Modelica Hybrid Reactive Design Semantics Sample Clauses

Modelica Hybrid Reactive Design Semantics solve(I j ∧ Qj ∧ Aj) ; cpre :=R c ; µ X • ([D ∧ |Aj| ∧ q ← q]H ▲ ((¬T ) ∧ inv(Z ) | T ∨ exit(Z )) ; until (c = cpre) do cpre :=R c ; solve(dj = d ∧ Aj ∧ Qj) od ; interleave(R) ; cpre :=R c ; X ) . a d where inv(Z ) ¾ ((zj > −s) z ≥ 0 (zj < s)) . a d z∈Z exit(Z ) ¾ ((zj < 0) z ≥ 0 (zj > 0)) z∈Z . . # interleave(A) ¾ Σ truer - false . dom(S ) = A • ( P : S • P) Σ solve(P) ¾ [ truer |- false | P ] ∧ ∧ The first step is to find an initial condition for the differential equations. This is obtained by the hybrid contract with postcondition I j Qj Aj, which we abbreviate using the solve function. This states that the initial value for variables must satisfy the initial equations, I , the discrete equations Qj, and the algebraic equations Aj. Usually, this collection of constraints such yield a deterministic assignment for the initial values. Following initialisation, we populate the variable cpre with a copy of the whole continuous state c. The former is used to populate expressions that contain the Modelica function pre and also at event iteration. Then, the main behavioural loop begins, denoted by the fixed-point operator µ. The first evolution of the continuous variables is first performed. ∧ | | ∧ This evolution is characterised by three conjuncts in the hybrid predicate: [D Aj ←