Positive Nonlinear Systems Synthesis Based on Optimal Control Methods

Abstract

This paper considers a nonlinear positive control system of autonomous intellectual agent’s motions. Single or multiple intellectual agents are capable of independent decision-making to achieve an odor source or radioactive source. Various biologically inspired behaviour-based approaches, such as chemotaxis, the moth inspired casting algorithm, flocking behavior and foraging, population development or species interaction are used for creation of control system of an intellectual agent. The agent is a tracking system, for example, unmanned aerial vehicle or a multicopter. The intellectual agent searches hazardous pollutants in dangerous environments. The task of a flying robot is to find the source of invisible pollutions. The aim of this work is to synthesize the control law, that provides a predetermined degree of exponential stability in a closed-loop positive system based on Lotka—Volterra equations. The methods of optimal control theory are used in the synthesis of the system. Asymptotic stability is achieved by solving the Riccati equation. The stability of the control system is an important criterion of quality to be ensured. Therefore, the intellectual agent is able to control the movements to the right and to the left, reaching the source. With the model proposed we provide the simulation and experimental results, which correspond to the quality metrics required. In this work, the control system has a given degree of exponential stability and the transient response, which confirms the possibility of using the model proposed in terrestrial mobile robots, unmanned aerial vehicles, autonomous underwater vehicles and other robots in searching a large area.