Composite Learning Prescribed Performance Control of Nonlinear Systems

This paper investigates a composite learning prescribed performance control (PPC) scheme for uncertain strict-feedback system. Firstly, a prescribed performance boundary (PPB) condition is developed for the tracking error, and the original system is transformed into an equivalent one by using a transformation function. In order to ensure that the tracking error satisfies the PPB, a sufficient condition is given. Then, a control scheme of PPC combined with neural network (NN) and backstepping technique is proposed. However, the unknown functions cannot be guaranteed to estimate accurately by this method. To solve this problem, predictive errors are defined by applying online recorded date and instantaneous date. Furthermore, novel composite learning laws are proposed to update NN weights based on a partial persistent excitation (PE) condition. Subsequently, the stability of the closed-loop system is guaranteed and all signals are kept bounded by using composite learning PPC method. Finally, simulation results verify the effectiveness of the proposed methods.

Adaptive Parameter Estimation With Convergence Analysis for the Prandtl–Ishlinskii Hysteresis Operator

Hysteresis is a nonlinear characteristic ubiquitously exhibited by smart material sensors and actuators, such as piezoelectric actuators and shape memory alloys. The Prandtl–Ishlinskii (PI) operator is widely used to describe hysteresis of smart material systems due to its simple structure and the existence of analytical inverse. A PI operator consists of a weighted superposition of play (backlash) operators. While adaptive estimation of the weights for PI operators has been reported in the literature, rigorous analysis of parameter convergence is lacking. In this article, we establish persistent excitation and thus parameter convergence for adaptive weight estimation under a rather modest condition on the input to the PI operator. The analysis is further supported via simulation, where a recursive least square (RLS) method is adopted for parameter estimation.

A Hysteresis Dynamic Mathematical Model Approach to Parametric Estimation System

The main contribution of this paper is the proposal of a recent hysteresis dynamic model which is successfully employed within a posited signal modulator. The modulation of signals is a commonly required stage in many engineering applications, such as telecommunications, power electronics, and control, among others. In this paper, the effectiveness of a signal modulator based on the well-known Delta modulator when it contains a dynamic hysteresis system within its main structure is presented. To do that, it is resorted to an application of the granted Hysteresis-Delta Modulator. This application consists of including the modulator within an adaptive scheme, since it is well known that the persistent excitation condition is required, for instance, in parameter estimation tasks. Hence, the main functional property of the modulator with hysteresis is its ability of producing a modulated signal with uniform high-frequency content even when its input is not a permanent persistent excitation signal. To highlight the main contribution of this paper, a numerical experiment of a parameter estimation system is developed to compare the performance of the modulator with the proposed hysteresis model and two other previously reported hysteresis systems. That is, three different scenarios have been tested in the parameter estimation of a nonminimum phase system. Finally, the numerical experiments confirm that the proposed hysteresis model along with the modulator provides the best performance as expected.

Performance Analysis of Maximum Likelihood Estimation for Multiple Transmitter Locations

The paper considers the consistence condition of Maximum Likelihood (ML) estimation for multiple transmitter locations in a wireless network with cooperative receiver nodes. It is found that the location set of receiver nodes should not locate (or asymptotically in some sense) merely in an algebraic curve of order 2M −1 if there are totally M transmitters. A sufficient condition for consistence of the ML estimation for M transmitters is that the limit set of locations contains a subset, comprised of (2M2 −M +2) points, which is non-C-2M-co-curved, a notion given by Definition IV-B. This condition can be compared to the persistent excitation condition used to guarantee the convergence of least squares algorithm. Numerical experiments are designed to demonstrate the theoretical discoveries in both positive and negative aspects.