Schrödinger equations for constructing infinite time horizon optimal regulators

Yuki Nishimura, Kanya Tanaka, Yuji Wakasa, Yuh Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we propose a new method for constructing approximate value functions for nonlinear optimal regulator problems with infinite time horizons. We consider a canonical quantization, which is an operation to change classical mass systems to quantum mass systems. First, we apply the canonical quantization to mass systems equivalent to the optimal regulator systems. Second, we construct approximate optimal regulators by using the canonical quantized mass systems. Third, we clarify the conditions under which approximate solutions converge to the strict solutions. In addition, we demonstrate some examples with one-dimensional systems.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
Publication statusPublished - 1 Jan 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670


  • Maximum principle
  • Nonlinear control systems
  • Optimal regulators

Cite this

Nishimura, Y., Tanaka, K., Wakasa, Y., & Yamashita, Y. (2011). Schrödinger equations for constructing infinite time horizon optimal regulators. In Proceedings of the 18th IFAC World Congress (1 PART 1 ed., pp. 8058-8063). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 44, No. 1 PART 1). IFAC Secretariat.