Add port of SOSTOOLS sosdemo2

1 files changed, 43 insertions, 0 deletions

diff --git a/examples/sostools/sosdemo2.py b/examples/sostools/sosdemo2.py
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+++ b/examples/sostools/sosdemo2.py
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+"""
+Example adapted from SOSTOOLS sosdemo2.
+
+See page 34 of PDF below for details.
+https://github.com/oxfordcontrol/SOSTOOLS/blob/SOSTOOLS400/docs/SOSTOOLS_400.pdf
+"""
+import polymatrix as poly
+import sumofsquares as sos
+
+# TODO: Expose Solver class in sumofsquares.__init__
+from sumofsquares.abc import Solver
+
+# state variables and dynamics RHS
+x1, x2, x3 = poly.from_names("x_1, x_2, x_3")
+x = poly.give_name(poly.v_stack((x1, x2, x3)), "x")
+
+f = poly.give_name(poly.v_stack((
+    (-x1**3 - x1*x3**2) * (x3**2 + 1),
+    (-x2 - x1**2 * x2) * (x3**2 + 1),
+    (-x3 + 3*x1**2*x3) * (x3**2 + 1) - 3*x3
+)), "f(x) * ((x_3 ** 2) + 1)")
+
+# Create Lyapunov function parametrized by w
+monomials = x ** 2
+w = sos.from_name("w", shape=monomials.shape)
+
+V = poly.give_name(w.T @ monomials, "V(x)")
+dV = V.diff(x)
+
+# Solve SOS problem
+constraints = (
+    sos.make_sos_constraint(V - (x.T @ x)), # last term to impose definiteness
+    sos.make_sos_constraint(- (dV @ f)),
+)
+
+prob, result = sos.solve_problem(cost=None, constraints=constraints, solver=Solver.CVXOPT)
+print(prob)
+
+# TODO: create SolverStatus enumeration
+assert result.solver_info.status == "optimal", f"Status {result.solver_info.status}"
+
+V_sol = V.eval(result.values)
+print(poly.to_sympy(V_sol).read(poly.make_state()))