TAILIEUCHUNG - Model-Based Design for Embedded Systems- P46

Model-Based Design for Embedded Systems- P46: This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. | 426 Model-Based Design for Embedded Systems FIGURE Results obtained using gRRT a and hRRT b with the same number of visited states. Suppose that we have sampled a discrete state qgoal q. Since all the staying sets are boxes the staying set Iq is denoted by the box B and called the bounding box. As mentioned earlier the coverage estimation is done using a box partition of the state space B and sampling of a continuous goal state can be done by two steps first sample a goal box bgoal from the partition second uniformly sample a point Vgoal in bgoal. Guiding is thus done in the goal box sampling process by defining at each iteration of the test generation algorithm a probability distribution over the set of the boxes in the partition. Essentially we favor the selection of a box if adding a new state in this box allows to improve the coverage of the visited states. This is captured by a potential influence function which assigns to each elementary box b in the partition a real number that reflects the change in the coverage if a new state is added in b. The current coverage estimation is given in form of a lower and an upper bound. In order to improve the coverage both the lower and the upper bounds need to be reduced see more details in 32 . The hRRT algorithm for hybrid automata in which the goal state sampling is done using this coverage-guided method is now called the gRRT algorithm which means guided hRRT . To illustrate the coverageefficiency of gRRT Figure shows the results obtained by the hRRT and the gRRT on a linear system after 50 000 iterations. We can see that the gRRT algorithm has a better coverage result. Indeed with the same number of states the states visisted by the gRRT are more equi-distributed over the reachable set than those visisted by hRRT. These algorithms were implemented in the prototype tool HTG which was successfully applied to treat a number of benchmarks in control applications and in analog and mixed-signal circuits 31 79 .

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