discreteSimulation

Method of discreteTimeMdss.

March a discrete-time mdss model forward one sample at a time.

Source: src/simulator/@discreteTimeMdss/discreteSimulation.m

What is solved

At sample $k$, given the current state $x_k$, solve the implicit multilinear map for the successor state and the algebraic/binary signals:

$$\Phi_{\mathrm{eq}}\, m(x_{k+1}, x_k, u_k, y_k, z_k) = 0, \qquad \Phi_{\mathrm{ineq}}\, m(x_{k+1}, x_k, u_k, y_k, z_k) \le 0,$$

where $\Phi=\Phi_c+\Phi_{+1}-\Phi_{-1}$ and $m$ is the norm-1 monomial vector. For a discrete mdss the “state-delta” row holds the successor state $x_{k+1}$, so the per-sample unknowns are $(x_{k+1}, y_k, z_k)$. Each sample is solved with solveStepBruteForce.

The discretizationType selects which input drives the step:

• forward / none → drive with $u_k$, store $y_k, z_k$ at sample $k$;
• backward → drive with $u_{k+1}$, store $y, z$ at sample $k{+}1$.

Retry and stopping

If a step returns NaN or violates the residual tolerances ($|F|$, $G$), it is retried once with an alternative algebraic guess and the smaller-residual result is kept:

$$\text{keep the retry if } \|F_{\text{new}}\| \le \|F\| \text{ and } \|G_{\text{new}}^{+}\| \le \|G^{+}\| .$$

If no feasible solution is found the march stops, the remaining trajectory is filled with NaN, and a warning is issued. Results are assembled into sim.variableTrajectory $=[x,\,y,\,z]$ with sim.time and sim.eventTime set to the sample times.

Input arguments

Output arguments

See also

discreteTimeMdss · solveStepBruteForce · determineParallizedSolvingOrder · msim

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