Control Of Nonlinear Time-delay Systems Research Articles

On the digital event-based control for nonlinear time-delay systems with exogenous disturbances

In this paper, the stabilization problem of nonlinear time-delay systems in presence of known exogenous disturbances and by means of quantized sampled-data event-based controllers is investigated. In particular, nonlinear systems with state delays are studied. Known exogenous disturbances affecting the plant dynamics are considered in order to address, for instance, tracking control problems commonly studied by considering the stabilization problem of the corresponding tracking error system in which the chosen reference signal appears as a known exogenous signal. The stabilization in the sample-and-hold sense theory is used as a tool to provide sufficient conditions for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the quantized sampled-data implementation of continuous-time controllers, updated through a proposed event-based mechanism, guarantees the semi-global practical stability property, with arbitrarily small final target ball of the origin, of the related closed-loop system. A spline approximation methodology is used in order to: (i) cope with the problem of the possible non-availability in the buffer of suitable past values of the system variables needed for the digital implementation of the controller; (ii) consider approximations related to the hardware implementation of the signal describing the known exogenous disturbance (e.g., the chosen reference signal). The provided results include the case of non-uniform quantization of the input/output channels and the case of aperiodic sampling. Applications are presented in order to validate the results, one of which concerning a single-link flexible joint robot arm with time delays.

Design and Optimization of Precision Fertilization Control System Based on Hybrid Optimized Fractional-Order PID Algorithm

In order to mitigate time-varying, lag, and nonlinearity impacts on fertilization systems and achieve precise control of liquid conductivity, we propose a novel hybrid-optimized fractional-order proportional-integral-derivative (PID) algorithm. This algorithm utilizes a fuzzy algorithm to tune the five parameters of the fractional-order PID algorithm, employs the Smith predictor for structural optimization, and utilizes Wild Horse Optimizer, improved by genetic algorithms, to optimize fuzzy rules. We conducted MATLAB simulations, precision experiments, and stability tests on this controller. MATLAB simulation results, along with precision experiment results, indicate that compared to PID controllers, Smith predictor-optimized PID controllers, and fuzzy-tuned fractional-order PID controllers, the proposed controller has the narrowest steady-state conductivity range, the shortest settling time, and the lowest overshoot, showcasing excellent overall dynamic performance. Stability test results demonstrate that the controller maintains stable operation under different pressure conditions. Therefore, this control system from our study achieves superior control effectiveness, providing a viable approach for the control of nonlinear time-delay systems.

Dynamic Gain Reduced-Order Observer-Based Global Adaptive Neural-Network Tracking Control for Nonlinear Time-Delay Systems.

In this article, a globally adaptive neural-network tracking control strategy based on the dynamic gain observer is proposed for a class of uncertain output-feedback systems with unknown time-varying delays. A reduced-order observer with novel dynamic gain is proposed. An n th-order continuously differentiable switching function is constructed to achieve the continuous switching control of the system, thus further ensuring that all the closed-loop signals are globally uniformly ultimately bounded (GUUB). It is proved that by adjusting the designed parameters, the tracking error converges to a region which can be adjusted to be small enough. The effectiveness of the control scheme is demonstrated by two simulation examples.

Receding Horizon Actor–Critic Learning Control for Nonlinear Time-Delay Systems With Unknown Dynamics

With the development of modern mechatronics and networked systems, the controller design of time-delay systems has received notable attention. Time delays can greatly influence the stability and performance of the systems, especially for optimal control design. In this article, we propose a receding horizon actor–critic learning control approach for near-optimal control of nonlinear time-delay systems (RACL-TD) with unknown dynamics. In the proposed approach, a data-driven predictor for nonlinear time-delay systems is first learned based on the Koopman theory using precollected samples. Then, a receding horizon actor–critic architecture is designed to learn a near-optimal control policy. In RACL-TD, the terminal cost is determined by using the Lyapunov–Krasovskii approach so that the influences of the delayed states and control inputs can be well addressed. Furthermore, a relaxed terminal condition is present to reduce the computational cost. The convergence and optimality of RACL-TD in each prediction interval as well as the closed-loop property of the system are discussed and analyzed. Simulation results on a two-stage time-delayed chemical reactor illustrate that RACL-TD can achieve better control performance than nonlinear model predictive control (MPC) and infinite-horizon adaptive dynamic programming. Moreover, RACL-TD can have less computational cost than nonlinear MPC.

