OpenLLM-France/wikimedia huggingface dataset:
# Grand Theft Auto: San Andreas/Missions/Ice Cold Killa
## Prerequisites

* Mission: Snail Trail
* Location: CJ's garage, Doherty, San Fierro

## Walkthrough

After the cutscene, your current pistol (if any) is replaced by a Silenced Pistol. Now head to Jizzy's club. The bouncers will not let you in, so climb up the plank by one of the supports of the Gant Bridge. Jump off onto the roof, and enter the skylight. Once inside, head downstairs to trigger a cutscene. After this, Jizzy makes a run for it. Take out the guards if you want, but head for the door. Follow Jizzy in the car, take him out, then grab the phone off the corpse to complete the mission.
Alternatively, take out the two door guards, and then blow up Jizzy's car (blue Pimpmobile). Then go in through the roof and trigger the cutscene. Jizzy will be forced to steal a motorbike, making it a lot easier to hunt him down.

## Tips

You can pop the tires of the Pimpmobile (or do whatever creative things to it ) outside before entering the club. That way, when Jizzy escapes, he would not get very far.
If you destroy the car, he will leave on a motorcycle, making it VERY easy to kill him without blowing up the cell phone. But don't crash it into the water; he will just get in the car in the water and the phone will be destroyed.

## Rewards

* Cash: $12,000
* Respect: +30

## New Missions Available

* Pier 69
# Grand Theft Auto: San Andreas/Missions/In the beginning
## Prerequisites

None

## Introduction

This is not technically a mission, since it doesn't bring you any reward, but rather refers to the events which occur upon starting a new game, but prior to triggering the first real mission. In the beginning is the name used for the savegame slot if you manage to save the game during this period; interestingly, these are also the first three words of the bible.

## Walkthrough

You start in Jefferson with very little to show for yourself, although contrary to the preceding dialogue, Tenpenny doesn't take all of your money, but, in fact, you start with $350. Since this is not really a mission, you have a choice as to what to do next.
There is nowhere you can currently save your game, but if you can scrape together at least $10,000, you can buy one of the safehouses, and save there. Some people like to do this to create a useful save game, which they can use to max out their stats, or complete other tedious missions (particularly spraying all 100 Gang Tags), before even starting the first mission. This way, if they should decide to play the game again from the beginning, they won't have to endure all the tedium again.
Alternatively, if you pass the first real mission you get a free safehouse to save at. To start this mission, you need to get to your house, which is marked with a "CJ" icon. Since this is the first interactive part of the game, I will describe a route to take to trigger the mission, but not with subsequent missions.
* Either get on the BMX bike marked with a blue arrow, or if you prefer, you can use another vehicle instead. Either way, I'm assuming you start from the location of the bike.
* Turn right out of the alley, and continue to the end of the road.
* Turn left here, then take the first right.
* Continue on this road until you cross over the freeway, then take the first left on to Grove Street.
* Continue along here until you see the red marker. This is your house. Put your vehicle in the attached garage if you want to keep it.

## New Missions Available

* Story Missions
** Big Smoke
* Asset Missions
** Los Santos Courier
* Vehicle Missions
** Taxi Driver
** Paramedic
** Pimping
** Vigilante
** Firefighter
** Burglar (not required for 100% completion)
* Challenge Missions
** BMX (requires 20%? Cycling Skill)
** 8-Track (requires 20%? Driving Skill)
* Collection Missions
** Oysters
** Gang Tags
** Unique Stunt Jumps (not required for 100% completion)
# Grand Theft Auto: San Andreas/Missions/Just Business
## Prerequisites

* Mission: Wrong Side of the Tracks
* Location: Big Smoke's house, Idlewood, Los Santos

## Walkthrough

A very difficult, but very fun mission, be prepared. Use your SMG, but make sure not to run out of ammo. Pick up the MP5s that the Russians drop and grab the armor behind a pillar. Meet up with Smoke and head outside for more shooting. After that comes the difficult part. The main targets for this whole section are the motorcycles. Take out the driver first and everything else falls. Kill everything, shoot the roadblocks and Smoke will head into the drainage basin. Take down every motorcycle and car gunman as soon as you see them. After the jump, shoot out the sewer gates or all of your work will be for nothing. Shoot the explosive barrels to take out the last motorcycles. Finally, Big Smoke is over.

