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In this paper, neural network control is presented for a rehabilitation robot with unknown system dynamics. To deal with the system uncertainties and improve the system robustness, adaptive neural networks are used to approximate the unknown model of the robot and adapt interactions between the robot and the patient. Both full state feedback control and output feedback control are considered in this paper. With the proposed control, uniform ultimate boundedness of the closed loop system is achieved in the context of Lyapunov’s stability theory and its associated techniques. The state of the system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters. Extensive simulations for a rehabilitation robot with constraints are carried out to illustrate the effectiveness of the proposed control.

This study focuses on a model reference adaptive control method that ensures identical orientation outputs for different prototypes of a two‐axis gimbal produced in mass production. In this method, unlike traditional MRAC structures, an MRAC structure is used in conjunction with state feedback control. First, the reasons for the need for an adaptation mechanism in gimbals and why Model Reference Adaptive Control (MRAC) alone won't be sufficient have been discussed. In the first section, various applications of MRAC have also been mentioned. Then, the mathematical foundation of the model reference adaptive controller used in this study is elaborately explained, followed by stability analyses. In the next step, an ideal reference model exhibiting desired behavior and a real system model with different dynamics are created in a simulation environment. This allows a comparison of the adaptation capabilities of only MRAC and MRAC+State Feedback controllers. Based on the information gathered in this section, the recommended approach in the article is tested on a real gimbal system, and the results are shared. The obtained results demonstrate that the MRAC+State Feedback control structure significantly reduces the error in the gimbal's orientation response compared to the reference model. This study focuses on a model reference adaptive control method that ensures identical orientation outputs for different prototypes of a two‐axis gimbal produced in mass production. In this method, unlike traditional MRAC structures, an MRAC structure is used in conjunction with state feedback control. Recommended approach tested on a real gimbal system, and the results are shared, which shows significant reduction of the error in the orientation response.

In this paper, a novel Virtual State-feedback Reference Feedback Tuning (VSFRT) and Approximate Iterative Value Iteration Reinforcement Learning (AI-VIRL) are applied for learning linear reference model output (LRMO) tracking control of observable systems with unknown dynamics. For the observable system, a new state representation in terms of input/output (IO) data is derived. Consequently, the Virtual State Feedback Tuning (VRFT)-based solution is redefined to accommodate virtual state feedback control, leading to an original stability-certified Virtual State-Feedback Reference Tuning (VSFRT) concept. Both VSFRT and AI-VIRL use neural networks controllers. We find that AI-VIRL is significantly more computationally demanding and more sensitive to the exploration settings, while leading to inferior LRMO tracking performance when compared to VSFRT. It is not helped either by transfer learning the VSFRT control as initialization for AI-VIRL. State dimensionality reduction using machine learning techniques such as principal component analysis and autoencoders does not improve on the best learned tracking performance however it trades off the learning complexity. Surprisingly, unlike AI-VIRL, the VSFRT control is one-shot (non-iterative) and learns stabilizing controllers even in poorly, open-loop explored environments, proving to be superior in learning LRMO tracking control. Validation on two nonlinear coupled multivariable complex systems serves as a comprehensive case study.

With the aid of quantized control, this paper presents new synchronization criteria of neural networks (NNs) with proportional delays. The NNs with constant delays and variable coefficients are obtained, which are equivalently transformed from the NNs with proportional delays. Taking the communication limitation into account, quantized controllers which include state feedback controllers and quantized adaptive controllers are designed for the first time for solving synchronization problem of NNs with proportional delays. By constructing Lyapunov function, utilizing new controllers, and applying new analytical methods, several criteria are derived to realize synchronization. Here, the obtained synchronization of NNs with proportional delays is not called exponential synchronization since the convergence rate is not fixed. Finally, numerical simulations are offered to substantiate our theoretical results.

This paper is concerned with the drive–response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

In this paper, we prove both necessary and sufficient maximum principles for infinite horizon discounted control problems of stochastic Volterra integral equations with finite delay and a convex control domain. The corresponding adjoint equation is a novel class of infinite horizon anticipated backward stochastic Volterra integral equations. Our results can be applied to discounted control problems of stochastic delay differential equations and fractional stochastic delay differential equations. As an example, we consider a stochastic linear-quadratic regulator problem for a delayed fractional system. Based on the maximum principle, we prove the existence and uniqueness of the optimal control for this concrete example and obtain a new type of explicit Gaussian state-feedback representation formula for the optimal control.

This paper derived a new simple hyperchaotic system from the famous Sprott, S system via the linear state feedback control. Compared with the available systems, the new system has eight terms, one constant, two parameters control, and a single quadratic nonlinear term. So this system is considered a simple relying on the number of terms and nonlinearities. The proposed system without equilibrium points and exhibits chaotic hidden attractors. Also, multistability or coexisting attractors are found through experimental simulations using phase portraits and the Lyapunov spectrum. Finally, anti-synchronization is implemented in the new system.

This paper is concerned with event-triggered H ∞ control of sampled-data systems. Its novelties lie in three aspects: (i) A novel accumulated-state-error-based event-triggered scheme is introduced by comparing the integral of the state error from t k to t with the system state sampled at t k . This condition works well due to the fact that the so-called Zeno behaviour does not occur. (ii) A novel Lyapunov functional is constructed to establish a criterion to ensure some certain H ∞ performance of the closed-loop system. This Lyapunov functional is dependent on the integral of the state error involved in the event-triggered scheme. (iii) Under the event-triggered sampling scheme, suitable state-feedback controllers can be designed rather than be given a priori. Moreover, a self-triggered implementation of the proposed event-triggered sampling scheme is presented as well. Finally, a batch reactor model and an inverted pendulum system are given to demonstrate the effectiveness of the proposed method.

The paper proposes a dynamic sliding mode control method based on the multivariable super-twisting algorithm for T-S fuzzy descriptor systems. Existing sliding mode control methods have significant limitations and still face chattering issues. The approach utilized in this paper fully leverages the advantages of the super-twisting algorithm, effectively reducing chattering during the control process and enhancing the system’s response speed and control accuracy. The reduction of chattering not only improves the control performance but also extends the system’s lifespan. Additionally, the paper conducts in-depth analysis of the entire system, using mathematical models and theoretical deductions to demonstrate that the proposed control method can effectively ensure system stability. This theoretical outcome provides a solid foundation for practical applications, ensuring the reliability of the control scheme.

We study state estimation of the linearized Schrödinger equation within a prescribed terminal time. We make use of a time–varying, complex–valued observer gain and boundary measurements to construct the observer, where the gain is designed such that the estimate error converges to zero within the terminal time. The observer gain proposed herein is developed via the backstepping method by selecting a target error equation that stabilizes to zero within the terminal time. Our time–varying observer gain diverges as time approaches the terminal time. Nevertheless, we can guarantee prescribed–time stabilization of the estimator error equation by characterizing the growth–in–time of the observer gain and comparing it to the stability of the target error equation. We develop the full–state feedback dual result, and we combine the boundary estimation and control results to develop prescribed–time output regulation.