ZigangPan/LinearQuadraticControl

ZigangPan`LinearQuadraticControl`

HinfinityControl

HinfinityControl[system,γ]

considers the H-infinity optimal control problem under imperfect state measurements (which is the four block problem). It calculates the solution to the algebraic Riccati equation associated with the full information problem and the optimal output feedback controller for the LTI

system

with all of the control inputs as control inputs and all of the disturbance inputs as disturbance inputs; the measurement outputs as measurement outputs and the controlled outputs as the signal whose squared energy minus

times the squared energy of the disturbance on the interval [0,∞) is the cost function. Under regularity assumptions, the algorithm returns

{cost,controller}

if γ is greater than the optimal disturbance attenuation level under imperfect state measurements, where

cost

is the solution to the corresponding algebraic Riccati equation for the full information problem that results from the application of the cost-to-come function analysis, and

controller

is the LTI representation of the optimal output feedback controller. Under regularity assumptions, if

is less than the optimal disturbance attenuation level, then the algorithm returns the

γstar

, which is the optimal disturbance attenuation level of the problem under imperfect state measurements. When regularity assumptions are not satisfied, the algorithm returns

{cost,controller}

if there exists a solution to the problem for the chosen

Examples

(1)

Basic Examples

(1)

In[1]:=

system1={{x1,x2,x3},{u1,u2,w1,w2,w3},{y1,y2,z1,z2,z3,z4},{{-1,1,-1,0,0,0,0,1},{-2,0,1,1,-1,0,0,1},{-3,0,-2,1,1,0,0,0},{1,0,0,0,0,1,0,0},{0,0,1,0,0,0,1,0},{1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0},{0,0,0,1,2,0,0,0},{0,0,0,2,1,0,0,0}},{1,2},{1,2},{1,2},{3,4,5},{1,2},{3,4,5,6}};systemcheck[system1]

Out[1]=

True

In[2]:=

HinfinityControl

[system1,1]

No stabilizing solution found!

Out[2]=

79089

32768

In[3]:=

N[%]

Out[3]=

2.4136

In[4]:=

HinfinityControl

[system1,2.5]

Out[4]=

{{{20.1161,9.29619,-9.25448},{9.29619,5.40086,-4.21781},{-9.25448,-4.21781,4.44345}},{{x1chk,x2chk,x3chk},{y1,y2},{u1,u2},{{-1.83943,1.,-0.381801,0.99932577855524140630905094440095126628875732421875,-0.73595125608594835764364461283548735082149505615234},{-20.937,-10.8017,9.02097,0.41029055293749294719418685417622327804565429687500,0.49362120201764186910864395940734539180994033813477},{-0.325249,0.937291,-3.69428,-0.73595125608594835764364461283548735082149505615234,0.84148531050986496993004948308225721120834350585938},{-8.26791,-4.93222,3.72409,0,0},{10.3245,5.86951,-4.71152,0,0}},{1,2},{1,2},{1,2},{},{1,2},{}}}

In[5]:=

myPositiveDefiniteMatrixQ[%〚1〛]

Out[5]=

True

SeeAlso

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ZigangPan`LinearQuadraticControl`