## Rewards

* Respect: +10

## New Missions Available

* Reuniting the Families (also requires: Gray Imports, Los Sepulcros, Robbing Uncle Sam, House Party, High Stakes, Low-rider)
# Grand Theft Auto: San Andreas/Missions/Horseshoes

50 horseshoes are located around Las Venturas, you find your first under the Welcome to Las Venturas sign on the freeway west of the city. Finding all of them increases your luck stat for gambling in the casinos in Los Venturas. Also, the Combat Shotgun, M4, SMG and Satchel Charges are delivered to the Four Dragons Casino.
To collect all the horseshoes you will probably need to use the Jetpack from the Black Project mission.

## Locations

* Under the Welcome to Las Venturas sign
* Gas Station, Emerald Isle
* Greenglass College
* Behind one of the buildings in the Whitewood Estates (near the Sawn-off Shotgun pickup)
* In the military fuel depot (you can collect it during the Up, Up and Away mission)
* Under one of the waterfalls in front of the Visage Casino
* On the apex of the black pyramid building
* In the alley way behind the multi-storey car park in Red Sands East
* On the roof of the Wedding Chapel next to Come-a-lot
* Under the road bridge ramp next to Randolph Industrial Estate
* In one of the gardens in Rockshore West
* On the wall of the blue restaurant building at Pilson Intersection
See the full Horseshoe location map
# Grand Theft Auto: San Andreas/Missions/House Party
## Prerequisites

* Mission: Management Issues
* Location (part 1): Burger Shot car park, Marina, Los Santos
* Location (part 2): OG Loc's house, Grove Street, Ganton, Los Santos
* Time (part 2): 20:00 - 06:00

## Walkthrough

This mission is a bit odd, in that it has two parts which can be done separately. You can even do another mission in between the two parts.
Part 1
After the cutscene, just head back to CJ's house and save there. You don't need a haircut or a new set of clothes.
Part 2
Head into the red marker at the appropriate time. Watch the cutscene and get ready for a shootout with the Ballas. The first wave is in front of you, just target, aim, shoot. It's simple. Then the second wave is on top of the bridge, once again, aim, shoot. Pick up the ammo if you really need it. The last wave comes from everywhere, take cover wherever you can and shoot the Ballas. Find armour if you really need it, or just find cover. If Sweet dies, mission failed, but don't worry too much about that. That's it for OG Loc!

## Rewards

* Respect: +10

## New Missions Available

* Reuniting the Families (also requires: Gray Imports, Los Sepulcros, Robbing Uncle Sam, Just Business, High Stakes, Low-rider)
# Grand Theft Auto: San Andreas/Missions/Interdiction
## Prerequisites

* Mission: Highjack
* Location: Mike Toreno's ranch, Tierra Robada

## Walkthrough

After the cutscene, head to El Castillo del Diablo to trigger the next cutscene. After this, pick up the RPG if you like, then use one of the vehicles to ascend Arco del Oeste to trigger the next cutscene. After this, a chopper arrives with the cargo, but it's being chased by some CIA choppers. Use the RPG (or better still a heat-seeking RPG) to take them down. Now head out to the dropzone just north of Verdant Meadows, and pick up the bag. Now return to El Castillo del Diablo (Toreno refers to it as 'Las Brujas' for some reason). There's a Seasparrow in the water nearby which you may want to take. When you get there, the red marker is inside one of the buildings there. Step inside to complete the mission.

## Tips

* You may want to keep the Seasparrow, since the next mission gives you somewhere to keep it.

## Rewards

* Cash: $1,000

## New Missions Available

* Verdant Meadows
# Jeep Liberty/Electrical/ESP

Jeep Libertys manufactured in 2006 and later come standard with ESP, or Electronic Stability Program. Among other things, ESP applies selective breaking to prevent wheel spin. This traction portion of the ESP has an effect similar to that of an LSD. So it doesn't interfere with off road driving, parts of the ESP system are disabled in 4-Hi and 4-Lo. The system relies heavily on the ABS wheel speed sensors to determine if a wheel is slipping. ESP may interfere with LSDs and lockers because it performs many of the same functions that they do. It should be noted that when ESP was introduced in 2006 the factory LSD option was dropped, whether this was because ESP defeats the purpose of a LSD or because it's incompatible with a LSD is not yet known.

