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Add gain scheduling to create_statefbk_iosystem()#827

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Merged

murrayrm merged 6 commits intopython-control:mainfrommurrayrm:gainsched-23Dec2022

Dec 30, 2022

Merged

Add gain scheduling to create_statefbk_iosystem()#827

murrayrm merged 6 commits intopython-control:mainfrommurrayrm:gainsched-23Dec2022

Dec 30, 2022

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murrayrm commentedDec 29, 2022

This PR adds functionality to thecreate_statefbk_iosystem function, allowing it to be used to set up a simple gain scheduled controller. From the documentation:

Gain scheduling on the desired state, desired input, or system state can be implemented by setting the gain to a 2-tuple consisting of a list of gains and a list of points at which the gains
were computed, as well as a description of the scheduling variables

  ctrl, clsys = ct.create_statefbk_iosystem(      sys, ([g1, ..., gN], [p1, ..., pN]), gainsched_indices=[s1, ..., sq])

The list of indices can either be integers indicating the offset into the controller input vector or a list of strings matching the names of the input signals.

Example:

    # Create a simple nonlinear system to check (kinematic car)    def unicycle_update(t, x, u, params):        return np.array([np.cos(x[2]) * u[0], np.sin(x[2]) * u[0], u[1]])    def unicycle_output(t, x, u, params):        return x    unicycle = ct.NonlinearIOSystem(        unicycle_update, unicycle_output, inputs = ['v', 'phi'],         outputs = ['x', 'y', 'theta'], states = ['x_', 'y_', 'theta_'])    # Speeds and angles at which to compute the gains    speeds = [1, 5, 10]    angles = np.linspace(0, pi/2, 4)    points = list(itertools.product(speeds, angles))    # Gains for each speed (using LQR controller)    Q = np.identity(unicycle.nstates)    R = np.identity(unicycle.ninputs)    gains = [np.array(ct.lqr(unicycle.linearize(        [0, 0, angle], [speed, 0]), Q, R)[0]) for speed, angle in points]    #    # Schedule on desired speed and angle    #    # Create gain scheduled controller    ctrl, clsys = ct.create_statefbk_iosystem(        unicycle, (gains, points), gainsched_indices=['vd', 'theta'])

Includes unit tests and documentation.