Fixed-Time Adaptive Neural Network Control for Nonlinear Systems With Input Saturation

Neural-Network-Based Adaptive Fixed-Time Control for a 2-DOF Helicopter System With Input Quantization and Output Constraints

This study proposes a neural-network (NN)-based adaptive fixed-time control method for a two-degree-of-freedom (2-DOF) nonlinear helicopter system with input quantization and output constraints. First, a hysteresis quantizer is employed to mitigate chattering during signal quantization, and adaptive variables are utilized to eliminate errors in the quantization process. Subsequently, the system uncertainties are approximated using a radial basis function NN. Simultaneously, a logarithmic barrier Lyapunov function (BLF) is constructed to prevent the system outputs from violating the constraint boundaries. Based on a rigorous Lyapunov stability analysis and the fixed-time stability criterion, the signals of the closed-loop system are proven to be bounded within a fixed time. Finally, numerical simulations and experiments verified the feasibility of the proposed method.

Collective Neural Dynamics for Sparse Motion Planning of Redundant Manipulators Without Hessian Matrix Inversion

Redundant manipulators have been widely used in various industries whose applications not only improve production efficiency and reduce manual labor but also promote innovation in robotics and artificial intelligence. Kinematic control plays a fundamental and crucial role in robot control. Over the past few decades, numerous motion control schemes have been proposed and applied to trajectory tracking tasks. However, most of these schemes do not consider the introduction of sparsity into the motion control of redundant manipulators, resulting in excessive joint movements, which not only consume extra energy but also increase the risk of unexpected collisions in complex environments. To solve this problem, we transform the issue of increasing the sparsity into a nonconvex optimization problem. Furthermore, a collective neural dynamics for sparse motion planning (CNDSMP) scheme for motion planning of redundant manipulators is proposed. By incorporating sparsity into the control scheme, the excessive joint movements are minimized, leading to improved efficiency and reduced collision risks. Through simulations, comparisons, and physical experiments, the effectiveness and superiority of the proposed scheme are demonstrated.

Adaptive Prescribed-Time Filtered Control Design for a Full-State Constrained Nonlinear System

In this article, an adaptive prescribed-time neural controller is developed for the tracking problem of a class of high-order nonlinear systems with full-state constraints. First, a prescribed-time bounded stability criterion is designed. Then, to handle the "explosion of complexity" problem of the backstepping method, an adaptive prescribed-time filter is constructed, in which the filter error is prescribed-time stable. Compared with existing methods, the newly designed transformation approach can accommodate a broader range of state constraint types. Then, the unknown nonlinear function is handled by radial basis function neural networks (RBFNNs). The adaptive prescribed-time neural control scheme is developed based on above. It can guarantee that the closed-loop system achieves the prescribed-time stability, and all states do not transgress the constraints. To demonstrate the effectiveness of the control strategy, comparative simulations are provided at the end.

Adaptive fuzzy prescribed time tracking control for nonlinear systems with input saturation

This article investigates the adaptive fuzzy prescribed time tracking control problem for a class of strict-feedback systems simultaneously considering the user-defined asymmetric tracking performance, input saturation, and external disturbances. From the perspective of ensuring the reliability for control implementation, a saturation-based fixed-time funnel boundary is constructed by embedding the modification signals related to input saturation errors into a funnel function, which is capable of automatically enlarging or recovering itself when input saturation occurs or disappears, thereby reducing the risk of system singularity. Subsequently, by constructing a fixed-time tracking performance function, any known bounded tracking error is recast into a new variable with a zero initial value. With such a treatment, funnel boundaries are no longer redeveloped for different initial tracking errors, and meanwhile the behavior of the tracking error is pre-specified as needed over a finite time interval. Also, auxiliary systems are devised to generate the aforesaid modification signals, while compensating for the adverse impact resulting from input saturation. Remarkably, by feat of the backstepping design based on the fuzzy approximation, it is proven that the tracking error converges to a user-defined region within a prescribed time (known as the practically prescribed time tracking), which is achieved without the fractional power feedback of system states. Finally, two simulation examples are presented to confirm the feasibility and effectiveness of the developed approach.

Improved disturbance observer-based fixed-time adaptive neural network consensus tracking for nonlinear multi-agent systems

This paper is concerned with the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems subject to unknown disturbances. Firstly, a modified fixed-time disturbance observer is devised to estimate the unknown mismatched disturbance. Secondly, a distributed fixed-time neural network control protocol is designed, in which neural network is employed to approximate the uncertain nonlinear function. Simultaneously, the technique of command filter is applied to fixed-time control, which circumvents the "explosion of complexity" problem. Under the proposed control strategy, all agents are enable to track the desired trajectory in fixed-time, and the consensus tracking error and disturbance estimation error converge to an arbitrarily small neighborhood of the origin, meanwhile, all signals in the closed-loop system remain bounded. Finally, a simulation example is provided to validate the effectiveness of the presented design method.

Fixed-Time Tracking Control for Nonlinear Cascade Systems with Unknown High Powers

This paper investigates the global fixed-time tracking control problem of nonlinear cascade systems with unknown high powers. In the process of control design, a upper bound and a lower bound of high powers are introduced to compensate the unknown system powers, and a state feedback controller is designed under any initial system conditions. Based on the Lyapunov stability analysis method and the fixed-time stability theory, it is verified that the proposed method can regulate the output tracking error to a disc region of the origin within a fixed-time and all the closed-loop signals are bounded. At last, the effectiveness of the proposed scheme is verified by some simulation results.

Further Results on Adaptive Practical Tracking for High-Order Nonlinear Systems With Full-State Constraints

In this article, an adaptive practical tracking control scheme is presented for full-state constrained high-order nonlinear systems. By skillfully introducing the adaptive gain, nonlinear transformed functions and sign functions into control design, a novel continuous state-feedback controller is constructed without imposing restrictive approximation techniques and feasibility conditions. Under mild assumptions, the boundedness of all the closed-loop signals can be guaranteed, full-state constraints are not transgressed for all time, and the tracking error tends to an arbitrarily small region of zero in a finite time.