Machine learning-based predictive control of nonlinear time-delay systems: Closed-loop stability and input delay compensation

The purpose of this work is to study machine-learning-based model predictive control of nonlinear systems with time-delays. The proposed approach involves initially building a machine learning model (i.e., Long Short Term Memory (LSTM)) to capture the process dynamics in the absence of time delays. Then, an LSTM-based model predictive controller (MPC) is designed to stabilize the nonlinear system without time delays. Closed-loop stability results are then presented, establishing robustness of this LSTM-based MPC towards small time-delays in the states. To handle input delays, we design an LSTM-based MPC with an LSTM-based predictor that compensates for the effect of input delays. The predictor is used to predict future states using the process measurement, and then the predicted states are used to initialize the LSTM-based MPC. Stabilization of the time-delay system with both state and input delays around the steady state is achieved through the featured design. The approach is applied to a chemical process example, and its performance and robustness properties are evaluated via simulations.

Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions

<abstract><p>The article studies $ H_\infty $ control as well as adaptive robust control issues on the predefined time of nonlinear time-delay systems with different power Hamiltonian functions. First, for such Hamiltonian systems with external disturbance and delay phenomenon, we construct the appropriate Lyapunov function and Hamiltonian function of different powers. Then, a predefined-time $ H_\infty $ control approach is presented to stabilize the systems within a predefined time. Furthermore, when considering nonlinear Hamiltonian system with unidentified disturbance, parameter uncertainty and delay, we devise a predefined-time adaptive robust strategy to ensure that the systems reach equilibrium within one predefined time and have better resistance to disturbance and uncertainty. Finally, the validity of the results is verified with a river pollution control system example.</p></abstract>

Asymptotic Tracking Control of Nonlinear Time-Delay Systems With Mismatched Disturbances

This brief considers the asymptotic tracking control problem of nonlinear time-delay system in the presence of mismatched disturbances. By using dynamic gain based design method, a delay-independent dynamic tracking controller is constructed. Besides, a smooth function is introduced into the virtual controller to compensate the mismatched disturbances. By choosing appropriate Lyapunov-Krasovskii functionals, it is shown that the closed-loop system signals are bounded, and the system output can asymptotically track the desired signal. Finally, a simulation example is conducted to show the effectiveness of the proposed control scheme.

Improved Design of Nonlinear Control Systems with Time Delay

It is well known that time delay in nonlinear control systems may lead to the deterioration or even destabilization of the closed-loop systems. Therefore, specific analysis techniques and design methods are needed to be developed for nonlinear control systems in the presence of time delay. This chapter aims to give a broad overview of the stability and control of nonlinear time-delay systems. Firstly, we present some motivations and a comprehensive survey for the study of time-delay systems. Then, a brief overview of some control approaches is provided, specifically, the Lyapunov-Krasoviskii functional method for high-order polynomial uncertainties nonlinear time-delay systems, and nonlinear time-delay systems with nonlinear input, the Lyapunov-Razumikhin method for triangular structure nonlinear time-delay systems, dynamic gain control for full state time-delay systems. Finally, an application in chemical reactor systems is provided and some related open problems are discussed.

Nussbaum-Type Neural Network-Based Control of Neuromuscular Electrical Stimulation With Input Saturation and Muscle Fatigue

Abstract Neuromuscular electrical stimulation (NMES) is a promising technique to actuate the human musculoskeletal system in the presence of neurological impairments. The closed-loop control of NMES systems is nontrivial due to their inherent uncertain nonlinearity. In this paper, we propose a Nussbaum-type neural network (NN)-based controller for the lower leg limb NMES systems. The control accounts for model uncertainties and external disturbances in the system and, for the first time, provides a solution with rigorous stability analysis to the adaptive NMES tracking problem with input saturation and muscle fatigue. The proposed controller guarantees a uniformly ultimately bounded (UUB) tracking for the knee-joint angular position. To evaluate the control performance, a simulation study is taken, where the performance comparison with a NN controller inspired by Ge et al. (2004, “Adaptive Neural Control of Nonlinear Time-Delay Systems With Unknown Virtual Control Coefficients,” IEEE Trans. Syst., Man, Cybern.-Part B, 34(1), pp. 499–516) is given. The simulation results show a good tracking performance of the proposed controller regardless of the time-varying muscle fatigue and moderate input saturation. The adaptation mechanism of the Nussbaum-type gain and the controller's robustness to the muscle fatigue and input saturation are discussed in details along with the simulations.

