Implement complex full non-square and diagonal complex uncertainty blocks

CITATION.cff

@@ -14,5 +14,5 @@ authors:
     orcid: "https://orcid.org/0000-0002-1987-9268"
     affiliation: "McGill University"
 title: "decargroup/dkpy"
-version: v0.1.10
+version: v0.1.11
 url: "https://github.com/decargroup/dkpy"

README.rst

@@ -141,6 +141,6 @@ If you use this software in your research, please cite it as below or see
         url={https://github.com/decargroup/dkpy},
         publisher={Zenodo},
         author={Steven Dahdah and Timothy Everett Adams and James Richard Forbes},
-        version = {{v0.1.10}},
+        version = {{v0.1.11}},
         year={2025},
     }

doc/conf.py

@@ -9,8 +9,8 @@
 project = "dkpy"
 copyright = "2024, Steven Dahdah, Timothy Everett Adams and James Richard Forbes"
 author = "Steven Dahdah, Timothy Everett Adams and James Richard Forbes"
-version = "0.1.10"
-release = "0.1.10"
+version = "0.1.11"
+release = "0.1.11"
 
 # -- General configuration ---------------------------------------------------
 # https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration

doc/examples.rst

@@ -144,3 +144,34 @@ Output::
 
 .. image:: _static/plot_mu.png
 .. image:: _static/plot_D.png
+
+
+D-K iteration with list of fit orders and simulation of perturbed systems 
+-------------------------------------------------------------------------
+
+In this example, the orders are specified in a list. Once the robust controller
+is synthesized, it is tested on a set of perturbed systems by generating a set
+of perturbations `Δ` that have H-infinity norm less than or equal to 1.
+
+In this example, a controller is designed for the linearized lateral dynamics
+of an aircraft from an example given in Section 14.1 of [M04]_.
+
+.. literalinclude:: ../examples/6_dk_iteration_airframe.py
+   :language: python
+
+Output::
+
+    mu: 0.9824275970458984
+
+.. image:: _static/example_6/plot_mu.png
+
+After the controller is synthesized, a set of off-nominal models are generated
+by interconnecting various admissible perturbations `Δ` with the nominal model.
+Then, the closed-loop systems are formed for each perturbed system. The time
+domain response of the systems can be obtained for a step response in the roll
+angle reference signal, no external disturbances, and moderate sensor noise. In
+particular, the response of the system states and actuator inputs are shown.
+
+.. image:: _static/example_6/plot_states.png
+
+.. image:: _static/example_6/plot_inputs.png

doc/references.rst

@@ -10,3 +10,7 @@ References
 .. [SP06] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control:
    Analysis and Design. West Sussex, England: Wiley, 2006.
    ISBN 978-0-47-001168-3.
+.. [M04] U. Mackenroth, Robust Control Systems: Theory and Case Studies.
+   Berlin, Heidelberg: Springer, 2004. ISBN 978-3-642-05891-2.
+
+

examples/1_example_dk_iter_fixed_order.py

@@ -19,17 +19,15 @@ def example_dk_iter_fixed_order():
     )
 
     omega = np.logspace(-3, 3, 61)
-    # Alternative MATLAB descr.
+    # Alternative MATLAB block structure description
     # uncertainty_structure = dkpy.UncertaintyBlockStructure(
     #     [[1, 1], [1, 1], [2, 2]]
     # )
-    uncertainty_structure = dkpy.UncertaintyBlockStructure(
-        [
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(2, 2),
-        ]
-    )
+    uncertainty_structure = [
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(2, 2),
+    ]
     K, N, mu, iter_results, info = dk_iter.synthesize(
         eg["P"],
         eg["n_y"],

examples/2_example_dk_iter_list_order.py

@@ -16,24 +16,22 @@ def example_dk_iter_list_order():
         d_scale_fit=dkpy.DScaleFitSlicot(),
         # fit_orders=[4, 4, 4],  # <- an alternative
         fit_orders=[
-            np.diag([4, 4, 0, 0]),
-            np.diag([4, 4, 0, 0]),
-            np.diag([4, 4, 0, 0]),
+            [4, 4, 0],
+            [4, 4, 0],
+            [4, 4, 0],
         ],
     )
 
     omega = np.logspace(-3, 3, 61)
-    # Alternative MATLAB descr.
+    # Alternative MATLAB block structure description
     # uncertainty_structure = dkpy.UncertaintyBlockStructure(
     #     [[1, 1], [1, 1], [2, 2]]
     # )
-    uncertainty_structure = dkpy.UncertaintyBlockStructure(
-        [
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(2, 2),
-        ]
-    )
+    uncertainty_structure = [
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(2, 2),
+    ]
     K, N, mu, iter_results, info = dk_iter.synthesize(
         eg["P"],
         eg["n_y"],

examples/3_example_dk_iter_auto_order.py

@@ -44,17 +44,15 @@ def example_dk_iter_auto_order():
     )
 
     omega = np.logspace(-3, 3, 61)
-    # Alternative MATLAB descr.
+    # Alternative MATLAB block structure description
     # uncertainty_structure = dkpy.UncertaintyBlockStructure(
     #     [[1, 1], [1, 1], [2, 2]]
     # )
-    uncertainty_structure = dkpy.UncertaintyBlockStructure(
-        [
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(2, 2),
-        ]
-    )
+    uncertainty_structure = [
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(2, 2),
+    ]
     K, N, mu, iter_results, info = dk_iter.synthesize(
         eg["P"],
         eg["n_y"],

examples/4_example_dk_iter_interactive.py

@@ -37,17 +37,15 @@ def example_dk_iter_interactive():
     )
 
     omega = np.logspace(-3, 3, 61)
-    # Alternative MATLAB descr.
+    # Alternative MATLAB block structure description
     # uncertainty_structure = dkpy.UncertaintyBlockStructure(
     #     [[1, 1], [1, 1], [2, 2]]
     # )
-    uncertainty_structure = dkpy.UncertaintyBlockStructure(
-        [
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(2, 2),
-        ]
-    )
+    uncertainty_structure = [
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(2, 2),
+    ]
     K, N, mu, iter_results, info = dk_iter.synthesize(
         eg["P"],
         eg["n_y"],

examples/5_example_dk_iteration_custom.py

@@ -31,10 +31,11 @@ def _get_fit_order(
         iteration,
         omega,
         mu_omega,
-        D_omega,
+        D_l_omega,
+        D_r_omega,
         P,
         K,
-        uncertainty_structure,
+        block_structure,
     ):
         print(f"Iteration {self.my_iter_count} with mu of {np.max(mu_omega)}")
         if self.my_iter_count < 3:
@@ -70,17 +71,15 @@ def example_dk_iter_custom():
     )
 
     omega = np.logspace(-3, 3, 61)
-    # Alternative MATLAB descr.
+    # Alternative MATLAB block structure description
     # uncertainty_structure = dkpy.UncertaintyBlockStructure(
     #     [[1, 1], [1, 1], [2, 2]]
     # )
-    uncertainty_structure = dkpy.UncertaintyBlockStructure(
-        [
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(1, 1),
-            dkpy.ComplexFullBlock(2, 2),
-        ]
-    )
+    uncertainty_structure = [
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(1, 1),
+        dkpy.ComplexFullBlock(2, 2),
+    ]
     K, N, mu, iter_results, info = dk_iter.synthesize(
         eg["P"],
         eg["n_y"],