option to target relative gamma in hinfsyn

Author: baggepinnen

examples/hinf_example_DC.jl

@@ -41,7 +41,7 @@ P = hinfpartition(G, WS, WU, WT)
 flag = hinfassumptions(P)
 
 # Synthesize the H-infinity optimal controller
-flag, C, γ = hinfsynthesize(P)
+flag, C, γ = hinfsynthesize(P, γrel=1)
 
 # Extract the transfer functions defining some signals of interest
 Pcl, S, CS, T = hinfsignals(P, G, C)

examples/hinf_example_MIT.jl

@@ -36,7 +36,7 @@ P = hinfpartition(G, WS, WU, WT)
 flag = hinfassumptions(P)
 
 # Synthesize the H-infinity optimal controller
-flag, C, γ = hinfsynthesize(P)
+flag, C, γ = hinfsynthesize(P, γrel=1)
 
 # Extract the transfer functions defining some signals of interest
 Pcl, S, CS, T = hinfsignals(P, G, C)

src/hinfinity_design.jl

@@ -44,12 +44,12 @@ function hinfassumptions(P::ExtendedStateSpace; verbose = true)
     # Check assumption A2
     if rank(D12) < size(D12, 2)
         verbose &&
-            @warn("The matrix D12 does not have full rank, ", "violation of assumption A2.")
+            @warn("The matrix D12 does not have full rank, ", "violation of assumption A2. The full control signal must have nonzero penalty at infinite frequency.")
         return false
     end
     if rank(D21) < size(D21, 1)
         verbose &&
-            @warn("The matrix D21 does not have full rank, ", "violation of assumption A2.")
+            @warn("The matrix D21 does not have full rank, ", "violation of assumption A2. The whole measurement vector y must be corrupted by noise at infinite frequency.")
         return false
     end
 
@@ -110,20 +110,29 @@ function _detectable(A::AbstractMatrix, C::AbstractMatrix)
 end
 
 """
-    flag, K, γ, mats = hinfsynthesize(P::ExtendedStateSpace; maxIter=20, interval=(2/3,20), verbose=true)
+    flag, K, γ, mats = hinfsynthesize(P::ExtendedStateSpace; maxIter = 20, interval = (2 / 3, 20), verbose = false, tolerance = 1.0e-10, γrel = 1.01)
 
 Computes an H-infinity optimal controller K for an extended plant P such that
-||F_l(P, K)||∞ < γ for the largest possible γ given P. The routine is
+||F_l(P, K)||∞ < γ for the smallest possible γ given P. The routine is
 known as the γ-iteration, and is based on the paper "State-space formulae for
 all stabilizing controllers that satisfy an H∞-norm bound and relations to
-risk sensitivity" by Glover and Doyle. See the Bib-entry below [1] above.
+risk sensitivity" by Glover and Doyle.
+
+
+# Arguments:
+- `maxIter`: Maximum number of γ iterations
+- `interval`: The starting interval for the bisection.
+- `verbose`: Print progress?
+- `tolerance`: Stop when the interval is this small.
+- `γrel`: If `γrel > 1`, the optimal γ will be found by γ iteration after which a controller will be designed for `γ = γopt * γrel`. It is often a good idea to design a slightly suboptimal controller, both for numerical reasons, but also since the optimal controller may contain very fast dynamics. If `γrel → ∞`, the computed controller will approach the 𝑯₂ optimal controller. Getting a mix between 𝑯∞ and 𝑯₂ properties is another reason to choose `γrel > 1`.
 """
 function hinfsynthesize(
     P::ExtendedStateSpace;
     maxIter = 20,
     interval = (2 / 3, 20),
     verbose = false,
     tolerance = 1e-10,
+    γrel = 1.01,
 )
 
     # Transform the system into a suitable form
@@ -136,6 +145,12 @@ function hinfsynthesize(
 
     if !isempty(γFeasible)
         # Synthesize the controller and trnasform it back into the original coordinates
+
+        if γrel > 1
+            γFeasible *= γrel
+            X∞Feasible, Y∞Feasible, F∞Feasible, H∞Feasible = _solvematrixequations(P̄, γFeasible)
+        end
+
         K = _synthesizecontroller(
             P̄,
             X∞Feasible,

src/plotting.jl

@@ -48,7 +48,7 @@ specificationplot
                     xscale --> :log10
                     yscale --> ControlSystems._PlotScaleFunc
                     linestyle --> :solid
-                    linecolor --> colors[mod(index - 1, 3)+1]
+                    color --> colors[mod(index - 1, 3)+1]
                     label --> (i == 1 ? s_labels[mod(index - 1, 3)+1] : "")
                     w ./ (hz ? 2pi : 1), singval[:, i]
                 end
@@ -73,7 +73,7 @@ specificationplot
                 xscale --> :log10
                 yscale --> ControlSystems._PlotScaleFunc
                 linestyle --> :dash
-                linecolor --> colors[mod(index - 1, 3)+1]
+                color --> colors[mod(index - 1, 3)+1]
                 linewidth --> 2
                 label --> (i == 1 ? w_labels[mod(index - 1, 3)+1] : "")
                 w ./ (hz ? 2pi : 1), singval[:, i]