Sampled Closed-Loop Control In Multi-Controller Multi-Objective Control Systems

Abstract

In this paper, we consider control systems that are controlled by multiple controllers each having its own objective function. The Nash and leader-follower Stackelberg options for designing the controls are considered. These control options are heavily used as decision options in non-zero sum differential game theory. In order to reap many of the benefits of feedback, the resulting designs are best implemented as closed-loop controls. However, closed-loop controls require continuous measurements of the system's state vector, which may be expensive or even impossible in many cases. As an alternative, in this paper we consider a sampled closed-loop implementation. Such an implementation requires measurements of the state vector only at pre-specified instants of time, and hence is much more practical and cost effective when compared to the continuous closed-loop implementation. We derive the necessary conditions for the general linear quadratic problem and develop the solutions for the Nash and Stackelberg controls in detail for the scalar case. An example of a control system with two controllers and state measurements available at integer multiples of 10% of the total interval of control is presented to illustrate the results.

Publication Date

10-1-2018

Publication Title

Conference Proceedings - IEEE SOUTHEASTCON

Volume

2018-April

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/SECON.2018.8478971

Socpus ID

85056076848 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85056076848

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