Control Strategies for Multi-Controller Multi-Objective Systems

This dissertation\u27s focus is control systems controlled by multiple controllers, each having its own objective function. The control of such systems is important in many practical applications such as economic systems, the smart grid, military systems, robotic systems, and others. To reap the benefits of feedback, we consider and discuss the advantages of implementing both the Nash and the Leader-Follower Stackelberg controls in a closed-loop form. However, closed-loop controls require continuous measurements of the system\u27s state vector, which may be expensive or even impossible in many cases. As an alternative, we consider a sampled closed-loop implementation. Such an implementation requires only the state vector measurements at pre-specified instants of time and hence is much more practical and cost-effective compared to the continuous closed-loop implementation. The necessary conditions for existence of such controls are derived for the general linear-quadratic system, and the solutions developed for the Nash and Stackelberg controls in detail for the scalar case. To illustrate the results, an example of a control system with two controllers and state measurements available at integer multiples of 10% of the total control interval is presented. While both Nash and Stackelberg are important approaches to develop the controls, we then considered the advantages of the Leader-Follower Stackelberg strategy. This strategy is appropriate for control systems controlled by two independent controllers whose roles and objectives in terms of the system\u27s performance and implementation of the controls are generally different. In such systems, one controller has an advantage over the other in that it has the capability of designing and implementing its control first, before the other controller. With such a control hierarchy, this controller is designated as the leader while the other is the follower. To take advantage of its primary role, the leader\u27s control is designed by anticipating and considering the follower\u27s control. The follower becomes the sole controller in the system after the leader\u27s control has been implemented. In this study, we describe such systems and derive in detail the controls of both the leader and follower. In systems where the roles of leader and follower are negotiated, it is important to consider each controller\u27s leadership property. This property considers the question for each controller as to whether it is preferable to be a leader and let the other controller be a follower or be a follower and let the other controller be the leader. In this dissertation, we try to answer this question by considering two models, one static and the other dynamic, and illustrating the results with an example in each case. The final chapter of the dissertation considers an application in microeconomics. We consider a dynamic duopoly problem, and we derive the necessary conditions for the Stackelberg solution with one firm as a leader controlling the price in the marke