hinfsynOptions
Option set for hinfsyn
and
mixsyn
Description
Examples
Specify Algorithm and Display for H-Infinity Synthesis
Use the LMI-based algorithm to compute an -optimal controller for a plant with one control signal and two measurement signals. Turn on the display that shows the progress of the computation. Use hinfsynOptions
to specify these algorithm options.
Load the plant and specify the numbers of measurements and controls.
load hinfsynExData P ncont = 1; nmeas = 2;
Create an options set for hinfsyn
that specifies the LMI-based algorithm and turns on the display.
opts = hinfsynOptions('Method','LMI','Display','on');
Alternatively, start with the default options set, and use dot notation to change option values.
opts = hinfsynOptions; opts.Method = 'LMI'; opts.Display = 'on';
Compute the controller.
[K,CL,gamma] = hinfsyn(P,nmeas,ncont,opts);
Minimization of gamma: Solver for linear objective minimization under LMI constraints Iterations : Best objective value so far 1 2 223.728733 3 138.078240 4 138.078240 5 74.644885 6 48.270221 7 48.270221 8 48.270221 9 19.665676 10 19.665676 11 11.607238 12 11.607238 13 11.607238 14 4.067958 15 4.067958 16 4.067958 17 2.154349 18 2.154349 19 2.154349 20 1.579564 21 1.579564 22 1.579564 23 1.236726 24 1.236726 25 1.236726 26 0.993342 27 0.993342 28 0.949318 29 0.949318 30 0.949318 31 0.945762 32 0.944063 33 0.941246 34 0.941246 35 0.940604 *** new lower bound: 0.931668 Result: feasible solution of required accuracy best objective value: 0.940604 guaranteed absolute accuracy: 8.94e-03 f-radius saturation: 0.404% of R = 1.00e+08 Optimal Hinf performance: 9.397e-01
Input Arguments
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'Display','on','RelTol',0.05
Display
— Display progress and generate report
'off'
(default) | 'on'
Display optimization progress and generate report in the command window, specified
as the comma-separated pair consisting of 'Display'
and
'on'
or 'off'
. The contents of the display
depend on the value of the 'Method'
option.
For 'Method' = 'RIC'
, the display shows the range of
performance targets (gamma
values) tested. For each
gamma
, the display shows:
The smallest eigenvalues of the normalized Riccati solutions X = X∞/γ and Y = Y∞/γ
The spectral radius
rho(XY) = max(abs(eig(XY)))
A pass/fail (
p/f
) flag indicating whether thatgamma
value satisfies the conditions X ≥ 0, Y ≥ 0, andrho(XY)
< 1The best achieved
gamma
performance value
For more information about the displayed information, see the Algorithms section
of hinfsyn
.
For 'Method' = 'LMI'
, the display shows the best achieved
gamma
value for each iteration of the optimization problem. It
also displays a report of the best achieved value and other parameters of the
computation.
Example: opts = hinfsynOptions('Display','on')
creates an option
set that turns the progress display on.
Method
— Optimization algorithm
'RIC'
(default) | 'LMI'
Optimization algorithm that hinfsyn
or
mixsyn
uses to optimize closed-loop performance, specified as
the comma-separated pair consisting of 'Method'
and one of the
following:
'RIC'
— Riccati-based algorithm. The Riccati method is fastest, but cannot handle singular problems without first adding extra disturbances and errors. This process is called regularization, and is performed automatically byhinfsyn
andmixsyn
unless you set the'Regularize'
option to'off'
. With regularization, this method works well for most problems.When
'Method' = 'RIC'
, the additional options listed under Riccati Method Options are available.'LMI'
— LMI-based algorithm. This method requires no regularization, but is computationally more intensive than the Riccati method.When
'Method' = 'LMI'
, the additional options listed under LMI Method Options are available.'MAXE'
— Maximum-entropy algorithm.When
'Method' = 'MAXE'
, the additional options listed under Maximum-Entropy Method Options are available.
For more information about how these algorithms work, see the Algorithms section
of hinfsyn
.
