Establishing Reachset Conformance for the Formal Analysis of Analog Circuits

Abstract

We present the first work on the automated generation of reachset conformant models for analog circuits. Our approach applies reachset conformant synthesis to add non-determinism to piecewiselinear circuit models so that they then enclose all possible behaviors of the real system. Since piecewiselinear models are hybrid, we introduce the first reachset conformant synthesis algorithm for hybrid system models. Furthermore we present a novel technique to compute the required non-determinism. The effectiveness of our approach is demonstrated on a real analog circuit. Since the resulting models enclose all measurements, they can be used for formal verification.

Neuro-Reachability of Networked Microgrids

“…where ∆ denotes the time step; ⊕ denotes the Minkowski addition. In (26), the first term computes the reachset propagation resulting from the NMs states, i.e., J (X − X * ). The second term computes the reachset propagation resulting from the inputs W F = J w (W − W * ) + F * , which composes both the uncertainty impact J w (W − W * ) and the linearization point impact F * .…”

“…The second term computes the reachset propagation resulting from the inputs W F = J w (W − W * ) + F * , which composes both the uncertainty impact J w (W − W * ) and the linearization point impact F * . And the third term in (26) computes the set of linearization error [24] to ensure an provable overapproximation of the nonlinear NMs dynamics. Further, the reachset during time interval [t − ∆, t] can be calculated as the union of the time-point reachable sets during the interval as R(…”

“…As discussed above, since the PDI-NMs model may not perfectly conform with the real NMs dynamics, the reachset R(t) from ( 26), computed with W and X 0 , possibly does not enclose X. Inspired by the conformance theory in [25], [26], E m is optimized to ensure that the conformance reachset R c (t) encloses the time-series NMs states X:…”

“…Fortunately, case studies in Section V will show that the ODE-Net-based dynamic model is quite accurate and the obtained neuro-reachsets is rather tight. Taking time period [t − ∆, t] as an example, following (26), the conventional reachset R(t) (Fig. 3(d)) is computed incorporating the evolution of NMs states (Fig.…”

“…For efficient volume computation, R c is over-approximated by hyperrectangles. Denote D = e J∆ R c (t − ∆) ⊕ ∆ 0 e J(∆−τ ) W F dτ ⊕ R el , which can be readily computed as the conventional reachset by (26). Denote E = ∆ 0 e J(∆−τ ) dτ .…”