Hierarchical Control of Linear Systems from the Abstraction Feedback Gain
Authors: 
Yang Kaihong, Ji HaiboAuthors Info & Claims
Yang Kaihong, Ji HaiboAuthors Info & ClaimsAbstract
In this paper, the problem of hierarchical control for a class of linear systems is addressed. Given a large-scale linear system, we obtain a stabilizing feedback gain for it from that of an abstract system. And then, we employ this feedback gain to design a new interface between the original system and the abstraction. Furthermore, the synthesis of the new interface can be allowed by a new simulation function characterized by a low-order matrix associated to the abstraction. Finally, an example is given to illustrate the proposed approach.
References
[1]
Girard A. and G. J.Pappas, "Hierarchical control system design using approximate simulation," Automatica, Vol. Volume 45, No. Issue 2, pp. pp.566-5712009.
[2]
Tang Y. and Y.Hong, "Hierarchical distributed control design for multi-agent systems using approximate simulation," Acta Automatica Sinica, Vol. Volume 39, No. Issue 6, pp. pp.868-8742013.
[3]
Tabuada P. and G. J.Pappas, "Hierarchical trajectory refinement for a class of nonlinear systems," Automatica, Vol. Volume 41, No. Issue 4, pp. pp.701-7082005.
[4]
Fu J., S.Shah, and H. G.Tanner, "Hierarchical control via approximate simulation and feedback linearization," Amer. Control Conf., Washington, DC, pp. pp.1816-18212013.
[5]
Fainekos G. E., A.Girard, H.Kress-Gazit, and G. J.Pappas, "Temporal logic motion planning for dynamic robots," Automatica, Vol. Volume 45, No. Issue 2, pp. pp.343-3522009.
[6]
Girard A. and G. J.Pappas, "Approximate hierarchies of linear control systems," Proc. IEEE Conf. Decis. Control, New Orleans, LA, pp. pp.3727-37322007.
[7]
Caines P. E. and Y.-J.Wei, "Hierarchical hybrid control systems: A lattice theoretic formulation," IEEE Trans. Autom. Control, Vol. Volume 43, No. Issue 4, pp. pp.501-5081998.
[8]
Girard A. and G. J.Pappas, "Approximation metrics for discrete and continuous systems," IEEE Trans. Autom. Control, Vol. Volume 52, No. Issue 5, pp. pp.782-7982007.
[9]
Tabuada P., "An approximate simulation approach to symbolic control," IEEE Trans. Autom. Control, Vol. Volume 53, No. Issue 6, pp. pp.1406-14182008.
[10]
Girard A. and G. J.Pappas, "Approximate bisimulation: A bridge between computer science and control theory," Eur. J. Control, Vol. Volume 17, No. Issue 5, pp. pp.568-5782011.
[11]
Grasse K. A., "A connection between simulation relations and feedback transformations in nonlinear control systems," Syst. Control Lett., Vol. Volume 61, No. Issue 5, pp. pp.631-6372012.
[12]
Colombo A. and A.Girard, "An approximate abstraction approach to safety control of differentially flat systems," Eur. Control Conf., Zurich, Switzerland, pp. pp.4226-42312013.
[13]
Girard A., "Controller synthesis for safety and reachability via approximate bisimulation," Automatica, Vol. Volume 48, No. Issue 5, pp. pp.947-9532012.
[14]
Girard A. and G. J.Pappas, "Hierarchical control using approximate simulation relations," In Proc. IEEE Conf. Decis. Control, San Diego,CA, pp. pp.264-2692006.
[15]
Pappas G. J., G.Lafferriere, and S.Sastry, "Hierarchically consistent control systems," IEEE Trans. Autom. Control, Vol. Volume 45, No. Issue 6, pp. pp.1144-11602000.
[16]
Pappas G. J. and S.Simic, "Consistent abstractions of affine control systems," IEEE Trans. Autom. Control, Vol. Volume 47, No. Issue 5, pp. pp.745-7562002.
[17]
Antoulas A. C., D. C.Sorensen, and S.Gugercin, "A survey of model reduction methods for large-scale systems," Contemp. Math., Vol. Volume 280, pp. pp.193-2202001.
[18]
Antoulas A. C., Approximation of Large-Scale Dynamical Systems, Siam, Houston, TX, 2005.
[19]
Girard A. and G. J.Pappas, "Approximate bisimulation relations for constrained linear systems," Automatica, Vol. Volume 43, No. Issue 8, pp. pp.1307-13172007.
[20]
Yang K. and H.Ji, "Design of the interfaces based on approximate hierarchies," Chinese Control Conf., Nanjing, China, pp. pp.3483-34882014.
[21]
Yang K. and H.Ji, "Hierarchical control of a class of high-dimensional linear systems," Acta Automatica Sinica, Vol. Volume 41, No. Issue 1, pp. pp.176-1792015. in Chinese.
[22]
Besselink B., "Model reduction for nonlinear control systems: with stability preservation and error bounds," PhD thesis, Technische Universiteit, Eindhoven, 2012.
[23]
Pappas G. J. and G.Lafferriere, "Hierarchies of stabilizability preserving linear systems," Proc. IEEE Conf. Decis. Control, pp. pp.2081-20862001.
[24]
Lofberg J., "Yalmip: A toolbox for modeling and optimization in matlab," Int. Symp. Comp. Aided Control Syst. Design, Taipei, Taiwan, pp. pp.284-2892004.
Recommendations
Brief paper: Hierarchical control system design using approximate simulation
In this paper, we present a new approach for hierarchical control based on the recent notions of approximate simulation and simulation functions, a quantitative version of the simulation relations. Given a complex system that needs to be controlled and ...
Multi-level hierarchical interface-based supervisory control
Hierarchical Interface-Based Supervisory Control employs interfaces that allow properties of a monolithic system to be verified through local analysis. By avoiding the need to verify properties globally, significant computational savings can be ...
SES extension to integrate abstraction hierarchy into DEVS modeling and simulation
DEVS '15: Proceedings of the Symposium on Theory of Modeling & Simulation: DEVS Integrative M&S SymposiumThe modeling and simulation (M&S) of complex systems often requires models described at different levels of abstraction. The system entity structure (SES) represents a design space via the elements of a system and their relationships in hierarchical and ...
Comments
Information & Contributors
Information
Published In
Publisher
John Wiley & Sons, Inc.
United States
Publication History
Published: 01 November 2016
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 30 Aug 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in