Control Of Uncertain Nonlinear Systems Research Articles

Temperature Control of Nonlinear Uncertain Systems via Model-Free Cascaded Controller: Application to an Infrared Emissometer

Temperature Control of Nonlinear Uncertain Systems via Model-Free Cascaded Controller: Application to an Infrared Emissometer

Practical prescribed-time fuzzy tracking control for uncertain nonlinear systems with time-varying actuators faults

The paper investigates the practical prescribed-time fuzzy tracking control problem for a category of nonlinear system subject to time-varying actuator faults. The presence of unknown nonlinear dynamics and actuator faults makes achieving tracking control within a prescribed-time challenging. To tackle this issue, we propose a novel practical prescribed-time fuzzy tracking control strategy, which is independent of the initial state of the system and does not rely on precise modeling of the system and actuators. We apply the approximation capabilities of fuzzy logic systems to handle the unknown nonlinear functions and unidentified actuator faults in the system. The piecewise controller and adaptive law constructed based on piecewise prescribed time-varying function and backstepping technique method establish the theoretical framework of practical prescribed-time tracking control, and extend the range of prescribed-time tracking control to infinity. Regardless of the initial conditions, the proposed control strategy can guarantee that all signals remain uniformly bounded within the practical prescribed time in the presence of unknown nonlinear item and time-varying actuator faults. Simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Feedback linearization control for uncertain nonlinear systems via generative adversarial networks

This article presents a novel approach to leverage generative adversarial networks(GANs) techniques to learn a feedback linearization controller(FLC) for a class of uncertain nonlinear systems. By estimating uncertainty through the adversarial process, where ground truth samples are exclusively obtained from a predefined integral model, the feedback linearization controller, learned through a minimax two-player optimization framework, enhances the reference tracking performance of the input-output uncertain nonlinear system. Furthermore, we provide theoretical guarantee of convergence and stability, demonstrating the safe recovery of robust FLC. We also address the common challenge of mode collapse in GANs training through the strict convexity of our synthesized generator structure and an enhanced adversarial loss. Comprehensive simulations and practical experiments are conducted to underscore the superiority and efficacy of our proposed approach.

Tracking control of uncertain nonlinear systems via adaptive Gaussian process prediction and real-time optimisation

Control of nonlinear systems in the presence of model mismatch and system constraints is quite challenging. To address the issue, this work proposes an adaptive Gaussian process-based real-time optimisation (AGP-RTO) control framework. Specifically, the control law consists of two components, a feedforward tracking control law and an uncertainty compensation control law. Because GP has high flexibility to capture complex unknown functions by using very few parameters and it inherently handles measurement noise, this work utilises the GP as an alternative to estimate the mismatch between the real plant and the approximated model. During every RTO execution, the GPs adaptively update the predictions of the model mismatch, then the predictions are embedded into a nonlinear optimisation problem for the correction of the model cost and constraint functions, which yields the uncertainty compensation control law. The proposed AGP-RTO framework ensures that the Karush-Kuhn-Tucker (KKT) conditions determined by the model match those of the plant upon convergence. Compared to many direct adaptive control methods, AGP-RTO does not rely on a high gain for fast adaptation and hence it improves the robustness of the closed-loop system. Compared to the modifier adaptation (MA) method, AGP-RTO avoids the plant-gradient estimation by using the finite difference scheme, besides it trains the GP models offline, which speeds up online evaluation and improves the applicability and efficacy of real-time control. Comparisons are carried out to illustrate the superiority of the AGP-RTO.

Neural Adaptive H∞ Sliding-Mode Control for Uncertain Nonlinear Systems with Disturbances Using Adaptive Dynamic Programming.

This paper focuses on a neural adaptive H∞ sliding-mode control scheme for a class of uncertain nonlinear systems subject to external disturbances by the aid of adaptive dynamic programming (ADP). First, by combining the neural network (NN) approximation method with a nonlinear disturbance observer, an enhanced observer framework is developed for estimating the system uncertainties and observing the external disturbances simultaneously. Then, based on the reliable estimations provided by the enhanced observer, an adaptive sliding-mode controller is meticulously designed, which can effectively counteract the effects of the system uncertainties and the separated matched disturbances, even in the absence of prior knowledge regarding their upper bounds. While the remaining unmatched disturbances are attenuated by means of H∞ control performance on the sliding surface. Moreover, a single critic network-based ADP algorithm is employed to learn the cost function related to the Hamilton-Jacobi-Isaacs equation, and thus, the H∞ optimal control is obtained. An updated law for the critic NN is proposed not only to make the Nash equilibrium achieved, but also to stabilize the sliding-mode dynamics without the need for an initial stabilizing control. In addition, we analyze the uniform ultimate boundedness stability of the resultant closed-loop system via Lyapunov's method. Finally, the effectiveness of the proposed scheme is verified through simulations of a single-link robot arm and a power system.