## External Links

Jeep Grand Cherokee ESP
# Jeep Liberty/Electrical/CB Radio/Upgraded CB Antenna Installation
## Upgraded CB Antenna Installation

This is a write up on my upgraded install of AdamisAdam (LOST) CB antenna install and the Cobra 75W install.
| Required Parts | Drill Antenna Mount |
| Tap and File Antenna Mount | Cut Antenna Mount Cover |
| Install Firestik AR-1A and Splitter | Replace Passenger Dash Panel |
| Mount CB Transceiver | Route Red Power Wire |
| Route Black Ground Wire | |

### Antenna

* Disconnect the (-) battery cable from the battery
* Remove radio Antenna
* Remove plastic cover from mount
* Place a rag over the antenna mount
* Drill 5/16” hole into the metal mount – remember to use oil
* Use 3/8” 24 thread tap and add threads to the mount hole (use oil)
* File down raised metal near the mounts plastic ring
* Cut out enough plastic from protective cover
* Replace the plastic protective cover
* Use lock nut and screw the spring into the mount
* Screw the cb antenna to the spring mount

### Firestik AR-1A and Splitter

* Firestik AR-1A to the splitter
* Connect female connector to 3’ cable
* Connect the Firestik to female-to-female connector
* Connect other end of the female connector to the 3’ extension cable

### Interior Panels

* Remove the bottom knee knocker panel on passenger side
* Remove the passenger side kick panel
* Drop down the panel under steering column
* Remove fuse cover panel from just inside the driver side door
* Remove mini panel above panel that’s on the right side of steering column.

### Cobra 75W CB and Cables

* Install cable mount to inside of steering column panel
* Run red wire over to the left side and through to the power/fuse box is located just inside of the door area (do not connect to power source yet)
* Run ground wire to under the center console farthest forward
* Crimp connectors to ends of wires
* Connect ground wire as shown in picture
* Run CB cable to under center of console and bring up through and connect to the cable mount and connect to cable from it
* Run the 3’ Extension cable from the antenna through the center console to the cable mount box and connect to it
* Disconnect the radio connector from the antenna cable
* Connect radio cable to the Firestik AR-1A
* Connect splitter to antenna cable
* Replace passenger side kick panel
* Replace Knee-knocker panel with Firestik on top of insulation (no good place to mount it or wire tie it to anything. (I about using Velcro)
* Wire tie excess cable from CB cable mount)
* Close steering column panel
* Install CB Hand-held unit mount to mini panel
* Connect ground connector and then connect red wire to power source

## External links

* Upgraded CB antenna install
* Cobra Electronics
* Firestik Antenna Company
# Jeep Liberty/Electrical/Satellite Radios

The only two currently available satellite radios manufacturers are Sirius and XM. Satellite radio requires a monthly service plan, but both Sirius and XM allow prospective customers to listen for free for a few days via their websites.

## Sirius

The Liberty can be equipped with Sirius from the factory or with Mopar parts later on. These installations give full integration with the other car equipment. Note, however, that even with factory and Mopar installs the only radio that will be able to display song information is the Chrysler RB1 navigation radio.

## XM

Daimler-Chrysler does not sell an XM radio option for the Jeep Liberty. There is however an aftermarket interface available, called XMDirect, that is compatible with many newer Chrysler radios. The interface is manufactured by Terk (Audiovox) and listed under the following model numbers depending on the store selling it: XMDCPK, CHYXMD100, XMDCHY100. The following Chrysler radios are compatible with the module:
* RAZ (2003-2005)
* RB1 (2003-2005)
* RBK (????-????)
* RBP (2003-2005)
* RBQ (2003-2005)
* RBU (2003-2005)
XMDirect only supports radios that use the Liberty's native PCI bus. It also doesn't support the Chrysler RB4 radio. If audio quality and fit aren't of concern, one could also simply use an XM receiver that features an FM modulator.

## External Links

* SIRIUS Satellite Radio
* XM Satellite Radio
# Jeep Liberty/Electrical/CB Radio/Original CB Antenna Installation
## Original CB Antenna Installation

| Fig 3 - Create Space Behind Fender | Fig 4 - Required Parts |
| Fig 5 - Antenna Mount Assembly | Fig 6 - Antenna Mount Assembly - Close |
| Fig 7 - CB to AM/FM Converter | Fig 8 - Drill Antenna Mount to 3/8" |
| Fig 9 - Drilled Antenna Mount | Fig 10 - File Antenna Mount |
| Fig 11 - Trim Antenna Mount Cover | |
Here's the HOW-TO on a very trick and clean CB antenna install in place of the stock one. (If I do say so myself.)
Goal: add CB antenna somewhere very low key, and also to NOT get in the way of the rear glass at all, or to catch too many trees.
Solution: Use good CB antenna in place of OEM AM/FM one, and add an AM/FM/CB splitter.
Parts list on bottom.

