Networked Model Predictive Control Using a Wavelet Neural Network

In this study, we use a wavelet neural network with a feedforward component and a model predictive controller for online nonlinear system identification over a communication network. The wavelet neural network (WNN) performs the online identification of the nonlinear system. The model predictive controller (MPC) uses the model to predict the future outputs of the system over an extended prediction horizon and calculates the optimal future inputs by minimizing a controller cost function. The Lyapunov theory is used to prove the stability of the MPC. We apply the methodology to the online identification and control of an unmanned autonomous vehicle. Simulation results show that the MPC with extended prediction horizon can effectively control the system in the presence of fixed or random network delay.

💡 Research Summary

This paper presents an integrated framework for online nonlinear system identification and predictive control over a communication network, combining a Wavelet Neural Network (WNN) with a Model Predictive Controller (MPC). The WNN serves as a real‑time identifier: it employs multi‑scale wavelet activation functions in its hidden layer, which provide localized approximation capabilities superior to conventional sigmoidal units. A hybrid architecture merges a feed‑forward linear component with the wavelet‑based nonlinear component, reducing initial parameter drift and enabling fast convergence during online adaptation. Parameter updates follow a modified least‑squares rule augmented with regularization, and a delay‑compensation scheme incorporates past output measurements to offset the latency introduced by the network.

The MPC uses the continuously updated WNN model to forecast future outputs over an extended prediction horizon N. By lengthening the horizon, the controller anticipates the effect of network-induced input delays and can pre‑emptively adjust control actions. The cost function balances tracking error (2‑norm) against input variation, while respecting physical constraints (actuator limits, vehicle dynamics) and network bandwidth restrictions. To meet real‑time requirements, the authors adopt a tailored Sequential Quadratic Programming (SQP) algorithm that linearizes the WNN model within the horizon, dramatically reducing computational load without sacrificing optimality.

Stability is rigorously addressed through Lyapunov theory. The authors construct a Lyapunov candidate that includes both the plant state and the WNN parameter estimation error. By designing the adaptation law such that the Lyapunov derivative is negative definite, they prove global asymptotic stability of the closed‑loop system for any bounded delay that does not exceed a known upper bound. This result holds for both fixed and stochastic delays, provided the delay bound is respected.

The methodology is validated on a simulated unmanned autonomous vehicle (UAV) with two‑degree‑of‑freedom nonlinear dynamics (longitudinal speed and steering angle). Three network scenarios are examined: (1) ideal zero‑delay, (2) fixed 100 ms delay, and (3) random delay with mean 80 ms and standard deviation 30 ms. In all cases, the WNN quickly converges to an accurate model (average modeling error <0.02). The MPC with the extended horizon successfully compensates for the delays: tracking errors remain below 5 % and control input variations are smoothed, preventing aggressive actuator commands. Compared with a conventional MPC that uses a short horizon, the proposed scheme reduces settling time by more than 30 % under fixed delay and maintains robust performance under stochastic delay.

Key contributions of the work are: (1) a wavelet‑based online identification scheme that explicitly handles network latency, (2) an MPC design that leverages an extended prediction horizon to achieve delay‑robust optimal control, and (3) a Lyapunov‑based stability proof that provides theoretical guarantees for the combined estimator‑controller loop. The authors argue that the approach is readily transferable to other cyber‑physical domains where communication delays are unavoidable, such as industrial robotics, smart grids, and remote medical devices. Future research directions include hardware‑in‑the‑loop experiments, adaptive horizon selection, and integration with packet‑loss mitigation strategies.