Integral sliding mode‐based event‐triggered nearly optimal tracking control for uncertain nonlinear systems

SummaryIn this paper, an event‐triggered nearly optimal tracking control method is investigated for a class of uncertain nonlinear systems by integrating adaptive dynamic programming (ADP) and integral sliding mode (ISM) control techniques. An ISM‐based discontinuous control law with a neural network (NN) adaptive term is designed to eliminate the influence of the uncertainties and obtain the sliding mode dynamics which is equivalent to the tracking error dynamics without uncertainties, and relax the known upper‐bounded condition of uncertainties. In order to guarantee the stability of tracking error system and the considerable optimality, under the ADP technique, a critic NN is applied to approximate the optimal value function for solving the event‐triggered Hamilton‐Jacobi‐Bellman equation and the event‐triggered nearly optimal feedback control is obtained. The feedback control law is updated and transmitted to plant only when events occur, thus both the communication and the computational resources can be saved. Furthermore, the stability of tracking error is proven thanks to Lyapunov's direct method. Finally, we provide two simulation examples to validate the developed control scheme.

Fuzzy Fixed-Time Fault-Tolerant Control of Uncertain Nonlinear Systems with Non-affine Faults and Its Application in Manipulator Systems

Fuzzy Fixed-Time Fault-Tolerant Control of Uncertain Nonlinear Systems with Non-affine Faults and Its Application in Manipulator Systems

Command-Filter-Approximator-Based Adaptive Control for Uncertain Nonlinear Systems and Its Application in PMSMs

Command-Filter-Approximator-Based Adaptive Control for Uncertain Nonlinear Systems and Its Application in PMSMs

Finite-Time Stability Control of Uncertain Nonlinear Systems With Self-Limiting Control Terms.

In this brief, we define a self-limiting control term, which has the function of guaranteeing the boundedness of variables. Then, we apply it to a finite-time stability control problem. For nonstrict feedback nonlinear systems, a finite-time adaptive control scheme, which contains a piecewise differentiable function, is proposed. This scheme can eliminate the singularity of derivative of a fractional exponential function. By adding a self-limiting term to the controller and the virtual control law of each subsystem, the boundedness of the overall system state is guaranteed. Then the unknown continuous functions are estimated by neural networks (NNs). The output of the closed-loop system tracks the desired trajectory, and the tracking error converges to a small neighborhood of the equilibrium point in finite time. The theoretical results are illustrated by a simulation example.

Event-Triggered Control for Nonlinear Uncertain Systems via a Prescribed-Time Approach

The event-triggered control problem is investigated for nonlinear uncertain systems via a prescribed-time approach. Different from the existing event-triggered control methods that can only achieve bounded or finite-time stability, this paper focuses on the prescribed-time stability under the event-based design method. First, a novel prescribed-time stability criterion is presented, which provides explicit theoretical supports and systematic guidelines for addressing the studied problem. Then, we put forward a new method for co-designing the controller and event-triggering mechanism by utilizing the idea of backstepping design. Based on the proposed stability criterion, it is proved that the controller constructed with the new method can regulate the system states to zero in the prescribed-time interval while avoiding the Zeno phenomenon, thus improving the previous prescribed-time stabilization results that are all based on the real-time control signals. Finally, a simulation example is given to show the effectiveness of proposed control strategy.

Event-triggered low-computation adaptive output-feedback fuzzy tracking control of uncertain nonlinear systems

A fuzzy adaptive tracking control scheme is studied for a family of uncertain systems with immeasurable system states. The controller takes up few computation and transmission resources to achieve prescribed boundaries of the dynamic and steady-state performance indicators. Compared with the existing schemes, the low computational complexity is reflected in the following two points: (1) a fuzzy state observer is introduced, where only the estimation of states are incorporated into the input space of fuzzy logic systems (FLSs). (2) The problem of complexity explosion can be avoided without utilizing additional command filters or auxiliary dynamic surface control techniques. In addition, using the event-triggered control scheme, the data in the transmission is significantly reduced. Finally, the effectiveness of the scheme is fully verified by simulation.

Adaptive estimation and control for uncertain nonlinear systems and full actuation control

Adaptive estimation and control for uncertain nonlinear systems and full actuation control

Adaptive Finite-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Full-State Constraints

This paper studies the adaptive finite-time fuzzy control issue associated with uncertain nonlinear systems that exhibit asymmetric constraints on the full state. A distinct function, constrained by nonlinear states, is designed to mitigate the excessive breach of these full-state boundaries. Unlike the standard barrier Lyapunov function (BLF) method, this approach solves symmetric and asymmetric full-state constraints without modifying the controller structure, and it does not require any additional assumptions about virtual control to be met. Simultaneously employing approximating functions using fuzzy logic systems and incorporating dynamic surface control technology integrated with a first-order filter, the unknown nonlinear functions emanating from the suggested controller strategy are estimated. Additionally, this approach addresses the prevalent problem of complexity explosion observed in conventional backstepping techniques. An adaptive finite-time fuzzy tracking control strategy is introduced, ensuring that all signals and tracking errors of the controlled system remain bounded in finite time. Finally, two simulation examples are given to illustrate the effectiveness of the proposed control scheme, confirming that all states remain within the predefined regions.

