### Abstract

This chapter presents optimal discrete-event supervisory control of robot behavior in terms of the language measure μ, presented in Chapter 1. In the discrete-event setting, a robot's behavior is modelled as a regular language that can be realized by deterministic finite state automata (DFSA). The controlled sublanguage of a DFSA plant model could be different under different supervisors that are constrained to satisfy different specifications [6]. Such a partially ordered set of sublanguages requires a quantitative measure for total ordering of their respective performance. The language measure [10] [8] serves as a common quantitative tool to compare the performance of different supervisors and is assigned an event cost matrix, known as the-matrix and a state characteristic vector, X-vector. Event costs (i.e., elements of the-matrix) are based on the plant states, where they are generated; on the other hand, the X-vector is chosen based on the designer's perception of the individual state's impact on the system performance. The elements of the-matrix are conceptually similar to the probabilities of the respective events conditioned on specific states; these parameters can be identified either from experimental data or from the results of extensive simulation, as they are dependent on physical phenomena related to the plant behavior. Since the plant behavior is often slowly time-varying, there is a need for on-line parameter identification to generate up-to-date values of the-matrix within allowable bounds of errors. The results of simulation experiments on a robotic test bed are presented to demonstrate efficacy of the proposed optimal control policy.

Original language | English (US) |
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Title of host publication | Quantitative Measure for Discrete Event Supervisory Control |

Publisher | Springer New York |

Pages | 157-181 |

Number of pages | 25 |

ISBN (Print) | 0387021086, 9780387021089 |

DOIs | |

State | Published - Dec 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)

### Cite this

*Quantitative Measure for Discrete Event Supervisory Control*(pp. 157-181). Springer New York. https://doi.org/10.1007/0-387-23903-0_6

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*Quantitative Measure for Discrete Event Supervisory Control.*Springer New York, pp. 157-181. https://doi.org/10.1007/0-387-23903-0_6

**Optimal control of robot behavior using language measure.** / Wang, Xi; Ray, Asok; Lee, Peter; Fu, Jinbo.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Optimal control of robot behavior using language measure

AU - Wang, Xi

AU - Ray, Asok

AU - Lee, Peter

AU - Fu, Jinbo

PY - 2005/12/1

Y1 - 2005/12/1

N2 - This chapter presents optimal discrete-event supervisory control of robot behavior in terms of the language measure μ, presented in Chapter 1. In the discrete-event setting, a robot's behavior is modelled as a regular language that can be realized by deterministic finite state automata (DFSA). The controlled sublanguage of a DFSA plant model could be different under different supervisors that are constrained to satisfy different specifications [6]. Such a partially ordered set of sublanguages requires a quantitative measure for total ordering of their respective performance. The language measure [10] [8] serves as a common quantitative tool to compare the performance of different supervisors and is assigned an event cost matrix, known as the-matrix and a state characteristic vector, X-vector. Event costs (i.e., elements of the-matrix) are based on the plant states, where they are generated; on the other hand, the X-vector is chosen based on the designer's perception of the individual state's impact on the system performance. The elements of the-matrix are conceptually similar to the probabilities of the respective events conditioned on specific states; these parameters can be identified either from experimental data or from the results of extensive simulation, as they are dependent on physical phenomena related to the plant behavior. Since the plant behavior is often slowly time-varying, there is a need for on-line parameter identification to generate up-to-date values of the-matrix within allowable bounds of errors. The results of simulation experiments on a robotic test bed are presented to demonstrate efficacy of the proposed optimal control policy.

AB - This chapter presents optimal discrete-event supervisory control of robot behavior in terms of the language measure μ, presented in Chapter 1. In the discrete-event setting, a robot's behavior is modelled as a regular language that can be realized by deterministic finite state automata (DFSA). The controlled sublanguage of a DFSA plant model could be different under different supervisors that are constrained to satisfy different specifications [6]. Such a partially ordered set of sublanguages requires a quantitative measure for total ordering of their respective performance. The language measure [10] [8] serves as a common quantitative tool to compare the performance of different supervisors and is assigned an event cost matrix, known as the-matrix and a state characteristic vector, X-vector. Event costs (i.e., elements of the-matrix) are based on the plant states, where they are generated; on the other hand, the X-vector is chosen based on the designer's perception of the individual state's impact on the system performance. The elements of the-matrix are conceptually similar to the probabilities of the respective events conditioned on specific states; these parameters can be identified either from experimental data or from the results of extensive simulation, as they are dependent on physical phenomena related to the plant behavior. Since the plant behavior is often slowly time-varying, there is a need for on-line parameter identification to generate up-to-date values of the-matrix within allowable bounds of errors. The results of simulation experiments on a robotic test bed are presented to demonstrate efficacy of the proposed optimal control policy.

UR - http://www.scopus.com/inward/record.url?scp=84889769344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889769344&partnerID=8YFLogxK

U2 - 10.1007/0-387-23903-0_6

DO - 10.1007/0-387-23903-0_6

M3 - Chapter

AN - SCOPUS:84889769344

SN - 0387021086

SN - 9780387021089

SP - 157

EP - 181

BT - Quantitative Measure for Discrete Event Supervisory Control

PB - Springer New York

ER -