Quick Example

Consider the switching time optimization problem in the form

\[\begin{split}\begin{array}{ll} \underset{\tau}{\mbox{minimize}} & \int_{t_0}^{t_f} \|x(t)\|_2^2\; \mathrm{d}t \\ \mbox{subject to} & \dot{x}(t) = \begin{cases} A_0 x(t) & t< \tau\\ A_1 x(t) & t\geq \tau \end{cases}\\ & x(0) = x_0\\ & 0\leq \tau \leq T \end{array}\end{split}\]

with variable \(\tau\in \mathbb{R}\), the dynamics defined by matrices \(A_0,A_1\in \mathbb{R}^{n\times n}\) and the initial state \(x_0\in \mathbb{R}^{n}\).

This problem can be solved by SwitchTimeOpt.jl as follows

using SwitchTimeOpt
using Ipopt

# Time Interval
t0 = 0.0; tf = 1.0

# Initial State
x0 = [1.0; 1.0]

# Dynamics
A = Array(Float64, 2, 2, 2)
A[:, :, 1] = randn(2, 2)  # A_0 matrix
A[:, :, 2] = randn(2, 2)  # A_1 matrix

# Create Problem
m = stoproblem(x0, A, t0=t0, tf=tf)

# Solve Problem
solve!(m)

# Get optimal Solution
tauopt = gettau(m)

# Get optimum value
objval = getobjval(m)