponentially ‐ISS of the considered system can be achieved through the implementation of the designed ETIC. Then, the theoretical results are employed in actual nonlinear stochastic systems, leading to the establishment of LMI‐based criteria for exponential ‐ISS. Ultimately, the feasibility of ETIC strategy is confirmed through two instances.

Data-driven cooperative consensus control of nonlinear multiagent systems based on adaptive event-triggered strategies

Data-driven cooperative consensus control of nonlinear multiagent systems based on adaptive event-triggered strategies

Infinite-time optimal feedback control of a 3-phase asynchronous motor exploiting a nonlinear finite element model

This paper presents modelling of a squirrel-cage induction motor and an optimal control method based on suboptimal control for nonlinear systems to minimise consumed energy and power losses in an induction motor drive. A coupled motor model with optimal control as a closed-loop integrated system is proposed. For modelling of the squirrel-cage asynchronous machine, a field-circuit-mechanical finite-element (FE) model is employed, in which mechanical motion is realised by a moving-mesh method and fixed mesh approach. For the control problem purpose, a surrogate induction motor model, described in a stationary rotor reference d–q frame, is applied. The optimal control is realised by a nonlinear feedback compensator method based on the state-dependent Riccati equation (SDRE) with an infinite time horizon with the surrogate model state-dependent parametrisation (SDP). To perform the control strategy, a SDRE technique with Moore–Penrose pseudoinverse is adopted. To improve the accuracy of the optimisation procedure, a finite element model was used to calculate the motor performance.

Control of nonlinear quantum systems: From nonlinear Rabi oscillations to robust two-stage optimal inverse engineering

Control of nonlinear quantum systems: From nonlinear Rabi oscillations to robust two-stage optimal inverse engineering

Digital-Twin Predictive Control of Nonlinear Systems With Time Delays, Unknown Dynamics, and Communication Delays.

With the advancement of computing technology and big data technology, digital twins have gradually been applied in various fields, such as manufacturing, energy, and healthcare. This article studies the predictive control of nonlinear dynamic systems using digital twins. Based on a digital-twin control system framework, predictive control is discussed for three different nonlinear systems with time delays: 1) known nonlinear systems; 2) unknown nonlinear systems; and 3) unknown nonlinear cyber-physical systems. Both a digital-twin predictive control strategy and a digital-twin control predictor are proposed to compensate for time delays and communication delays actively. With the strategy and predictor, the digital-twin controller of a time-delay nonlinear system can be designed to achieve the desired performance based on the nonlinear system without time delays, which vastly simplifies the controller design procedure. A digital model is constructed using data to deal with unknown nonlinear dynamics. The three different closed-loop digital-twin predictive control systems are analyzed to derive a unified stability criterion. The simulation results show how the proposed digital-twin predictive control method performs well for nonlinear systems with time delays, unknown dynamics, and/or communication delays.

Relaxed event-triggered tracking control of positive T-S fuzzy systems via a membership function method.

In this paper, the sampled-data-based event-triggered tracking control for the positive nonlinear system is discussed. The event-triggered mechanism naturally causes a mismatch between the membership functions of the system model and the fuzzy controller. Meanwhile, the positive constraint and tracking behavior increase the complexity of system analysis and bring conservative analysis results. How to achieve positive and event-triggered tracking control while ensuring good tracking performance has become challenging. To address the challenge, firstly, the positive T-S fuzzy model is established to characterize the positive tracking nonlinearsystem. Subsequently, a novel Lyapunov-Krasovskii functional is constructed, which takes into account the tracking errors and transmission delays induced by the event-triggered mechanism. Furthermore, the piecewise linear membership functions (PLMFs) are used to relax the conservativeness of analysis results. Then, to ensure the system positivity and obtain the approximation errors of PLMFs, an outer constraint is proposed to handle the mismatched membership functions caused by the sampled-data-based event-triggered mechanism. Finally, the proposed approaches are demonstrated to achieve good tracking performance while reducing communication resources through a numerical example and a two-linked tank practical example.

Mixed Fuzzy Intermittent Control for Nonlinear ODE-PDE Coupled Systems

Mixed Fuzzy Intermittent Control for Nonlinear ODE-PDE Coupled Systems

Finite-Time Neuroadaptive Cooperative Control for Nonlinear Multiagent Systems Under Nonaffine Faults and Partially Unknown Control Directions.

This article investigates the cooperative control of complex nonlinear multiagent systems (CNMASs), in which the agents suffer from nonaffine faults and the control directions of some agents are unknown. A finite-time adaptive control scheme is presented for the CNMASs. A finite-time command filter is designed to solve the "explosion of complexity" issues, overcome chattering issues, and relax the limitations of the filter input. The impact of filter errors is alleviated by an improved error compensation mechanism. Based on piecewise Nussbaum functions, the partially unknown control direction is addressed. The proposed finite-time cooperative control strategy on the basis of local information can ensure that all signals in the closed-loop system are finite-time bounded, and the absolute value of the cooperative control errors can converge to a given upper bound in a finite time. The rapidity and robustness of the proposed method are verified by two comparative simulation examples. A real multirobot cooperative control experiment is used to verify the effectiveness of the presented method.

