Interactive Generator of Commands
The analytical model of generator of commands (command generator, CG) to swarm system, based on description of an interactive dialogue between a human operator and computer, is worked out. The model is based on the fundamental theory of semi-Markov proces
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Tula State University, Tula 300012, Russia [email protected], [email protected], [email protected] 2 Tula State Pedagogical University, Tula 300026, Russia [email protected]
Abstract. The analytical model of generator of commands (command generator, CG) to swarm system, based on description of an interactive dialogue between a human operator and computer, is worked out. The model is based on the fundamental theory of semi-Markov process, in particular, on the theory of the ordinary and the 2-parallel semi-Markov processes. In CG under investigation an interactive algorithm is represented as the sequence of 2-parallel processes, which are associated to simple ergodic semi-Markov process, some states of which generate commands to swarm system. Formulae for time characteristics of flow of command to swarm system with use time and stochastic characteristics of elementary actions of human operator and time and stochastic characteristics of operators of computer algorithm are obtained. Keywords: Human operator · Computer · Command generator · Interactive dialogue · Semi-Markov process · Time characteristics · Stochastic characteristics
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Introduction
One of features of physical swarm systems is lack of intelligence, that does not allow construct fully autonomous units, which can operate automatically taking into account only his aim task and an environment state [1]. Due to the fact in the near future dominant solution will be remote control of swarm wherein a human operator within the guidelines and control practice will be interact with computer. As a result of dialogue will be formed flow of commands to swarm units. Both the human operator and the computer operate due their own algorithm every elementary operation of which is executed during an occasional time, and result of execution is occasional too. So, natural and most common approach to modeling of occasional sequence of changing states in time both human and computer is so-called 2-parallel semi-Markov process [2–5]. This approach allows at the preparation of activity both human and computer to logically completed fragments to evaluate time and stochastic characteristics of command generator and further to study behavior of swarm under flow of command with determined characteristics. c Springer International Publishing Switzerland 2016 Y. Tan et al. (Eds.): ICSI 2016, Part II, LNCS 9713, pp. 601–608, 2016. DOI: 10.1007/978-3-319-41009-8 65
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E. Larkin et al.
Command Generator
Structure of semi-Markov process, which simulates interactive CG, is shown on Fig. 1. Model consists of J(β) simplest 2-parallel semi-Markov processes, every of which includes states {aj(β,1) , aj(β,2) , bj(β,1) , bj(β,2) }, 1(β) ≤ j(β) ≤ J(β) and is described by: adjacency matrix ⎡ ⎤ 0100 ⎢0 0 0 0⎥ 2 ⎥ (1) r j(β) = ⎢ ⎣0 0 1 0⎦, 0000 and semi-Markov matrix
⎡
⎤ 0 fa[j(β)] (t) 0 0 ⎢0 0 0 0⎥ 2 ⎥, h j(β) (t) = ⎢ ⎣0 0 fb[j(β)] (t) 0 ⎦ 0 0 0 0
(2)
where fa[j(β)] (t) — is density of time of residence the process in state aj(β,1) till its switch to state aj(β,2) ; fb[j(β)] (t)
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