Tracking control for nonaffine systems: a self-organizing approximation approach

Guaranteeing Global Stability for Neuro-Adaptive Control of Unknown Pure-Feedback Nonaffine Systems via Barrier Functions

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.

Tracking Control of Unknown and Constrained Nonlinear Systems via Neural Networks With Implicit Weight and Activation Learning

For systems with irregular (asymmetric and positively-negatively alternating) constraints being imposed/removed during system operation, there is no uniformly applicable control method. In this work, a control design framework is established for uncertain pure-feedback systems subject to the aforementioned constraints. By introducing a novel transformation function and with the help of auxiliary constraining boundaries, the original output-constrained system is augmented to unconstrained one. Unknown nonlinearity is approximated by neural networks (NNs) with not only neural weight updating but also activation online adjustment. The resultant control scheme is able to deal with constraints imposed or removed at some time moments during system operation without the need for altering control structure. When applied to high-speed trains, the developed control scheme ensures position tracking under speed constraints, simulation demands, and confirms the effectiveness of the proposed method.

Globally Exponentially Stable Tracking Control of Self-Restructuring Nonlinear Systems

This article proposes a neural networks (NNs)-based tracking control approach for a class of uncertain high-order self-restructuring nonaffine dynamic systems. Unlike most existing NN-based works that normally ignore the precondition on the functionality and reliability of NN unit and thus can only ensure semiglobal stability, the proposed method explicitly addresses the issue of reliable in-loop operation of NN approximation-based control unit, resulting in a safeguarded NN-based control solution capable of ensuring globally stable tracking. Furthermore, the control method proposed guarantees exponentially globally stable tracking for systems with self-restructuring nonlinearities and uncertainties, distinguishing itself from those that only yield uniformly ultimately bounded (UUB) regulation/tracking results for nonlinear systems with fixed structures. All of these features are achieved by the proposed strategy consisting of two cooperative control units: 1) safeguard control and 2) NN-based control. The role of the safeguard control is to force the states (starting from any initial condition) to enter a stable region, so that the NN-based control can be activated trustworthily and safely. It is such cooperation of the two units that not only ensures the tracking error entering the stable region first within a prespecified finite time but also guarantees the tracking error converging to zero exponentially thereafter, resulting in global zero-error tracking. Both the theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.

Optimal Robot-Environment Interaction Under Broad Fuzzy Neural Adaptive Control

This article proposes a novel control strategy based on a broad fuzzy neural network (BFNN) which is subjected to contact with the unknown environment. Compared with the conventional fuzzy neural network (NN), a prominent feature can be achieved by taking the advantage of the broad learning system (BLS) to explicitly tackle the problem of how to choose a sufficient number of NN units to approximate the unknown dynamic model. Aiming at providing a soft compliant contact scheme without the requirement of the environment model, an adaptive impedance learning is developed to establish the optimal interaction between the robot and the environment. Meanwhile, the problems related to the state constraints are addressed by incorporating a barrier Lyapunov function (BLF) into the design of a trajectory tracking controller. The proposed method can achieve desired tracking and interaction performance while guaranteeing the stability of the closed-loop system. In addition, simulation and experimental studies are performed to verify the effectiveness of BFNN under optimal impedance control with a two degree-of-freedom (DOF) manipulator and a Baxter robot, respectively.

Adaptive Neural-Network Control of MIMO Nonaffine Nonlinear Systems With Asymmetric Time-Varying State Constraints

In this paper, a novel robust adaptive barrier Lyapunov function (BLF)-based backstepping controller has been proposed for a class of interconnected, multi-input-multi-output (MIMO) unknown nonaffine nonlinear systems with asymmetric time-varying (ATV) state constraints. The design involves a neural-network-based online approximator to cope with uncertain dynamics of the system. To tune its weights, a novel adaptive law is proposed based on the Hadamard product. A theorem has also been proposed to have the bounds on virtual control signals beforehand. This theorem eliminates the need for tedious offline computation for the feasibility condition on the virtual controller in BLF-based controller design. To overcome the problem of unknown control gain in the nonaffine system, Nussbaum gain has been used during the design. A simulation study on the robot manipulator in task space has been performed to illustrate the effectiveness of the proposed methodology.

