Cooperative control of multi-agent system under time delay

Abstract

In this Ph.D. dissertation, multi-agent systems are studied in detail using two of the most common examples in practice, which are vehicle platooning systems and formation control of unmanned aerial vehicles. For a better understanding of the study, some basic information such as graph theory, matrix theory, and time-delayed systems are given. Then, the "Cluster Treatment of Characteristic Roots" paradigm, which forms the backbone of the study, is explained, and the existing methods in the literature have been explained. In this study, a new Bezout Resultant matrix-based CTCR method has been proposed, and the steps of the algorithm are explained via simulation examples in detail. The main advantage of the proposed method is that it provides computational convenience for the time-delayed systems in which the degree of characteristic equation is relatively large and not decomposed into factors in obtaining the stability posture of the system in terms of time delay. First, the distributed controller algorithm is selected as the state feedback controller. The closed-loop system matrix is constructed for the cases with and without time delay. The controller coefficients that make the system stable are obtained by using the Routh table and Lyapunov-based methods for the case where the time delay is neglected. However, in the presence of delay, the system is converted into retarded time delay system, and the stability posture is obtained with CTCR methods for single and multiple time delays. Morover, the formation geometry between vehicles is considered as constant policy and constant headway policy. For constant policy, the characteristic equation of the system for delayless and single time delay case, is decomposed into factors, which makes the stability analysis easier. But, this case is not possible for the characteristic equation involved multiple time delay, which direct us to utilize Bezout Resultant matrix-based CTCR method. For constant time headway policy, it is seen that, the characteristic equation cannot decomposed into factors for any cases. So, the sufficient condition is derived for determining the stability of multi-agent system for delay-free case with converted the system matrix to block companion form and block Schwarz form. Then, a PID controller based distributed controller protocol is proposed. The cooperative control problem of multi-agent system with distributed PID controller is converted into an asymptotic stability problem through matrix and state transformations in the absense of time delay. Finally, a Lyapunov function is created and the controller parameters are choosen with the help of linear matrix inequality. In the presence of time delay, the closed-loop system is converted into a neutral-type time delay system. And, the stability posture of the multi-agent system is obtained with the help of Kronecker multiplication and elementary transformation based CTCR method. Finally, all the theoretical studies and simulation results are evaluated with a real-time experimental study. An industrial controller-based real-time simulation for the platoon system with five connected vehicle including a virtual leader is proposed. The constant time headway policy is selected to modeled the desired inter-vehicle distance and the vehicle dynamic states-based distributed control strategy is used to converge to their desired velocities and inter-vehicle distances. Then the multi-agent platooning control problem is converted into LTI system stability analysis problem. The delay-based stability analysis is studied by means of Bezout Resultant matrix-based CTCR method. Numerical simulations are provided to verify the validity of the proposed method. The real-time experiments are carried out on industrial computers to show the applicability of the proposed method in real time systems. The study concluded by evaluating the results and recommendations.