DSC-based RBF neural network control for nonlinear time-delay systems with time-varying full state constraints

The presented control scheme in this paper aims at stabilizing uncertain time-delayed systems requiring all states to change within the preset time-varying constraints. The controller design framework is based on the backstepping method, drastically simplified by the dynamic surface control technique. Meanwhile, the radius basis function neural networks are utilized to deal with the unknown items. To prevent all state variables from violating time-varying predefined regions, we employ the time-varying barrier Lyapunov functions during the backstepping procedure. Moreover, appropriate Lyapunov–Krasovskii functionals are used to cancel the influence of the time-delay terms on the system’s stability. Under the presented control laws and Lyapunov analysis, it is proven that constraints on all state variables are not breached, good tracking performance of desired output is achieved, and all signals in the closed-loop systems are bounded. The effectiveness of our control scheme is confirmed by a simulation example.

Adaptive control of nonlinear time-delay systems in the presence of output constraints and actuators faults

This paper aims to design a controller to compensate the faults for a class of time-delay nonlinear systems. This controller is based on the back-stepping design approach. A barrier Lyapunov function has been employed to ensure the satisfaction of output constraints. This controller is proposed for nonlinear systems with parameter uncertainty, time-delay and uncertain faults in actuators while no bounds for parameters, delays and actuators faults are supposed. The boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighbourhood of the origin without violation of the constraint. In the end, the simulation results show the effectiveness of the proposed control method.

Self-triggered impulsive control of nonlinear time delay systems: Application to chemotherapeutic dose-regimen design

This paper proposes a self-triggered impulsive control for nonlinear time-delay systems, where the time instant of the next impulsive input is calculated based on the last measurement and the values of the systems’ parameters. Contrary to event-triggered scheme where the actuation is discrete but a continuous monitoring of the system’s states is necessary, in the self-triggered approach, both sampling and actuation are performed at distinct moments of time. Utilizing Lyapunov–Razumikhin method and by upper-bounding the system’s trajectory, the global asymptotic stability of the system’s equilibrium is verified when the rate of change in the Lyapunov function is exponential. In the general case, the global ultimate boundedness of the system’s trajectory is shown where the ultimate bound can be set arbitrarily small. As an application, for the first time, the problem of dose regimen design is formulated in the sampled data framework. Then, based on the obtained theoretical results, the appropriate regimen is suggested. In particular, time-triggered and self-triggered therapy protocols for docetaxel, a phase specific chemotherapeutic drug which is administered intravenously, are proposed. Clinical constraints such as maximum tolerated dose, discontinuous drug administration, and intermittent measurements are met in the proposed therapy protocols. According to in-silico results, both proposed self-triggered and time-triggered dose regimens outperform the traditional weekly fixed dose administration. Finally, the robustness of the proposed schemes to parameter uncertainties is evaluated through an extensive set of simulations.

Adaptive Fuzzy Event-Triggered Command-Filtered Control for Nonlinear Time-Delay Systems

This article focuses on an adaptive fuzzy dynamic event-triggered tracking control for nonlinear time-delay systems with unmodeled dynamics via a command filter method. Fuzzy logic systems are utilized to address the unknown nonlinear functions. The upper bound of the approximation error is allowed to be unknown and can be compensated by skillfully introducing a hyperbolic tangent function to the design of the adaptive laws. Meanwhile, without requiring any assumptions, time delays can be handled by appropriately incorporating the delayed nonlinear functions into the Lyapunov–Krasovskii functional. Then, a dynamic event-triggered control mechanism is designed to dynamically adjust the threshold parameter. Finally, a new adaptive controller is constructed such that all states of the closed-loop system are bounded. The system output is demonstrated to follow the desired signal. Two examples are given to illustrate the validity of the presented method.

Stability and control of fuzzy time delay systems with unmatched preconditions

The stability and control of nonlinear time-delay systems of Takagi-Sugeno (T-S) fuzzy model are studied in this paper. The integral inequality of a free weight matrix is chosen to give a less conservative delay-dependent stability criterion in the form of linear matrix inequalities (LMIs). The premise mismatch strategy is applied, it is combined with Finsler lemma, a more flexible design method of fuzzy state feedback controller is proposed. This method does not require the controller and system to share the common premise membership function and the number of rules. The controller design strategy proposed in this paper can effectively solve the control problem of fuzzy systems when the number of state variables is not equal to the number of input variables (r≠c), or mi⁢(x⁢(t))≠hi⁢(x⁢(t)),i=1,2,…,r. Finally, two simulation examples are given to prove the advancement and effectiveness of the proposed theory.

