hinfsynOptions

Option set for hinfsyn and mixsyn

Syntax

opts = hinfsynOptions

opts = hinfsynOptions(Name,Value)

Description

opts = hinfsynOptions creates the default option set for the hinfsyn and mixsyn commands.

opts = hinfsynOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

Examples

Specify Algorithm and Display for H-Infinity Synthesis

Use the LMI-based algorithm to compute an ${\mathit{H}}_{\infty }$-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

General Options

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 that gamma value satisfies the conditions X ≥ 0, Y ≥ 0, and rho(XY) < 1

• The 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 by hinfsyn and mixsyn 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.

Riccati Method Options

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 controller K 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 (see hinfsyn). 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.

LMI Method Options

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))).

Maximum-Entropy Method Options

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