Neuroadaptive tracking control of uncertain nonlinear systems with spatiotemporal constraints

This study investigates the neuroadaptive tracking control problem for a class of strict-feedback nonlinear systems with spatiotemporal constraints. An adaptive neural network-based control system is developed to alleviate the effects of modeling uncertainties and external disturbances. In particular, the proposed method ensures that the system tracking error has a predefined performance boundary (spatial constraint). Moreover, using a novel time-scale transformation method, uncertain nonlinear systems can achieve a prescribed finite-time convergence to a time-varying scaling function in the pointing position (temporal constraint). Finally, the efficiency of the proposed method is verified with two simulation examples.

Adaptive Quantized Control for Uncertain Nonlinear Systems with Asymmetric Fuzzy Dead Zones

Adaptive Quantized Control for Uncertain Nonlinear Systems with Asymmetric Fuzzy Dead Zones

Adaptive output-feedback control for uncertain nonlinear systems with function control coefficients

This article addresses the global adaptive output-feedback state regulation problem for a class of uncertain nonlinear systems with generalized control coefficients. Remarkably, the system under investigation simultaneously possesses function control coefficients, input matching uncertainty, and unknown growth rate, which is essentially different from the closely related existing literature. Such nonlinearities from function control coefficients and uncertainties from unknown growth rate bring great technical difficulties to controller design. A novel dynamic gain is introduced to deal with the extra system nonlinearities from function control coefficients and unknowns from the growth rate. In addition, the extended state observer is developed to reconstruct the unmeasured states of the system. By integrating the dynamic gain and extended state observer, an adaptive output-feedback controller is designed, which ensures that the states of the system globally converge to zero, and the estimation of the input matching uncertainty converges to its actual value. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

Switching-based adaptive fault-tolerant control for uncertain nonlinear systems against actuator and sensor faults

In previous research on fault switching of redundant actuators using monitoring modules, the interference of sensor faults on monitoring results has not received enough attention. In this paper, a new fault-tolerant control (FTC) method combining adaptive compensation and active switching is proposed for a class of uncertain nonlinear systems with backup actuators against actuator and sensor faults. While using command filtered backstepping to reduce computational burden, a direct adaptive compensation scheme is designed to ensure that sensor faults within tolerable bounds do not trigger actuator switching. Based on this, a new lumped monitoring function (MF) containing prescribed performances and tolerable sensor fault bounds is designed to detect and isolate faulty actuators and ensure that the tracking error always satisfies prescribed transient and steady-state performances. Two simulation cases are used for illustrating the proposed method. It is proved that the proposed method can effectively reduce the interference of sensor faults on actuator fault detection and improve the accuracy of actuator switching.

Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application

The calculation complex problem is one of the significant obstacles in the real-time implementation of traditional backstepping controllers. In this paper, we consider the simplification problem of the adaptive backstepping tracking controller for uncertain nonlinear systems with unknown input saturation. Compared with traditional backstepping controllers, virtual stabilizing functions and their derivatives are needless in our controller, which effectively reduces the computation burden. And then the one-order compensation subsystem is employed to eliminate the effect of nonlinear uncertainties based on the adaptive control scheme and the congelation of variables technique. Next, the performance of the closed-loop nonlinear system is analyzed based on the Lyapunov stability theorem. In the final, simulation and experimental results are given to show the effectiveness of our controller.

Parallel extended state observer based control for uncertain nonlinear systems

In this paper, a parallel extended state observer (PESO) is proposed by merging a series of different order linear tracking differentiators and first-order nonlinear differentiators. Both measurement noises and system uncertainties are taken into account in design procedures. A distinct feature of the parallel structure is that the observed information of each part is independent of each other, which effectively avoids the accumulation of the observation error of each part. The PESO is utilized to estimate the total disturbance, which reflects the combined impacts of internal uncertainties and external disturbances. Based on the observation results generated by the PESO, a composite controller is developed for output feedback control of uncertain nonlinear systems. The convergence performance of the proposed PESO and PESO-based controller is rigorously verified. Finally, some numerical simulation results are provided to verify the effectiveness and superiority of the proposed method.

Disturbance observer based actor-critic learning control for uncertain nonlinear systems

This paper investigates the disturbance observer based actor-critic learning control for a class of uncertain nonlinear systems in the presence of unmodeled dynamics and time-varying disturbances. The proposed control algorithm integrates a filter-based design method with actor-critic learning architecture and disturbance observer to circumvent the unmodeled dynamic and the time-varying disturbance. To be specific, the actor network is employed to estimate the unknown system dynamic, the critic network is developed to evaluate the control performance, and the disturbance observer is leveraged to provide efficient estimation of the compounded disturbance which includes the time-varying disturbance and the actor-critic network approximation error. Consequently, high-gain feedback is avoided and the improved tracking performance can be expected. Moreover, a composite weight adaptation law for actor network is constructed by utilizing two types of signals, the cost function and the modeling error. Eventually, theoretical analysis demonstrates that the developed controller can guarantee bounded stability. Extensive simulations and experiments on a robot manipulator are implemented to validate the performance of the resulted control strategy.