Example: opts = hinfsynOptions('Mathod','LMI')
creates an option
set that specifies the LMI-based optimization algorithm.
RelTol
— Relative accuracy on optimal H∞ performance
0.01 (default) | positive scalar
Relative accuracy on the optimal H∞
performance, specified as the comma-separated pair consisting of
'RelTol'
and a positive scalar value. The algorithm stops testing
γ values when the relative difference between the last failing
value and last passing value is less than RelTol
.
Example: opts = hinfsynOptions('RelTol',0.05)
creates an option
set that sets the relative accuracy to 0.05.
AbsTol
— Absolute accuracy on optimal H∞ performance
10-6 (default) | positive scalar
Absolute accuracy on the optimal H∞
performance, specified as the comma-separated pair consisting of
'AbsTol'
and a positive scalar value.
Example: opts = hinfsynOptions('AbsTol',1e-4)
creates an option
set that sets the absolute accuracy to 0.0001.
AutoScale
— Automatic plant scaling
'on'
(default) | 'off'
Automatic plant scaling, specified as the comma-separated pair consisting of
'AutoScale'
and one of the following:
'on'
— Automatically scales the plant states, controls, and measurements to improve numerical accuracy.hinfsyn
always returns the controllerK
in the original unscaled coordinates.'off'
— Does not change the plant scaling. Turning off scaling when you know your plant is well scaled can speed up the computation.
Example: opts = hinfsynOptions('AutoScale','off')
creates an
option set that turns off automatic scaling.
Regularize
— Automatic regularization
'on'
(default) | 'off'
Automatic regularization of the plant, specified as the comma-separated pair
consisting of 'Regularize'
and one of:
'on'
— Automatically regularizes the plant to enforce requirements on P12 and P21 (seehinfsyn
). Regularization is a process of adding extra disturbances and errors to handle singular problems.'off'
— Does not regularize the plant. Turning off regularization can speed up the computation when you know your problem is far enough from singular.
Example: opts = hinfsynOptions('Regularize','off')
creates an
option set that turns off regularization.
LimitGain
— Limit on controller gains
'on'
(default) | 'off'
Limit on controller gains, specified as the comma-separated pair consisting of
'LimitGain'
and either 'on'
or
'off'
. For continuous-time plants, regularization of plant
feedthrough matrices D12 or
D21 (see hinfsyn
) can result in controllers with large coefficients and fast
dynamics. Use this option to automatically seek a controller with the same performance
but lower gains and better conditioning.
LimitRS
— Limit on norm of LMI solutions
0 (default) | scalar in [0,1]
Limit on norm of LMI solutions, specified as the comma-separated pair consisting
of 'LimitRS'
and a scalar factor in the range [0,1]. Increase this
value to slow the controller dynamics by penalizing large-norm LMI solutions. See
[1].
TolRS
— Reduced-order synthesis tolerance
0.001 (default) | positive scalar
Reduced-order synthesis tolerance, specified as the comma-separated pair
consisting of 'TolRS'
and a positive scalar value.
hinfsyn
computes a reduced-order controller when 1
<= rho(R*S) <= TolRs
, where rho(A)
is the
spectral radius, max(abs(eig(A)))
.
S0
— Frequency at which to evaluate entropy
Inf
(default) | real scalar
Frequency at which to evaluate entropy, specified as a real scalar value. For more
information, see the Algorithms section of hinfsyn
.
Output Arguments
opts
— Options for hinfsyn
and mixsyn
hinfsyn
options object
Options for the hinfsyn
or mixsyn
computation, returned as an hinfsyn
options object. Use the object
as an input argument to hinfsyn
or mixsyn
. For
example:
[K,CL,gamma,info] = hinfsyn(P,nmeas,ncont,opts);
References
[1] Gahinet, P., and P. Apkarian. "A linear matrix inequality approach to H∞-control." Int J. Robust and Nonlinear Control, Vol. 4, No. 4, 1994, pp. 421–448.
Version History
Introduced in R2018b
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