APL, dynamic programming, and the optimal control of electromagnetic brake retarders

ABSTRACT

The basis of dynamic programming is described. It is a method for finding the best way to control a system when that system can be controlled by its inputs. As an example, the optimal (or best) control of an electromagnetic brake retarder is derived. In this example the current to the brake retarder is the input being controlled. APL is shown to be a convenient language for writing a dynamic programming algorithm. A set of APL subroutines is provided for solving two-dimensional problems with one input. Adept APL programmers may enjoy the challenge of generalizing this code to problems of arbitrary dimensions.

REFERENCES

• 1: Richard Ernest Bellman, Dynamic Programming, Dover Publications, Incorporated, 2003
• 2: William H. Press , Brian P. Flannery , Saul A. Teukolsky , William T. Vetterling, Numerical recipes: the art of scientific computing, Cambridge University Press, New York, NY, 1986
• 3: Kirk, D. Optimal Control Theory, An Introduction, Prentice Hall, 1970.
• 4: Kimbrough, S. Optimal Control of Electromagnetic Brake Retarders, SAE Paper 942325, 1994 SAE Truck and Bus Conference.

INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.8 Problem Solving, Control Methods, and Search
          Subjects: Dynamic programming
  I.6 SIMULATION AND MODELING

  J. Computer Applications
  J.7 COMPUTERS IN OTHER SYSTEMS
      Subjects: Command and control

General Terms:
Algorithms, Languages, Performance

Keywords:
APL, dynamic programming, electromagnetic brake, optimal control