Control Of Nonlinear Systems Research Articles

Adaptive prescribed-time sliding mode control of nonlinear systems with unknown dynamics

One of the main difficulties for application of sliding mode control is the presence of chattering. It is a well known fact that the amplitude of chattering is proportional to the magnitude of discontinuous control. The problem can be alleviated by making the magnitude as small as possible while still ensuring the existence of the sliding mode. In this paper, a novel predefined-time single layer adaptive scheme based on equivalent concept with a relaxed assumption about unknown dynamics is proposed for dynamically tuning the gain associated with the control magnitude, and applying this scheme in sliding mode control algorithms enables decreasing the control action magnitude to the minimum possible value remaining the characteristic of finite-time convergence. Simulation results are shown to verify the effectiveness of the designed scheme.

Non-singular control strategies for a class of strict-feedback nonlinear time-delay systems

This paper focuses on the non-singular control for strict-feedback nonlinear time-delay systems. The boundedness of all the signals of the closed-loop system is rigorously proved by introducing a class of Lyapunov-Krasovskii functionals, including exponential functions. Besides, novel auxiliary functions with continuous derivatives are proposed to construct the control law to avoid the discontinuity of the virtual controllers. Besides, the amount of computation is reduced by applying the new auxiliary functions when the other control methods require loads of calculations for handling singular problems. In the end, numerical examples are given to validate the effectiveness of the proposed control scheme.

Accelerated Gradient Approach For Deep Neural Network-Based Adaptive Control of Unknown Nonlinear Systems.

Recent connections in the adaptive control literature to continuous-time analogs of Nesterov's accelerated gradient method have led to the development of new real-time adaptation laws based on accelerated gradient methods. However, previous results assume that the system's uncertainties are linear-in-the-parameters (LIP). To compensate for non-LIP uncertainties, our preliminary results developed a neural network (NN)-based accelerated gradient adaptive controller to achieve trajectory tracking for nonlinear systems; however, the development and analysis only considered single-hidden-layer NNs. In this article, a generalized deep NN (DNN) architecture with an arbitrary number of hidden layers is considered, and a new DNN-based accelerated gradient adaptation scheme is developed to generate estimates of all the DNN weights in real-time. A nonsmooth Lyapunov-based analysis is used to guarantee the developed accelerated gradient-based DNN adaptation design achieves global asymptotic tracking error convergence for general nonlinear control affine systems subject to unknown (non-LIP) drift dynamics and exogenous disturbances. A comprehensive set of simulation studies are conducted on a two-state nonlinear system, a robotic manipulator, and a complex 20-D nonlinear system to demonstrate the improved performance of the developed method. Our simulation studies demonstrate enhanced tracking and function approximation performance from both DNN architectures and accelerated gradient adaptation.

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

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

Self-Organizing Type-2 Fuzzy Double Loop Recurrent Neural Network for Uncertain Nonlinear System Control.

Nonlinear systems, such as robotic systems, play an increasingly important role in our modern daily life and have become more dominant in many industries; however, robotic control still faces various challenges due to diverse and unstructured work environments. This article proposes a double-loop recurrent neural network (DLRNN) with the support of a Type-2 fuzzy system and a self-organizing mechanism for improved performance in nonlinear dynamic robot control. The proposed network has a double-loop recurrent structure, which enables better dynamic mapping. In addition, the network combines a Type-2 fuzzy system with a double-loop recurrent structure to improve the ability to deal with uncertain environments. To achieve an efficient system response, a self-organizing mechanism is proposed to adaptively adjust the number of layers in a DLRNN. This work integrates the proposed network into a conventional sliding mode control (SMC) system to theoretically and empirically prove its stability. The proposed system is applied to a three-joint robot manipulator, leading to a comparative study that considers several existing control approaches. The experimental results confirm the superiority of the proposed system and its effectiveness and robustness in response to various external system disturbances.

