ZigangPan/LinearQuadraticControl

ZigangPan`LinearQuadraticControl`

HinfinityControlPSM

HinfinityControlPSM[system,γ]

considers the H-infinity optimal control problem under perfect state measurements. It calculates the solution to the associated algebraic Riccati equation and the optimal state 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 are ignored and the controlled outputs as the signal whose squared energy minus

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

{z,controllergain}

is greater than the optimal disturbance attenuation level under perfect state measurements, where

is the solution to the corresponding algebraic Riccati equation, and

controllergain

is the optimal state feedback gain matrix of the 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 perfect state measurements.

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]:=

HinfinityControlPSM

[system1,1]

No stabilizing solution found!

Out[2]=

49451

32768

In[3]:=

N[%]

Out[3]=

1.50912

In[4]:=

HinfinityControlPSM

[system1,1.6]

Out[4]=

{{{7.6810428075306447226466843858361244201660156250000,4.6795828475380378819181714789010584354400634765625,-3.2594354311013562508492213964927941560745239257813},{4.6795828475380378819181714789010584354400634765625,4.5873618928235497804735132376663386821746826171875,-1.9171893912159529982375261170091107487678527832031},{-3.2594354311013562508492213964927941560745239257813,-1.9171893912159529982375261170091107487678527832031,1.5643059830123360320897063502343371510505676269531}},{{-4.3174233551934427429349246570685257514317830403646,-4.3743408493551105584471214468875485989782545301649,1.7433776153256934391164476336497399542066786024306},{5.0417423398826330209014183007335911194483439127604,4.8003829362919890024999050284451287653711107042101,-2.0910011671062125573586046003684815433290269639757}}}

SeeAlso

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ZigangPan`LinearQuadraticControl`