Composite Learning Control With Application to Inverted Pendulums

Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However, the condition of persistent excitation (PE) still has to be satisfied to guarantee parameter convergence in CAC. This paper proposes a novel model reference composite learning control (MRCLC) strategy for a class of affine nonlinear systems with parametric uncertainties to guarantee parameter convergence without the PE condition. In the composite learning, an integral during a moving-time window is utilized to construct a prediction error, a linear filter is applied to alleviate the derivation of plant states, and both the tracking error and the prediction error are applied to update parametric estimates. It is proven that the closed-loop system achieves global exponential-like stability under interval excitation rather than PE of regression functions. The effectiveness of the proposed MRCLC has been verified by the application to an inverted pendulum control problem.Comment: 5 pages, 6 figures, conference submissio

Neural Network Observer-Based Finite-Time Formation Control of Mobile Robots

This paper addresses the leader-following formation problem of nonholonomic mobile robots. In the formation, only the pose (i.e., the position and direction angle) of the leader robot can be obtained by the follower. First, the leader-following formation is transformed into special trajectory tracking. And then, a neural network (NN) finite-time observer of the follower robot is designed to estimate the dynamics of the leader robot. Finally, finite-time formation control laws are developed for the follower robot to track the leader robot in the desired separation and bearing in finite time. The effectiveness of the proposed NN finite-time observer and the formation control laws are illustrated by both qualitative analysis and simulation results

Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems

This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order

Enhanced Adaptive Fuzzy Control With Optimal Approximation Error Convergence

In this paper, an enhanced adaptive fuzzy control (AFC) strategy with guaranteed convergence of an optimal fuzzy approximation error (FAE) is presented for a class of uncertain nonlinear systems in the general Brunovsky form. Based on the fuzzy logic system (FLS) with variable universes of discourse, relaxed sufficient conditions that guarantee the optimal FAE being convergent are given, and the upper bound of the optimal FAE is obtained. The control singularity problem resulting from the unknown affine term is resolved by a novel fuzzy approximation equation, and the parameter adaptive law of the FLS is derived by the Lyapunov synthesis. By means of the optimal FAE bound result, it is proved that the closed-loop system achieves partially asymptotic stability under a certain selection of control parameters. The proposed approach retains all advantages of a previous similar approach under relaxed constraint conditions. Thus, it provides a more flexible solution to the AFC with optimal FAE convergence. Simulation studies have demonstrated high-precision tracking performance with smooth control input of the proposed approach.ASTAR (Agency for Sci., Tech. and Research, S’pore