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Safe fault tolerant control is one of the key technologies to improve the reliability of dynamic complex nonlinear systems with limited inputs, which is hard to solve and definitely a great challenge to tackle. Thus the paper presents a novel safety-optimal FTC (Fault Tolerant Control) approach for a category of completely unknown nonlinear systems incorporating actuator fault and asymmetric constrained-input, which can guarantee the system's operation within a safe range while showcasing optimal performance. Firstly, a CBF (Control Barrier Function) is incorporated into the cost function to penalize unsafe behaviors, and then we translate the intractable safety-optimal FTC problem into a differential ZSG (Zero-Sum Game) problem by defining the control input and the actuator fault as two opposing sides. Secondly, a neural-network-based identifier is employed to reconstruct system dynamics using system data, and the resolution of handling asymmetric constrained-input with the introduced non-quadratic cost function is achieved through the design of an adaptive critic scheme, aiming to reduce computational expenses accordingly. Finally, through the theoretical stability analysis, it is demonstrated that all signals in the closed-loop system are consistently UUB (Uniformly Ultimately Bounded). Furthermore, the proposed method's effectiveness is also verified in the simulation experiments conducted on a model of a single-link robotic arm system with actuator failure. The result shows that the algorithm can fulfill the safety-optimal demand of fault tolerant control in fault system with asymmetric constrained-input.

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A composite terminal sliding mode controller (CTSMC) for a kind of uncertain nonlinear system (UNS) is developed in this study. The primary aim of the design is to enhance the control performance of the CTSMC by learning its unknown parameters using a newly fuzzy neural network (FNN). Firstly, the stability and convergence of CTSMC for UNS with known parameters are demonstrated. Secondly, since some parameters of actual UNS are unmeasurable, a self-organizing feature selection fuzzy neural network (SOFSFNN) is intended to approach these unknown parts. Finally, the CTSMC using SOFSFNN is applied to UNS. The outcomes demonstrate that it has minimal tracking error, good robustness, and the ability to dynamically modify the network structure.

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We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is ∂ t | u | q - 1 u - div | D u | p - 2 D u = div | F | p - 2 F in Ω T : = Ω × ( 0 , T ) with parameters p > 1 and q > 0 and Ω âŠ‚ R n . In this paper, we are concerned with the ranges q > 1 and p > n ( q + 1 ) n + q + 1 . A key ingredient in the proof is an intrinsic geometry that takes both the solution u and its spatial gradient Du into account.

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Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.

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This paper studies a safe model predictive control (MPC)-based disturbance rejection control for a broad range of uncertain nonlinear systems subject to complex state safety constraints. The system under study is composed of a nominal model and an uncertain term that encapsulates modeling uncertainty, control mismatch, and external disturbances. In order to estimate the system state and total uncertainty, an extended state observer (ESO) is first designed. Utilizing the output of the ESO, the control compensates for the total uncertainty in real time and concurrently implements a control barrier function (CBF)-based MPC for the compensated system. The proposed control framework guarantees both safety and disturbance rejection. Compared to the baseline algorithm CBF-MPC, the proposed method significantly enhances system stability with a smaller root mean square (RMS) error of the system state from the equilibrium point. Rigorous theoretical analysis and simulation experiments are provided to validate the effectiveness of the proposed scheme.

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This paper introduces an adaptive trajectory-tracking control method for uncertain nonlinear systems, leveraging a time-varying threshold event-triggered mechanism to achieve predefined-time tracking. Compared to conventional time-triggering approaches, the employment of a time-varying threshold event-triggered mechanism significantly curtails communication resource wastage without compromising the system's performance. Furthermore, a novel adaptive control algorithm with predefined timing is introduced. This method guarantees that tracking errors converge to within a small vicinity of the origin within a predefined timeframe, ensuring all signals in the closed-loop system remain bounded. Moreover, by adjusting a controller-related parameter, we can predefine the upper bound of the convergence time. Finally, the efficacy of the control scheme is corroborated by simulation results obtained from a nonlinear manipulator system.

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This paper investigates the prescribed performance control problems of strict-feedback nonlinear systems with state quantization, input quantization, unknown disturbances and unknown nonlinear functions. Since the quantized states are discontinuous, the differentiability of the stabilizing functions in the backstepping technique cannot be guaranteed. To this end, a smooth approximation of the quantized states is first obtained by introducing a class of functions. Based on this smooth approximation, a quantized control scheme is presented such that all the closed-loop signals are bounded with the prescribed performance bounds. It is shown that the unknown nonlinearities and the unknown disturbances are not estimated and the derivatives of the stabilizing functions are eliminated. Lastly, two examples are provided to illustrate the effectiveness of the presented method.

