simulate

Method of continuousTimeMss.

Integrate a continuous-time mss model as an explicit ODE.

Source: src/simulator/@continuousTimeMss/simulate.m

What is solved

An mss state equation is explicit, so the initial value problem is the plain ODE

$$\dot x = f\big(x, u(t)\big) = \Phi_F\, m\big(x, u(t)\big), \qquad x(t_0) = x_0,$$

integrated over [inputTime(1), inputTime(end)] with the MATLAB ode object. The solver is taken from sim.solverType, the option struct is merged in by applySolverOptions, and solve produces the trajectory that is written to sim.time and sim.variableTrajectory (states in rows, time points in columns).

The inputs are not part of the state: $u(t)$ is reconstructed from inputTime/inputTrajectory by linear interpolation with linear extrapolation outside the sampled range, so the solver may step anywhere inside the span.

Jacobian gating

Explicit Runge–Kutta solvers never evaluate a Jacobian, so the Jacobian handle is attached based on the solver, not the model class.

For

ode45, ode23, ode78, ode89, ode113

no Jacobian is passed to ode; every other solver (ode15s, ode23t, …) receives the analytic

$$\frac{\partial f}{\partial x} = \big[\, J_{f,x}\ \ J_{f,u} \,\big] \Big|_{\text{state columns}},$$

i.e. the full signal Jacobian restricted to the state columns, since the solver differentiates with respect to $x$ only.

CPN evaluation path

For a CPNTensor everything that does not depend on $(t,x)$ is hoisted out of the callbacks:

• the state-equation block is compiled once with CPNTensor.prepareForMTISIM (structure and parameter matrices sliced to columnIndexStateEq / stateEquationIndex) and evaluated through the MTISIM kernel;
• the Jacobian sub-tensor is sliced once and evaluated with computeJacobian — and only when the solver actually needs it;
• the input interpolants are built once as griddedInterpolant objects rather than re-running interp1 over the whole input matrix per callback;
• the signal vector $v=[x;\,u]$ is assembled into a buffer allocated once. When the model uses the natural [x; u] layout — what rmss, ss2mss and connect produce — the scatter into that buffer becomes two contiguous slice assignments; the check (strictly ascending, first, last, count) proves the index vectors are exactly 1:nState and nState+1:nVar, so a permuted layout never takes the fast path.

Generic tensor path

Any other mtiTensor is evaluated through the model itself: functionValue supplies $\dot x$ and stateJacobian supplies the Jacobian, whose first nState columns are handed to the solver. The inputs are interpolated with interp1(..., 'linear', 'extrap').

See also

continuousTimeMss · applySolverOptions · functionValue · stateJacobian · msim

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