Simulation

The system can be simulated with the obtained switching times by running

x, xsw, optval, t = simulate(m)
x, xsw, optval, t = simulate(m, tau)      # Specify switching time vector
x, xsw, optval, t = simulate(m, tau, t)   # Specify switching times and time vectors

The outputs of the simulation are

• x State trajectory. Each \(x(t)\) can be obtained as x[:, i]
• xsw States at each switching time. Each \(x(\tau_i)\) can be obtained as xsw[:, i]
• optval Simulated value function optimum
• t Time vector during the simulation

Additional Functions for Nonlinear Dynamics

In case of nonlinear dynamics it is possible to simulate the system linearized at the linearization points obtained after the optimization

x, xsw, optval, t = simulatelinearized(m)
x, xsw, optval, t = simulatelinearized(m, tau, t)  # Specify switching times time vector

In addition, it is possible to easily obtain the input vector trajectory at each time instant by running

u, t = simulateinput(m)
u, t = simulateinput(m, t)  # Specify time vector

Each vector \(u(t)\) can be obtained by slicing the output u[:, i].