### Installation Instructions

First, you must partially unbolt the front fender. Remove top three bolts, and loosen the two side bolts (10 mm). (Fig 1)
Box wrench required for this one bolt (10 mm). (Fig 2)
You need to get your hand, and later a ratchet, behind the fender from the top. (Fig 3)
Everything. (Fig 4)
Double female nut. (Fig 5 & 6)
The converter from AM/FM radio to CB wire plug is a key component. (Fig 7)
Drill out slowly to 3/8". I drilled about 5 times sizing up as I went to avoid damaging the OEM part. (Fig 8 & 9)
Next file down the top to create an even seat for the antenna double female nut to rest on. (Fig 10)
Trim the trim so the bolt head sticks out the bottom. (Fig 11)
Finished shot. (Fig 12 & 13)
I already have better reception than my first try and that's before tuning SWR or the radio!
Now I just gotta get the SWR tuned!

### Parts List

* Firestik: AR-1A, Match-Maker, CB/AM/FM, CB Antenna Splitter (retail $16)
* Wilson Silver 3' antenna.
* Double female antenna wire connector
* 3' Jumper CB wire ($9)
* Double female 3/8" nut for bottom of antenna (free)
* CB wire to FM wire converter ($9)
* will add spring soon

### Unsuccessful Swivel Mount

Finished product! This was the unsuccessful first installation. The Firestik swivel mount broke off on the first mile of driving at 70+ mph! It bent down, I pulled over and, well, it broke in my hand. Better than on highway and losing a brand new Wilson Silver! I decided to take a different route this time and drilled out the stock bracket to accept a 3/8" bolt and just mount the CB antenna right to that. I'm going to add a spring to help ease the stress - only problem is I JUST barely clear the garage now. Check out updated pictures at bottom.
* Completed Installation (Unsuccessful Swivel Mount)
* Completed Installation - Close (Unsuccessful Swivel Mount)

## External Links

* CB Antenna Installation
# Jeep Liberty/Electrical/PCI Bus

The "PCI" bus is the central communications bus in the Jeep Liberty. The BCM, PCM, TCM, WCM, EVIC, dash cluster, and audio equipment use it to communicate with each other. The bus is a superset of OBD-II and uses the J1850 VPW communication format. It travels throughout the entire car and the OBD-II port taps directly into it. The ELM327 chip from Elm Electronics should allow reading and writing to the bus via a serial port. One of the many available OBD-II interface tools could also be used. The Liberty won't switch to the newer and faster CAN bus until it is federally required in 2008.
# LMIs in Control/Matrix and LMI Properties and Tools/LMIs in Control/pages/Dicrete-time Algebraic Riccati Equation

Algebraic Riccati Equations are particularly significant in Optimal Control, filtering and estimation problems. The need to solve such equations is common in the analysis and linear quadratic Gaussian control along with general Control problems. In one form or the other, Riccati Equations play significant roles in optimal control of multivariable and large-scale systems, scattering theory, estimation, and detection processes. In addition, closed forms solution of Ricatti Equations are intractable for two reasons namely; one, they are nonlinear and two, are in matrix forms.

## The System

The system is defined as:
$y_{t}=Ay_{t-1}+Bu_{t-1},$

## The Data

A typical specification of the discrete-time linear quadratic control problem is to minimize
    $\sum _{t=1}^{T}(y_{t}^{T}Qy_{t}+u_{t}^{T}Ru_{t})$
subject to the state equation
    $y_{t}=Ay_{t-1}+Bu_{t-1},$
where y is an n × 1 vector of state variables, u is a k × 1 vector of control variables, A is the n × n state transition matrix, B is the n × k matrix of control multipliers, Q (n × n) is a symmetric positive semi-definite state cost matrix, and R (k × k) is a symmetric positive definite control cost matrix.