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In this study, the problem of non-overshooting tracking control (NOTC) for a class of strict-feedback systems with prescribed finite-time (FT) is studied. In order to obtain a simple closed-loop system (CLS), we first propose a criterion lemma for prescribed FT stable control. A prescribed FT controller is designed by using backstepping and the proposed criterion lemma. According to the CLS, many conditions of NOTC are analyzed. Compared with the related results, the NOTC conditions obtained in this paper are relatively extensive, which reduces conservatism. The algorithm makes the system overshoot zero, so this result increases the accuracy. The final simulation results show that this algorithm is effective.

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This article introduces an observer-based control strategy tailored for regulating plasma glucose in type 1 diabetes mellitus patients, addressing challenges like unknown time-varying delays and meal disturbances. This control strategy is based on an extended Bergman minimal model, a nonlinear glucose-insulin model to encompass unknown inputs, such as unplanned meals, exercise disturbances, or delays. The primary contribution lies in the design of an observer-based state feedback control in the presence of unknown long delays, which seeks to support and enhance the performance of the traditional artificial pancreas by considering realistic scenarios. The observer and control gains for the observer-based control are computed through linear matrix inequalities formulated from Lyapunov conditions that guarantee closed-loop stability. This design deploys a soft and gentle dynamic response, similar to a natural pancreas, despite meal disturbances and input delays. Numerical tests demonstrate the scheme's effectiveness in glycemic level regulation and hypoglycemic episode avoidance.

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Applications of causal techniques to neural time series have increased extensively over last decades, including a wide and diverse family of methods focusing on electroencephalogram (EEG) analysis. Besides connectivity inferred in defined frequency bands, there is a growing interest in the analysis of cross-frequency interactions, in particular phase and amplitude coupling and directionality. Some studies show contradicting results of coupling directionality from high frequency to low frequency signal components, in spite of generally considered modulation of a high-frequency amplitude by a low-frequency phase. We have compared two widely used methods to estimate the directionality in cross frequency coupling: conditional mutual information (CMI) and phase slope index (PSI). The latter, applied to infer cross-frequency phase-amplitude directionality from animal intracranial recordings, gives opposite results when comparing to CMI. Both metrics were tested in a numerically simulated example of unidirectionally coupled Rössler systems, which helped to find the explanation of the contradictory results: PSI correctly estimates the lead/lag relationship which, however, is not generally equivalent to causality in the sense of directionality of coupling in nonlinear systems, correctly inferred by using CMI with surrogate data testing.

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Introduction: With the help of robot technology, intelligent rehabilitation of patients with lower limb motor dysfunction caused by stroke can be realized. A key factor constraining the clinical application of rehabilitation robots is how to realize pattern recognition of human movement intentions by using the surface electromyography (sEMG) sensors to ensure unhindered human-robot interaction. Methods: A multilayer CNN-LSTM prediction network incorporating the self-attention mechanism (SAM) is proposed, in this paper, which can extract and learn the periodic and trend characteristics of the sEMG signals, and realize the accurate autoregressive prediction of the human motion information. Firstly, the multilayer CNN-LSTM network utilizes the CNN layer for initial feature extraction of data, and the LSTM network is used to improve the enhancement of the historical time-series features. Then, the SAM is used to improve the global feature extraction performance and parallel computation speed of the network. Results: In comparison with existing test is carried out using actual data from five healthy subjects as well as a clinical hemiplegic patient to verify the superiority and practicality of the proposed algorithm. The results show that most of the model's prediction R > 0.9 for different motion states of healthy subjects; in the experiments oriented to the motion characteristics of patient subjects, the angle prediction results of R > 0.99 for the untrained data on the affected side, which proves that our proposed model also has a better effect on the angle prediction of the affected side. Discussion: The main contribution of this paper is to realize continuous motion estimation of ankle joint for healthy and hemiplegic individuals under non-ideal conditions (weak sEMG signals, muscle fatigue, high muscle tension, etc.), which improves the pattern recognition accuracy and robustness of the sEMG sensor-based system.