Adaptive practical prescribed-time control for uncertain nonlinear systems with time-varying parameters

In this paper, adaptive practical prescribed-time (PPT) control is proposed for a class of uncertain nonlinear systems with time-varying parameters and unmodeled dynamics. By constructing a novel time-varying scaling function and utilizing nonlinear mapping, the PPT control is successfully resolved. The dynamical uncertainties resulting from unmodeled dynamics are estimated by employing an auxiliary available signal, and the unknown continuous terms are handled by the aid of radial basis function neural networks (RBFNNs). A novel adaptive control method is developed by introducing the compensating signals and dynamic surface control as well as practical prescribed-time control. All the signals involved are proved to be semi-globally uniformly ultimately bounded, and the tracking error could enter the pre-specified convergence region within a pre-specified time. The robotic manipulator system is used to demonstrate the effectiveness of the proposed control approach.

Decentralized event-trigger-based predefined-time adaptive control of large-scale nonlinear systems

Decentralized event-trigger-based predefined-time adaptive control of large-scale nonlinear systems

Adaptive Neural Control of Constrained MIMO Nonlinear Systems With Asymmetric Input Saturation and Dead Zone.

In this article, the adaptive neural control is studied for multiple-input-multiple-output (MIMO) nonlinear systems with asymmetric input saturation, dead zone, and full state-function constraints. A suitable transformation is introduced to overcome the dead zone and saturation nonlinearity, and radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. What is more, we apply the Nussbaum function and time-varying barrier Lyapunov function (BLF) to deal with the unknown control gains and full state-function constraints, respectively. Based on the backstepping method, a universal adaptive neural control scheme is presented such that not only the state-function constraints of the closed-loop system cannot be violated and all signals of the closed-loop systems are bounded, but also the tracking error converges to a small neighborhood containing the origin. The effectiveness of the proposed control scheme is verified by an application to the mass-spring-damper system and a numerical example.

Consensus Control of Nonlinear Fractional-Order Multiagent Systems With Input Saturation: A T–S Fuzzy Method

Consensus Control of Nonlinear Fractional-Order Multiagent Systems With Input Saturation: A T–S Fuzzy Method

Fault-tolerant control of nonlinear cluster system for fixed-wing UAV piston engine faults based on hierarchical architecture

Due to the information exchange between fixed-wing UAV clusters, the fault and disturbance information generated when the actuator, including the engine, is transmitted from the faulty UAVs to the healthy UAVs. Given this situation, this paper proposes a cluster fault-tolerant control strategy based on hierarchical architecture. Firstly, this paper analyzes the influence of vibration caused by engine failure on fixed-wing UAVs and illustrates the necessity of considering this factor with simulation experiments. Secondly, this paper designs a hierarchical architecture, which divides the distributed control of the fixed-wing cluster system into consistency control of the upper layer and fault-tolerant tracking control of the lower layer, so that the fault information will only exist in the faulty UAVs, ensuring that the healthy UAVs will not be affected, thus avoiding the occurrence of fault propagation and improving the overall fault tolerance of the cluster. Finally, by analyzing the stability of the Lyapunov function, it is shown that this method can still follow the leader in systems with the followers' failures, and the effectiveness of this method is verified by comparing simulation results.

Global Asymptotic Stabilization Control for Uncertain Nonlinear Systems With Input Quantization and Unknown Output Function

Global Asymptotic Stabilization Control for Uncertain Nonlinear Systems With Input Quantization and Unknown Output Function

Approximate controllability of general impulsive stochastic systems with effects in infinite dimension

In this research, we investigated the feasibility of approximate control for nonlinear impulsive stochastic differential systems defined over infinite-dimensional domains. Our approach is based on the assumption that the associated linear systems are controllable. To this end, we established sufficient conditions to ensure the existence and uniqueness of approximate control solutions for each type of control considered. The theoretical framework is grounded in the application of Banach Fixed Point Theory (BFPT), which serves as a fundamental tool for deriving our results. Furthermore, illustrative examples are provided, incorporating digital media simulations to demonstrate the practical applicability and effectiveness of the proposed method.

Adaptive Intelligent Control for Nonlinear Stochastic Cyber-Physical Systems With Unknown Deception Attacks: Switching Event-Triggered Scheme

Adaptive Intelligent Control for Nonlinear Stochastic Cyber-Physical Systems With Unknown Deception Attacks: Switching Event-Triggered Scheme

Improved Dynamic Surface Control for Uncertain Nonlinear Systems With Application to Fighter Jet System

Improved Dynamic Surface Control for Uncertain Nonlinear Systems With Application to Fighter Jet System