SysOpt - Systems Modelling and Optimisation

Overview

sysopt is a python3 framework for component based modelling, simulation and optimisation of continuous time dynamic and control systems.

It allows users to design modular plant and control systems, simulate the trajectory of closed loop systems, and run joint parameter/path optimisation studies.

• Install via pip install sysopt
• Documentation and user guide at https://sysopt.readthedocs.io .

A Minimal Example

Test problem 3 from Herber and Allison¹ provides a minimal example of sysopt usage. First, we define some components (plant, and controller), assemble a composite model then setup a optimsation problem for that model and solve it.

from sysopt import Metadata, Composite, SolverContext, PiecewiseConstantSignal, Parameter
from sysopt.modelling.builders import FullStateOutput
from sysopt.blocks import ConstantSignal

k_star = 0.8543 # Known optimal gain. 
t_f = 10

# Define the plant    
def dxdt(t, x, u, p):
    return [x[1], - p[0] * x[0]  + u[0]]

def x0(p):
    return [0, 0]

plant_metadata = Metadata(inputs=['u'], states=['x', 'v'], parameters=['k'])
plant = FullStateOutput(plant_metadata, dxdt, x0)

# Define the controller
controller = ConstantSignal(['u'], name='Controller')

# Define the Composite system via components and wires
model = Composite(name='Model', components=[plant, controller])
model.declare_outputs(['x', 'v', 'u'])
model.wires = [(controller.outputs, plant.inputs),
               (plant.outputs, model.outputs[0:2]),
               (controller.outputs, model.outputs[2])]

k = Parameter('k'')
u = PiecewiseConstantSignal('u', 100)
parameters = {
    plant.parameters['k']: k,
    controller.parameters['u']:u
}
# Setup the joint optimisation problem. 
with SolverContext(model=model, t_final=t_f, parameters=parameters) as solver:

    
    y_final = model.outputs(solver.t_final)
    
    cost = -y_final[0]

    constraints = [u <= 1, u >= -1,
                   y_final[1] >= 0, y_final[1] <= 0]

    problem = solver.problem(arguments=[k, u],  
                             cost=cost,
                             subject_to=constraints)
    
    soln = problem.solve(guess=[0, 0])
    k_min, u_min = soln.argmin
    assert abs(k_min - k_star) < 1e-2

Footnotes

1. Herber, Daniel R., and James T. Allison. "Nested and simultaneous solution strategies for general combined plant and control design problems." Journal of Mechanical Design 141.1 (2019). ↩