Skip to main content
SpringerLink
Log in

Optimal input sets for time minimality in quantized control systems

  • Published:
Mathematics of Control, Signals and Systems Aims and scope Submit manuscript

Abstract

Limited capacity of communication channels has brought to the attention of many researchers the analysis of control systems subject to a quantized input set. In some fundamental cases such systems can be reduced to quantized control system of type x +=x+u, where the u takes values in a set of 2m+1 integer numbers, symmetric with respect to 0. In this paper we consider these types of systems and analyse the reachable set after K steps. Our aim is to find a set of m input values such that the reachable set after K steps contains an interval of integers [−N, . . . , N] with N as large as possible. For m=2,3 and 4, we completely solve the problem and characterize the metric associated to this quantized control system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Chapter © 2015

References

  1. Marigo A, Bicchi A, Piccoli B (2003) Encoding steering control with symbols. In: Proceedings of the IEEE international conference on decision and control

  2. Bicchi A, Chitour Y, Marigo A (2004) Reachability and steering of rolling polyhedra: a case study in discrete nonholonomy. IEEE Trans Automat Control 49(5):710–726

    Google Scholar 

  3. Bicchi A, Marigo A, Piccoli B (2002) On the reachability of quantized control systems. IEEE Trans Automat Control 47(4):546–563

    Google Scholar 

  4. Brockett R, Liberzon D (2000) Quantized feedback stabilization of linear systems. IEEE Trans Automat Control 45(7):1279–1289

    Google Scholar 

  5. Chitour Y, Piccoli B (2001) Controllability for discrete systems with a finite control set. Math Control Signals Syst 14(2):173–193

    Google Scholar 

  6. Delchamps DF (1989) Extracting state information from a quantized output record. Syst Control Lett 13:365–371

    Google Scholar 

  7. Delchamps DF (1990) Stabilizing a linear system with quantized state feedback. IEEE Trans Automat Control 35(8):916–926

    Google Scholar 

  8. Elia N, Mitter S (2001) Stabilization of linear systems with limited information. IEEE Trans Automat Control 46(9):1384–1400

    Google Scholar 

  9. Guy R (2004) Unsolved problems in number theory. Springer, Berlin Heidelberg, New York

  10. Marigo A, Bicchi A (1998) Steering driftless nonholonomic systems by control quanta. In: Proceedings of the IEEE international conference on decision and control

  11. Pancanti S, Leonardi L, Pallottino L, Bicchi A (2002) Optimal control of quantized input systems. In: Tomlin C, Greenstreet M (eds) Hybrid systems: computation and control, vol LNCS 2289 of lecture notes in computer science, pp 351–363. Springer, Berlin Heidelberg, New York

  12. Chitour Y, Marigo A, Prattichizzo D, Bicchi A (1996) Rolling polyhedra on a plane, analysis of the reachable set. In: Workshop on algorithmic foundations of robotics

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “La Sapienza”, P. Aldo Moro 2, 00185, Roma, Italy

    Alessia Marigo

Authors
  1. Alessia Marigo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessia Marigo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marigo, A. Optimal input sets for time minimality in quantized control systems. Math. Control Signals Syst. 18, 101–146 (2006). https://doi.org/10.1007/s00498-005-0156-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00498-005-0156-5

Keywords

Search

Navigation