This paper investigates the adaptive tracking control problem for uncertain nonlinear systems using self-organizing deep neural networks (SODNNs). Conventional DNN-based control approaches typically employ fixed depth architectures with multiple hidden-layers to model uncertain nonlinear dynamics. Such fixed structures often face an inherent trade-off between approximation accuracy and computational efficiency, resulting in either excessive computational burden or insufficient representational capability. To address these issues, an event-triggered self-organizing mechanism is proposed, which enables the DNN to dynamically adjust its network depth by adding or removing hidden-layers when prescribed triggering conditions are violated. In this way, the network structure is dynamically adapted to the evolving system dynamics, achieving an effective balance between approximation precision and computational burden. Furthermore, an adaptive learning rate strategy is developed, in which the learning rates of individual layers are adjusted online based on the state tracking error and the norm of the corresponding weight gradients. This mechanism enhances approximation efficiency, control performance and robustness against uncertainties. Rigorous Lyapunov-based analysis is provided to guarantee that all closed-loop signals are ultimately bounded under the proposed control framework. The effectiveness and practical feasibility of the proposed method are validated through numerical simulations and real-time experiments conducted on a Franka Emika Panda robotic manipulator.

This paper presents an adaptive command filtered control scheme using composite auxiliary signals for a class of uncertain strict-feedback nonlinear systems subject to input saturation. To explicitly constrain the filtered errors, barrier functions are incorporated into the command filtering loop, effectively mitigating their adverse impact on system stability and alleviating the “explosion of complexity" phenomenon inherent in backstepping designs. Furthermore, by constructing a composite auxiliary system, the proposed method achieves a unified compensation mechanism for both bounded filtered errors and input saturation effects. Compared with existing approaches, the proposed strategy simultaneously addresses filtered error and input saturation issues without relying on smooth saturation approximations, thereby avoiding approximation-induced errors and enhancing overall control performance. The effectiveness and practical applicability of the method are validated through numerical simulations and real-time experiments conducted on a Franka Emika Panda robotic arm.

This study addresses the safe consensus tracking issue for a specific category of multiagent systems (MASs) featuring a static directed communication graph. Each follower agent is subject to external disturbances and governed by unknown pure-feedback nonaffine dynamics. To facilitate the back-stepping approach in nonaffine systems, the mean value theorem (MVT) is employed. Additionally, dynamic surface control (DSC) is implemented to mitigate the intricacies typically encountered in back-stepping frameworks. For the approximation of the unknown nonlinearities, radial basis function neural networks (NNs) are utilized. Integrating these methodologies with principles from graph theory and barrier Lyapunov functions (BLFs), we propose a tailored neuro-adaptive distributed control scheme. The objective of this scheme is to ensure that followers can accurately track the leader’s path while maintaining the globally uniformly bounded (GUB) property of all system signals within the closed loop. Comparative simulation results demonstrate the effectiveness and superiority of the proposed control method.

Determining the neural network (NN) approximation sets for adaptive control of strict-feedback uncertain systems has posed a persistent challenge. This article proposes a novel and constructive solution that incorporates signal substitution technique, barrier functions (BFs), and backstepping approach. By applying the signal substitution technique, all system states are transformed into state error variables, facilitating the approximation of unknown system functions through NNs. The use of BFs subsequently allows for the restriction of state errors, enabling the calculation of exact bounds for the NN weight estimators. This process reveals the determination of the approximation sets of NN in advance. Illustrative examples are conducted to validate the effectiveness of the proposed approach.