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In this article, the issue of joint state and fault estimation is ironed out for delayed state-saturated systems subject to energy harvesting sensors. Under the effect of energy harvesting, the sensors can harvest energy from the external environment and consume an amount of energy when transmitting measurements to the estimator. The occurrence probability of measurement loss is computed at each instant according to the probability distribution of the energy harvesting mechanism. The main objective of the addressed problem is to construct a joint state and fault estimator where the estimation error covariance is ensured in some certain sense and the estimator gain is determined to accommodate energy harvesting sensors, state saturation, as well as time delays. By virtue of a set of matrix difference equations, the derived upper bound is minimized by parameterizing the estimator gain. In addition, the performance evaluation of the designed joint estimator is conducted by analyzing the boundedness of the estimation error in the mean-squared sense. Finally, two experimental examples are employed to illustrate the feasibility of the proposed estimation scheme.

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We propose and experimentally demonstrate a wireless-channel key distribution scheme based on laser synchronization induced by a common wireless random signal. Two semiconductor lasers are synchronized under injection of the drive signal after electrical-optical conversion and emit irregular outputs that are used to generate shared keys. Our proof-of-concept experiment using a complex drive signal achieved a secure key generation rate of up to 150 Mbit/s with a bit error rate below 3.8 × 10-3. Numerical simulation results show that the proposed scheme has the potential to achieve a distribution distance of several hundred meters. It is believed that common-signal-induced laser synchronization paves the way for high-speed wireless physical-layer key distribution.

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This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier's regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

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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.

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Much attention have been devoted to control of chaos in nonlinear system in the last few decades and several control procedures have been derived to find the stability target in difference and differential equations. In this study, a novel hybrid chaos control procedure is derived which allows to stabilize the chaos in most accepted discrete chaotic equations of population growth models about the globally accepted stable equilibrium. Since the system depends on the parameters κ, α, and r, the chaos in the given system may be stabilized in different fixed points states of order p, when it is kicked with the parameter κ. From this point of view, the procedure is simple, flexible, and gives the advantage to take the numerous parameter values to reach the demanded stability in periodic states of order p. This hybrid approach to control makes it novel as compared to existing methods. Further, we provide the geometrical interpretation followed by a few examples, control curves, bifurcation plots, time-series plots, and Lyapunov exponent to illustrate our numerical results.

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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.

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This paper investigates the fault-tolerant prescribed performance control problem for a class of multiple-input single-output unknown nonlinear systems subject to process faults and actuator failures. In contrast to the related works, we consider a general class of nonlinear systems with both multiplicative nonlinearities and additive nonlinearities corrupted by the process faults; only the boundedness of the process faults and the continuity of the nonlinear functions are required, without the explicit or fixed structures of the fault functions. To conquer this problem, a less-demanding and low-complexity fault-tolerant prescribed performance control approach is proposed. The controller is independent of the specific information of faults or the system model and does not invoke fault diagnosis or neural/fuzzy approximation to acquire such knowledge. It achieves the reference tracking with the predefined rate and accuracy. A comparative simulation on a single-link robot is conducted to illustrate the effectiveness and superiority of the proposed approach.

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In control systems, multirate sampled data systems are widely used because they improve system performance and adaptability, especially when systems deal with both continuous and discrete signals or entirely asynchronous sampling signals. This paper addresses the challenges of system stability and optimization in these multirate systems, specifically for a certain class of nonlinear systems. Existing controllers, though capable in certain contexts, tend to be overly complex and often lack guidance on appropriate sampling interval selection for these intricate systems. Our approach takes into account both system stability and practical considerations, providing a criterion for selecting multiple sample periods that guarantees system stability, as well as an optimal choice of parameters by Neural Ordinary Differential Equation (NODE) for the linear practical controller that maximizes performance according to a predefined performance index. With the construction of a set of linear stabilizers that are implemented using multirate sampled data, the stability and controller design at three different sampling levels are studied. To demonstrate the effectiveness of our proposed strategy, the simulations and real world application of a single-link robot system are presented.

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It is the first report about fault-tolerant-based prescribed performance control of switched nonlinear systems under multiple faults. The concerned faults include not only external faults but also actuator faults. In the process of backstepping control design, prescribed performance control is fully considered, and the combination of unknown nonlinear functions is estimated by multi-dimensional Taylor network. Finally, the developed adaptive fault-tolerant control strategy guarantees the boundedness of all controlled signals while prescribed tracking performance is satisfied. In an effort to further manifest the validity of the fault-tolerant controller, a numerical simulation and a practical simulation are introduced.