TAILIEUCHUNG - Model-Based Design for Embedded Systems- P art 16

Model-Based Design for Embedded Systems- P16:The unparalleled flexibility of computation has been a key driver and feature bonanza in the development of a wide range of products across a broad and diverse spectrum of applications such as in the automotive aerospace, health care, consumer electronics, etc. | 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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