Whole-body control (WBC) has emerged as an important framework in manipulation for mobile manipulators. However, most existing WBC frameworks require known dynamics. Considering whole-body manipulation and optimization with unknown dynamics, this article presents the WBC of a nonholonomic mobile manipulator using model predictive control (MPC) and fuzzy logic system. First, by constructing a dynamics-based feedback linearized robotic multi-input-multi-output (MIMO) system, an MPC-based WBC strategy is proposed for mobile manipulator. Such a strategy can provide the optimal control inputs with the specified optimization index and constraints. Thereafter, a primal-dual neural network effectively addresses the constrained quadratic programming (QP) problem over a finite receding horizon brought by the MPC. Then, in order to convert the intermediate control signals into the optimal control torques that can be executed by actuators, an adaptive FLS is employed to approximate the unknown dynamics. The novel elements of the current design control approach refer to the dynamics-based feedback linearized robotic MIMO system and the combination of an MPC module with an adaptive fuzzy controller. Finally, the trajectory tracking experiments performed on a mobile dual-arm robot demonstrate the effectiveness of the proposed method.

Most existing approximation-based adaptive control (AAC) approaches for unknown pure-feedback nonaffine systems retain a dilemma that all closed-loop signals are semiglobally uniformly bounded (SGUB) rather than globally uniformly bounded (GUB). To achieve the GUB stability result, this article presents a neuro-adaptive backstepping control approach by blending the mean value theorem (MVT), the barrier Lyapunov functions (BLFs), and the technique of neural approximation. Specifically, we first resort the MVT to acquire the intermediate and actual control inputs from the nonaffine structures directly. Then, neural networks (NNs) are adopted to approximate the unknown nonlinear functions, in which the compact sets for maintaining the approximation capabilities of NNs are predetermined actively through the BLFs. It is shown that, with the developed neuro-adaptive control scheme, global stability of the resulting closed-loop system is ensured. Simulations are conducted to verify and clarify the developed approach.

In this article, the problem of adaptive tracking control is tackled for a class of high-order nonlinear systems. In contrast to existing results, the considered system contains not only unknown nonlinear functions but also unknown rational powers. By utilizing the fuzzy approximation approach together with the barrier Lyapunov functions (BLFs), we present a new adaptive tracking control strategy. Remarkably, the BLFs are employed to determine a priori the compact set for maintaining the validity of fuzzy approximation. The primary advantage of this article is that the developed controller is independent of the powers and can be capable of ensuring global stability. Finally, two illustrative examples are given to verify the effectiveness of the theoretical findings.

In this article, the adaptive fuzzy tracking control problem for a class of uncertain strict-feedback systems with unknown nonlinearities is investigated withparticular emphasis on global stability. The proposed control scheme is designed by integrating the barrier Lyapunov functions (BLFs) with the techniques of fuzzy approximation and backstepping. The novel integral BLFs (iBLFs) are introduced to overcome the design difficulties induced by the virtual control coefficients and determinea priorithe compact set for guaranteeing the validity of fuzzy approximation. Compared with existing approximation-based control results, the developed controller not only guarantees global stability without requiring prior information of system nonlinearities and assumptions on the time derivatives of virtual control coefficients, but also prevents the “explosion of complexity” issue without attaching additional filters. The simulation results further confirm the effectiveness of the theoretical findings.

This article considers the funnel output tracking control for a class of high-order uncertain nonlinear systems with the powers of positive odd rational numbers, aiming to accomplish output tracking with prescribed accuracy when both the system nonlinearities and the powers of the system are unknown. For such a purpose, a robust funnel control algorithm, i.e., a continuous, static, and universal, state-feedback controller is explicitly constructed, which achieves the state errors evolving within the predesigned performance space. Benefits of the proposed funnel output tracking controller comparing with the current approaches lie in the fact that the exact knowledge of system nonlinearities, including generally required bounding functions, is not needed to be a priori. Moreover, all the powers in each high-order subsystem are permitted to be any unknown positive odd rational numbers as well. The efficacy of the developed algorithm is confirmed through two illustrative examples.

In this article, a globally stable adaptive control strategy for uncertain strict-feedback systems is proposed within predefined neural network (NN) approximation sets, despite the presence of unknown system nonlinearities. In contrast to the conventional adaptive NN control results in the literature, a primary benefit of the developed approach is that the barrier Lyapunov function is employed to predefine the compact set for maintaining the validity of NN approximation at each step, thus accomplishing the global boundedness of all the closed-loop signals. Simulation results are performed to clarify the effectiveness of the proposed methodology.