Skip to main content
Log in

Full analysis of the triple integrator problem

  • Determinate Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the full analysis of the problem of optimal control using the method of synthesizing variables. The problem of control was formulated as that with fixed ends of the trajectory of the phase coordinate vector, fixed time interval, and bounded control. The plant dynamics was described by the model of the triple integrator, the functional being the power consumption. The results obtained can be used in the real-time design of power-saving control actions in the control systems of plants whose dynamics obeys differential equations of the third order.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., et al., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1969.

    Google Scholar 

  2. Muromtsev, Yu. L., Lyapin, L.N., and Satina, E.V., Method of Synthesizing Variables for Optimal Control of Linear Plants, Izv. Vuzov, Prib., 1993, nos. 11, 12, pp. 19–25.

  3. Lyapin, L.N. and Muromtsev, Yu. L., Analysis and On-line Design of the Optimal Control in the Problem of Double Integrator on the Set of Operational States, Izv. Vuzov, Prib., 1990, no. 3, pp. 57–64.

  4. Muromtsev, D. Yu., Muromtsev, Yu. L., and Orlova, L.P., Design of Power-saving Control of Multi-stage Processes by a Combined Method, Avtom. Telemekh., 2002, no. 3, pp. 169–178.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 3–12.

Original Russian Text Copyright © 2005 by Kozlov, Muromtsev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozlov, A.I., Muromtsev, D.Y. Full analysis of the triple integrator problem. Autom Remote Control 66, 1–9 (2005). https://doi.org/10.1007/s10513-005-0001-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10513-005-0001-9

Keywords

Navigation