The primary focus of this research paper is to explore the realm of dynamic learning in sampled-data strict-feedback nonlinear systems (SFNSs) by leveraging the capabilities of radial basis function (RBF) neural netwo...
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The primary focus of this research paper is to explore the realm of dynamic learning in sampled-data strict-feedback nonlinear systems (SFNSs) by leveraging the capabilities of radial basis function (RBF) neural networks (NNs) under the framework of adaptive control. First, the exact discrete-time model of the continuous-time system is expressed as an Euler strict-feedback model with a sampling approximation error. We provide the consistency condition that establishes the relationship between the exact model and the Euler model with meticulous detail. Meanwhile, a novel lemma is derived to show the stability condition of a digital first-order filter. To address the non-causality issues of SFNSs with sampling approximation error and the input data dimension explosion of NNs, the auxiliary digital first-order filter and backstepping technology are combined to propose an adaptive neural dynamic surface control (ANDSC) scheme. Such a scheme avoids the n$$ n $$-step time delays associated with the existing NN updating laws derived by the common n$$ n $$-step predictor technology. A rigorous recursion method is employed to provide a comprehensive verification of the stability, guaranteeing its overall performance and dependability. Following that, the NN weight error systems are systematically decomposed into a sequence of linear time-varying subsystems, allowing for a more detailed analysis and understanding. In order to ensure the recurrent nature of the input variables, a recursive design is employed, thereby satisfying the partial persistent excitation condition specifically designed for the RBF NNs. Meanwhile, it can verify that the NN estimated weights converge to their ideal values. Compared with the common n$$ n $$-step predictor technology, there is no need to redesign the learning rules due to the designed NN weight updating laws without time delays. Subsequently, after capturing and storing the convergence weights, a novel neurallearning dynamic surface contro
This paper presents a method for achieving synchronization of chaotic systems with unknown dynamics, using a predefined-time neural learning control approach. The proposed method includes a control law for synchroniza...
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This paper presents a method for achieving synchronization of chaotic systems with unknown dynamics, using a predefined-time neural learning control approach. The proposed method includes a control law for synchronization and a parameter updating law that are designed to ensure stability according to the predefined-time Lyapunov theory. The analysis of stability indicates that the synchronization errors using this approach converge to a small region around zero within the predefined time. The effectiveness of the proposed method is demonstrated through simulation examples.
This article presents neurallearning based adaptive impedance control for a lower limb rehabilitation exoskeleton with flexible joints (LLREFJ). First, the full model consisting of both the rigid link and the flexibl...
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This article presents neurallearning based adaptive impedance control for a lower limb rehabilitation exoskeleton with flexible joints (LLREFJ). First, the full model consisting of both the rigid link and the flexible joint is obtained for the LLREFJ. Second, neural networks are used to compensate for the system uncertainties and external disturbance and an adaptive impedance controller is proposed by establishing an impedance error. In order to improve the control performance and enhance the system robustness, periodic dynamics is considered according to the repetitive motion of the rehabilitation process and handled by a repetitive learning algorithm. Then, the stability of the full system is proved rigorously by Lyapunov methods. Finally, comparative simulation reveals that the designed adaptive neural learning controller has improved the control performance.
This article studies the dynamic neurallearning issue for strict-feedback nonlinear systems with full state constraints by utilizing the nonlinear transformed function (NTF) method. To handle the issue of state const...
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This article studies the dynamic neurallearning issue for strict-feedback nonlinear systems with full state constraints by utilizing the nonlinear transformed function (NTF) method. To handle the issue of state constraints control, a NTF is introduced to convert the original constrained states into the equivalent unconstrained ones. For the transformed system states, a stable adaptive neuralcontrol strategy is put forward in combination with the dynamic surface technology. Subsequently, a new lemma, instead of the traditional system decomposition method, is developed to simplify the recurrent verification process of neural network (NN) inputs. Such a new lemma promotes the validation of exponential convergence for NN weight estimates in a steady-state time, and the convergent weights are stored as the learned knowledge. Moreover, a novel corollary is given to verify that the unknown system dynamics under two cases with and without state constraints are almost the same during the steady-state control process, thereby indicating the learned dynamical knowledge from the case with state constraints is also suitable for the case without state constraints. For the two cases, by reusing the learned knowledge, a neural learning controller is established for the better control performance and less online calculations. Simulation studies testify the efficacy of the developed method.
One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an a...
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One of the amazing successes of biological systems is their ability to "learn by doing" and so adapt to their environment. In this paper, first, a deterministic learning mechanism is presented, by which an appropriately designed adaptive neuralcontroller is capable of learning closed-loop system dynamics during tracking control to a periodic reference orbit. Among various neural network (NN) architectures, the localized radial basis function (RBF) network is employed. A property of persistence of excitation (PE) for RBF networks is established, and a partial PE condition of closed-loop signals, i.e., the PE condition of a regression subvector constructed out of the RBFs along a periodic state trajectory, is proven to be satisfied. Accurate NN approximation for closed-loop system dynamics is achieved in a local region along the periodic state trajectory, and a learning ability is implemented during a closed-loop feedback control process. Second, based on the deterministic learning mechanism, a neural learning control scheme is proposed which can effectively recall and reuse the learned knowledge to achieve closed-loop stability and improved control performance. The significance of this paper is that the presented deterministic learning mechanism and the neural learning control scheme provide elementary components toward the development of a biologically-plausible learning and control methodology. Simulation studies are included to demonstrate the effectiveness of the approach.
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