Observer-based practical prescribed time control for fractional-order nonlinear systems with asymmetric state constraints

Observer-based practical prescribed time control for fractional-order nonlinear systems with asymmetric state constraints

Robust Control Based on Adaptative Fuzzy Control of Double-Star Permanent Synchronous Motor Supplied by PWM Inverters for Electric Propulsion of Ships

This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially, a modeling technique employing a matrix transformation method is introduced, generating decoupled and independent star windings to eliminate inductive couplings, while maintaining model consistency and torque control. The precise DSPMSM model serves as the foundation for an unknown nonlinear backstepping controller, approximated directly using an adaptive fuzzy controller. Through the Lyapunov direct method, system stability is demonstrated. All signals in the closed-loop system are ensured to be uniformly ultimately bounded (UUB). The proposed control system aims for low tracking errors, while also mitigating the impact of parametric uncertainties. The effectiveness of the adaptive fuzzy nonlinear control system is validated through tests conducted in hardware-in-the-loop (HIL) simulations, utilizing the OPAL-RT platform, OP4510.

Observer-based adaptive neutral network inverse optimal containment control for nonlinear multiagent systems with input quantization

This article focuses on the issue of addressing an adaptive neural network (NN) inverse optimal containment control for nonlinear multiagent systems (MASs), which are subject to immeasurable states and quantized input signals simultaneously. To tackle this problem, we utilize a NN to model unknown agents and design a NN observer to estimate the immeasurable states. Additionally, we decompose the hysteretic quantized input into two bounded nonlinear functions. By employing the adaptive backstepping approach and inverse optimal principle, we formulate an adaptive NN inverse optimal containment control method. The developed inverse optimal containment control scheme guarantees that the controlled system is input-to-state stabilizable (ISS). Finally, we validate the effectiveness of our proposed control scheme through simulation results.

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.

A novel normalized versatile based innovative controller for nonlinear biological systems

A novel normalized versatile based innovative controller for nonlinear biological systems

A Simple Controller Design for a Class of Uncertain Nonlinear Control Systems Guaranteed to Achieve Arbitrary Exponential Convergence Rates

This paper first proposes the concepts of high-efficiency stabilizable systems and high-efficiency controller. Then, using the time-domain analysis methodology, it is proved that a class of uncertain nonlinear systems can indeed become high-efficiency stabilizable systems under certain conditions; at the same time, we also provide its corresponding high-efficiency controller. Finally, some numerical simulation results are offered to illustrate and demonstrate the correctness of the main theorem and the design process of such a high-efficiency controller

Adaptive containment fault‐tolerant control for saturated nonlinear multiagent systems with multiple faults and periodic disturbances

AbstractThis paper addresses the problem of adaptive containment fault‐tolerant control for nonlinear multiagent systems with periodic disturbances. Different from most existing fault‐tolerant control schemes, the form of multiple faults is explicitly considered in this paper, including actuator faults and sensor faults. By combining the Fourier series expansion with neural networks, the unknown nonlinear dynamics subject to time‐dependent periodic disturbances are approximated. Then, the “complexity of explosion” issue that exists in traditional backstepping‐based results is avoided by introducing a first‐order sliding‐mode differentiator. It is proved that the developed containment control policies can ensure that all signals of the close‐loop systems are uniformly ultimately bounded, and all followers can converge to a convex area formed by multiple leaders. Simulation results verify the validity of the proposed scheme.

Artificial neural network‐based adaptive control for nonlinear dynamical systems

SummaryThis research article presents an artificial neural network (ANN)‐based indirect adaptive control method for nonlinear dynamical systems. In this article, a modified Elman recurrent neural network (MERNN) is proposed as an identifier and controller for controlling nonlinear systems. The architecture of the proposed controller is a modified form of the existing Elman recurrent neural network. The parameter training of ANN‐based controllers is obtained by using the most popular optimization algorithm which is known as the back‐propagation algorithm. A comparative study includes Elman, Diagonal, Jordan, feed‐forward neural network (FFNN), and radial basis function network (RBFN)‐based controllers to compare with the proposed MERNN controller. To determine the controller's robustness, parameter variations, and disturbance signals have been considered. The performance analysis of the proposed controller is illustrated by two simulation examples. The simulation results reveal that MERNN can not only identify the unknown dynamics of the plant but also adaptively control it compared to the others.