Zero-Error Consensus Tracking With Preassignable Convergence for Nonaffine Multiagent Systems

In this paper, we investigate the consensus tracking control problem for networked multiagent systems (MASs) with unknown nonaffine dynamics. Our goal is to achieve asymptotic (rather than ultimately uniformly bounded) consensus tracking, which is quite challenging especially if nonvanishing/nonparametric uncertainties are involved and at the same time the control protocol is required to be fully distributed and continuous everywhere. Here, we present a conceptually new and structurally simple solution with distributed and continuous control action. The developed method is capable of ensuring zero-error tracking with a unique converging feature in that the consensus tracking error first converges to a small adjustable residual set around zero within a prescribed finite time, and then further shrinks to zero exponentially. The key technique lies in the utilization of a state transformation based on certain scaling function. Our method also prevents the restrictive requirement that all subsystems have access to the linearly parameterized information as imposed in most existing consensus tracking results for nonlinear MAS.

Barrier Function-Based Adaptive Control for Uncertain Strict-Feedback Systems Within Predefined Neural Network Approximation Sets

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.

Dealing With the Issues Crucially Related to the Functionality and Reliability of NN-Associated Control for Nonlinear Uncertain Systems

The "universal" approximating/learning feature of neural network (NN), widely and extensively used for control design, is contingent upon some critical conditions, either of which, if not satisfied, would render such feature vanished. In this paper, we show that these conditions are literally linked with several fundamental issues that have been overlooked in most existing NN-based control designs, either unconsciously or deliberately. We further propose a collective approach to explicitly address these issues, establishing a strategy enabling the NN unit to be fully functional in the control loop during the entire process of system operation and ensuring the more reliable and more effective NN-associated control performance. This is achieved by incorporating the control with a new structural NN unit, consisting of a group of diversified neurons with self-adjusting subneurons, each being driven/stimulated by input signals confined within a compact set. Meanwhile, the continuity of the control signal and the boundedness of all the closed-loop signals are ensured. Both the theoretical analysis and numerical simulation validate the effectiveness of the proposed method.The "universal" approximating/learning feature of neural network (NN), widely and extensively used for control design, is contingent upon some critical conditions, either of which, if not satisfied, would render such feature vanished. In this paper, we show that these conditions are literally linked with several fundamental issues that have been overlooked in most existing NN-based control designs, either unconsciously or deliberately. We further propose a collective approach to explicitly address these issues, establishing a strategy enabling the NN unit to be fully functional in the control loop during the entire process of system operation and ensuring the more reliable and more effective NN-associated control performance. This is achieved by incorporating the control with a new structural NN unit, consisting of a group of diversified neurons with self-adjusting subneurons, each being driven/stimulated by input signals confined within a compact set. Meanwhile, the continuity of the control signal and the boundedness of all the closed-loop signals are ensured. Both the theoretical analysis and numerical simulation validate the effectiveness of the proposed method.

Barrier Function-Based Neural Adaptive Control With Locally Weighted Learning and Finite Neuron Self-Growing Strategy

This paper presents a new approach to construct neural adaptive control for uncertain nonaffine systems. By integrating locally weighted learning with barrier Lyapunov function (BLF), a novel control design method is presented to systematically address the two critical issues in neural network (NN) control field: one is how to fulfill the compact set precondition for NN approximation, and the other is how to use varying rather than a fixed NN structure to improve the functionality of NN control. A BLF is exploited to ensure the NN inputs to remain bounded during the entire system operation. To account for system nonlinearities, a neuron self-growing strategy is proposed to guide the process for adding new neurons to the system, resulting in a self-adjustable NN structure for better learning capabilities. It is shown that the number of neurons needed to accomplish the control task is finite, and better performance can be obtained with less number of neurons as compared with traditional methods. The salient feature of the proposed method also lies in the continuity of the control action everywhere. Furthermore, the resulting control action is smooth almost everywhere except for a few time instants at which new neurons are added. Numerical example illustrates the effectiveness of the proposed approach.

Neural network-based distributed attitude coordination control for spacecraft formation flying with input saturation

This brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude. A quaternion-based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding-mode observer, separation principle theorem, Chebyshev neural networks, smooth projection algorithm, and robust control technique. Using graph theory and a Lyapunov-based approach, it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time-varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft. Numerical simulations are presented to demonstrate the performance of the proposed distributed controller.