Observer-based adaptive neural control of nonlinear time-delay systems with unknown output function and unknown control directions

This paper is concerned with the problem of output feedback adaptive tracking control for a class of uncertain nonlinear time-delay systems (NTDS) with both uncertain output function and unknown control directions. By introducing a linear state transformation, the original system is transformed into a new system for which output feedback control design becomes feasible. Without the precise information on output function, an input-driven high-gain state observer is presented to estimate the unavailable states of the new system. Moreover, some radial basis function neural networks (RBFNNs) are employed to approximate the lumped unknown nonlinear functions during the procedure of control design. Then, by combining the Lyapunov–Krasovskii functional method, the Nussbaum gain function approach and the backstepping technique, a novel adaptive output feedback control scheme including only one parameter to be updated is developed for such systems. As a result, all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) while the tracking error can remain in a small neighbourhood of zero. Finally, two simulation examples are given to validate the effectiveness and applicability of the proposed design method.

Accessibility and System Reduction of Nonlinear Time-Delay Control Systems

This article addresses the problem of checking the accessibility property for nonlinear single-input-single-output retarded time-delay systems with constant commensurable delays, described by higher order input-output functional differential equations. Necessary and sufficient conditions are found to check the accessibility property, and sufficient conditions are found to decompose the system equations into accessible and non-accessible subsystems. The conditions are presented in terms of autonomous elements, i.e., functions that cannot be influenced by system input. The results are generalizations from the delay-free case. However, the proofs do not transfer to the time-delay case easily, since algebraic structures with different properties are used here.

Removing Feasibility Conditions on Adaptive Neural Tracking Control of Nonlinear Time-Delay Systems With Time-Varying Powers, Input, and Full-State Constraints.

This article investigates the tracking control for input and full-state-constrained nonlinear time-delay systems with unknown time-varying powers, whose nonlinearities do not impose any growth assumption. By utilizing the auxiliary control signal and nonlinear state-dependent transformation (NSDT) to counteract the effect of input saturation and cope with full-state constraints, respectively, and then introducing lower and higher powers and Lyapunov-Krasovskii (L-K) functionals in control design together with the adaptive neural-networks (NNs) method, an adaptive neural tracking control design is provided without feasibility conditions. It is proved that NNs approximation is valid, all the closed-loop signals are semiglobally bounded, and input and full-state constraints are not violated.

Finite-Dimensional Periodic Event-Triggered Control of Nonlinear Time-Delay Systems With an Application to the Artificial Pancreas

This letter addresses the periodic event-triggered stabilization in the sample-and-hold sense of nonlinear time-delay systems by means of a finite-dimensional state feedback law. Differently from most related literature, no continuity assumptions are required on the state feedback available in continuous time, which can hence be designed for instance by universal constructions yielding possible discontinuities, provided that such a feedback depends on a finite number of commensurate time delays. An application to the problem of glucose regulation is then presented, showing the effectiveness of the approach taken.

Observer-based finite-time robust control of nonlinear time-delay systems via Hamiltonian function method

ABSTRACT This paper investigates the observer-based finite-time robust control problem of a general class of nonlinear time-delay systems via Hamiltonian function method, and proposes some new finite-time robust stabilisation results. First, by applying Hamiltonian realisation method, the paper develops an equivalent Hamiltonian form of original system. Then, based on the equivalent Hamiltonian form, we design the corresponding observer system, study the observer-based finite-time robust stabilisation problem and present some new observer-based robust stabilisation results by constructing some suitable Lyapunov functionals. Finally, the study of an illustrative example shows that the results obtained of the paper work well in the observer-based finite-time robust stabilisation the system.

Adaptive tracking control for nonlinear time-delay systems with time-varying full state constraints

This paper presents an adaptive tracking control approach for a class of uncertain nonlinear strict-feedback systems subject to time-varying full state constraints and time-delays. To stabilize such systems, an adaptive tracking controller is structured by combining the neural networks and the backstepping technique. To guarantee all states do not violate the time-varying constraint sets, the appropriate time-varying Barrier Lyapunov functions are employed at each stage of the backstepping procedure. By using the Lyapunov-Krasovskii functionals, the effect of time delay is eliminated. It is proved that the output follows the desired signal well without violating any constraints, and all the signals in the closed-loop system are semiglobal uniformly ultimately bounded by using the Lyapunov analysis. Finally, a comparison study simulation is provided to illustrate the effectiveness of the proposed control strategy.