• Journal of Institute of Control, Robotics and Systems
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• v.19 no.9
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• pp.827-833
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• 2013

In this paper, an efficient computational method is presented for state space analysis of bilinear systems via Legendre wavelets. The differential matrix equation is converted to a generalized Sylvester matrix equation by using Legendre wavelets as a basis. First, an explicit expression for the inverse of the integral operational matrix of the Legendre wavelets is presented. Then using it, we propose a preorder traversal algorithm to solve the generalized Sylvester matrix equation, which greatly reduces the computation time. Finally the efficiency of the proposed method is discussed using numerical examples.

• The KIPS Transactions:PartD
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• v.13D no.1 s.104
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• pp.111-116
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• 2006

Given a state, it is essential to for the finite state model analysis (such as model checking) to decide whether or not the state is reachable. W a site of the model is small, the whole state space is to be explored exhaustively. However, it is very difficult or even impossible if a size of the model is large. In this case, the model can be reduced into a smaller one via abstraction which does not allow e false positive error. this paper, we devise such an abstraction and apply it to the Nemorize game solving. As a result, unsolved game due to the state explosion problem is solved with the proposed abstraction.

• The KIPS Transactions:PartD
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• v.12D no.1 s.97
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• pp.81-90
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• 2005

Given a model and a property, model checking determines whether the model satisfies the property. In case the model does not satisfy the property model checking gives a counterexample which explains where the violation occurs. Since counterexamples are useful for model debugging as well as model understanding, counterexample generation is one of the indispensable components in the model checking tool. This paper presents efficient counterexample generation techniques when a safety property is falsified. These techniques are used to solve Push Push games which consist of 50 games. As a result, all the games are solved with the proposed techniques. However, with the original NuSMV, 42 games are solved but 8 failed. In addition, we obtain $86{\%}$ time improvement and $62{\%}$ space improvement compared to the original NuSMV in solving the game.