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.

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.

An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems.

This paper investigates the problem of stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov-Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T-S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.

Cooperative tracking control of nonlinear multiagent systems using self-structuring neural networks.

This paper considers a cooperative tracking problem for a group of nonlinear multiagent systems under a directed graph that characterizes the interaction between the leader and the followers. All the networked systems can have different dynamics and all the dynamics are unknown. A neural network (NN) with flexible structure is used to approximate the unknown dynamics at each node. Considering that the leader is a neighbor of only a subset of the followers and the followers have only local interactions, we introduce a cooperative dynamic observer at each node to overcome the deficiency of the traditional tracking control strategies. An observer-based cooperative controller design framework is proposed with the aid of graph tools, Lyapunov-based design method, self-structuring NN, and separation principle. It is proved that each agent can follow the active leader only if the communication graph contains a spanning tree. Simulation results on networked robots are provided to show the effectiveness of the proposed control algorithms.

H∞ model reduction of Takagi-Sugeno fuzzy stochastic systems.

This paper is concerned with the problem of H(∞) model reduction for Takagi-Sugeno (T-S) fuzzy stochastic systems. For a given mean-square stable T-S fuzzy stochastic system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with an H(∞) performance but also translates it into a linear lower dimensional system. Then, the model reduction is converted into a convex optimization problem by using a linearization procedure, and a projection approach is also presented, which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

This paper investigates the position and velocity tracking control problem of high-speed trains with multiple vehicles connected through couplers. A dynamic model reflecting nonlinear and elastic impacts between adjacent vehicles as well as traction/braking nonlinearities and actuation faults is derived. Neuroadaptive fault-tolerant control algorithms are developed to account for various factors such as input nonlinearities, actuator failures, and uncertain impacts of in-train forces in the system simultaneously. The resultant control scheme is essentially independent of system model and is primarily data-driven because with the appropriate input-output data, the proposed control algorithms are capable of automatically generating the intermediate control parameters, neuro-weights, and the compensation signals, literally producing the traction/braking force based upon input and response data only--the whole process does not require precise information on system model or system parameter, nor human intervention. The effectiveness of the proposed approach is also confirmed through numerical simulations.