# A distributed penalty-based zeroing neural network for time-varying optimization with both equality and inequality constraints and its application to cooperative control of redundant robot manipulators

## TL;DR

This paper introduces a new neural network algorithm for solving time-varying optimization problems in multi-agent systems, with applications to robot control.

## Contribution

A novel distributed penalty-based zeroing neural network is proposed for time-varying constrained optimization in multi-agent systems.

## Key findings

- The PB-ZNN model achieves consensus and constraint satisfaction in a semi-centralized manner.
- The DPB-ZNN algorithm solves discrete-time problems in a fully distributed way with proven convergence.
- Numerical experiments confirm the algorithm's effectiveness in cooperative robot manipulator control.

## Abstract

This study addresses the distributed optimization problem with time-varying objective functions and time-varying constraints in a multi-agent system (MAS). To tackle the distributed time-varying constrained optimization (DTVCO) problem, each agent in the MAS communicates with its neighbors while relying solely on local information, such as its own objective function and constraints, to compute the optimal solution. We propose a novel penalty-based zeroing neural network (PB-ZNN) to solve the continuous-time DTVCO (CTDTVCO) problem. The PB-ZNN model incorporates two penalty functions: The first penalizes agents for deviating from the states of their neighbors, driving all agents to reach a consensus, and the second penalizes agents for falling outside the feasible range, ensuring that the solutions of all agents remain within the constraints. The PB-ZNN model solves the CTDTVCO problem in a semi-centralized manner, where information exchange between agents is distributed, but computation is centralized. Building on the semi-centralized PB-ZNN model, we adopt the Euler formula to develop a distributed PB-ZNN (DPB-ZNN) algorithm for solving the discrete-time DTVCO (DTDTVCO) problem in a fully distributed manner. We present and prove the convergence theorems of the proposed PB-ZNN model and DPB-ZNN algorithm. The efficacy and accuracy of the DPB-ZNN algorithm are illustrated through numerical examples, including a simulation experiment applying the algorithm to the cooperative control of redundant manipulators.