Quantised adaptive consensus control of heterogeneous nonlinear multi-agent systems under external disturbance

This paper is primarily devoted to the distributed consensus tracking control for heterogeneous nonlinear multi-agent systems (MASs) with a directed communication topology. Taking the considered heterogeneous nonlinear MASs own unknown nonlinear term and quantised input signals, the adaptive radial basis function neural networks (RBFNNs)-based approximator is utilised to tackle these interesting challenges. Next, considering the boundness of disturbances, the upper bound of time-varying disturbance is utilised in the controller design. Then, a distributed dynamic compensator is developed to complete coordination task, which only requires to exchange output information via the communication network. In addition, the compensator transforms the adaptive output consensus problem into asymptotic tracking problem, without needing extra stability conditions. Finally, by means of the Lyapunov stability theory, the satisfying result of the consensus error converging to zero asymptotically can be obtained. Through simulations, the effectiveness of the developed protocol is illustrated.

Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonlinear Systems With Full State Constraints

Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonlinear Systems With Full State Constraints

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

Modeling and Nonlinear Predictive Control of Solar Thermal Systems in District Heating

This study presents data-driven modeling and nonlinear model predictive control of solar thermal plants in district heating, for the purpose of operation optimization. The study considers the efficient operation of a solar thermal plant in Hillerød, Denmark. A dynamic model is estimated as a system of stochastic differential equations using grey-box modeling and real-world data. The presented nonlinear model predictive controller design is based on repeated trajectory linearization and the dynamic model. Several objective designs are considered, e.g., maximizing energy or temperature. The study provides simulations for analyzing the model fitness and controller performances. The model is shown to fit the daytime operation of the plant. The designed controllers are shown to improve efficiency, increasing the transported energy up to 28%.

Data-driven adaptive consensus control for heterogeneous nonlinear Multi-Agent Systems using online reinforcement learning

In this paper, a distributed control algorithm based on a data-driven approach is developed to solve the consensus control of heterogeneous nonlinear Multi-Agent Systems (MAS). The consensus obtained from the solution of the Hamilton–Jacobi–Bellman (HJB) equation is challenging for unknown nonlinear systems. To address this issue, improved online reinforcement learning (RL) is employed to generate an approximate solution for each agent to achieve consensus. Unlike model-based RL and traditional algorithms, this method leverages I/O data to guide the learning of policies without any prior knowledge of agent dynamics. Furthermore, the adaptability of algorithm to heterogeneous nonlinear agents is enhanced by implementing online updates to the control strategy and dynamic linearization (DL). The convergence analysis of the algorithm is provided, along with the impact of the learning rateparameters on the consensus of MAS. By comparing with other data-driven methods, simulations are conducted to verify the stability and adaptability of the proposed algorithm.

Improved Command-Filtering-Based Fixed-Time Fuzzy Adaptive Control for Uncertain Nonlinear Systems With Full State Constraints

Improved Command-Filtering-Based Fixed-Time Fuzzy Adaptive Control for Uncertain Nonlinear Systems With Full State Constraints

Fuzzy-tolerant-strategy for constrained nonlinear system via adaptive observer

This article considers the tracking control of nonlinear system with state constraints and faults. A fuzzy tolerant control approach on adaptive sliding-mode observer is proposed to accomplish good tracking performance. Firstly, for the purpose of getting the unknown state, a state estimator based on the fuzzy logic systems (FLSs) is designed. Secondly, a fuzzy observer by variable structure method is posed to approximate the faults, and the finite time convergence of observation error is proven. Furthermore, a two-layer nested adaptive law is constructed to improve the observer. Thirdly, a fuzzy backstepping tolerant controller based on super-twisting differentiator is proposed. In which, the barrier Lyapunov function is designed to counter the state constraints, and the super-twisting estimator is employed to estimate the derivative of virtual control input. Finally, two simulation results are analyzed to demonstrate the potential of the developed schemes.