## The LMI: Discrete-Time Algebraic Riccati Inequality

Title and mathematical description of the LMI formulation.
       ${\begin{aligned}{\text{ Consider}}\;A_{d}\in \mathbb {R} ^{n\times m},B_{d}\in \mathbb {R} ^{n\times m},P,Q\in \mathbb {S} ^{n},{\text{where}}\;\\P>0,\\Q\geq 0,\\R>0.\\{\text{ The Discrete-Time Algebraic Riccati inequality is given by}}\;\\A_{d}^{T}PA_{d}-A_{d}^{T}PB_{d}(R+B_{d}^{T}PB_{d})^{-1}B_{d}^{T}PA_{d}+Q-P&\geq 0,\\\\{\text{ can be written using the Schur complement lemma as}}\;\\{\begin{bmatrix}A_{d}^{T}-P+Q&&A_{d}^{T}PB_{d}\\\star &&R+B_{d}^{T}PB_{d}\\\end{bmatrix}}&\geq 0\\\end{aligned}}$
Equivalently, this discrete-time algebraic Riccati inequality is satisfied under any of the following necessary and sufficient conditions.
1. There exist $P,Q\in \mathbb {S} ^{n},{\text{and}}\;R\in \mathbb {S} ^{m},$ where $P>0,Q\geq 0,andR>0,$ such that
${\begin{bmatrix}Q&&0&&A_{d}^{T}P&&P\\\star &&R&&B_{d}^{T}P&&0\\\star &&\star &&P&&0\\\star &&\star &&\star &&P\\\end{bmatrix}}$ ${\begin{aligned}\geq 0\end{aligned}}$,
2. There exist $X,Q\in \mathbb {S} ^{n},{\text{and}}\;R\in \mathbb {S} ^{m},$ where $X>0,Q\geq 0,andR>0,$ such that
${\begin{bmatrix}Q&&0&&A_{d}^{T}&&1\\\star &&R&&B_{d}^{T}P&&0\\\star &&\star &&X&&0\\\star &&\star &&\star &&X\\\end{bmatrix}}$ ${\begin{aligned}\geq 0\end{aligned}}$,

## Conclusion:

If the solution exists, LMIs give a unique, stabilizing, symmetric matrix P.

## Implementation:

Matlab code for this LMI in the Github repository:

## External links

* https://https://arxiv.org/abs/1903.08599/ LMI Properties and Applications in Systems, Stability, and Control Theory.- - A List of LMIs by Ryan Caverly and James Forbes
# LMIs in Control/Matrix and LMI Properties and Tools/Lyapunov Stability of a System With Polynomial Dynamics

[UNDER CONSTRUCTION] - CME
Find the local Lyapunov function for a system with known polynomial dynamics.

## Required Data

The system dynamics to be tested in the form ${\dot {x}}=f(x)$ where $f(x)$ is a polynomial function of the states $x$.
A function or functions representing the local domain over which stability is to be determined, $X:=\{x:p_{i}(x)\geq 0,i=1,...,k\}$. Commonly this is a ball of specified radius such that $p(x)=R^{2}-x^{T}x$. [Is this assuming P-Compactness of the set?]

## Find the Lyapunov Function

Suppose there exists Lyapunov function $V(x)$, a scalar $\epsilon >0$, and $s_{0},s_{i},t_{0},t_{i}\in \Sigma _{s}$ (where $\Sigma _{s}$ is the set of Sum-of-Squares polynomials, all of which are positive) such that:
$V(x)=s_{0}(x)+\sum \limits _{i}s_{i}(x)p_{i}(x)+\epsilon x^{T}x$
$-{\dot {V}}(x)=-\nabla V(x)^{T}f(x)=t_{0}(x)+\sum \limits _{i}t_{i}(x)p_{i}(x)+\epsilon x^{T}x$
The Lyaponov function, if it exists, will be positive and always decreasing over the desired set $X$

## Example

Code example in SOStools probably worthwhile!

## Reference

SOS tools manual is a good one
Tie in the reference from SOS tools? The Khalil?

## Related LMIs

Add things here about SOS methods
Global Lyapunov Search
# LMIs in Control/Matrix and LMI Properties and Tools/Nevanlinna Pick Interpolation with Scaling
## Nevanlinna-Pick Interpolation with Scaling

The Nevanlinna-Pick problem arises in multi-input, multi-output (MIMO) control theory, particularly $H_{\infty }$ robust and optimal controller synthesis with structured perturbations.
The problem is to try and find ${\gamma }_{opt}=inf(||DHD^{-1}||_{\infty })$ such that $H$ is analytic in $C_{+},$   $D=D^{\ast }>0,$ and $D\in \mathbb {D}$ define the scaling, and finally, ‌ $H({\lambda }_{i})u_{i}=v_{i}$   $i=1,...,m$   $(1)$

## The System

The scaling factor $\mathbb {D}$ is given as a set of $mxm$ block-diagonal matrices with specified block structure. The matrix valued function H({\lambda}) analytic on the open upper half plane is a Nevanlinna function if $Im(H({\lambda }))\geq 0$ $({\lambda }\in {\pi }^{+})$. The Nevanlinna LMI matrix $N$ is defined as $N=G_{in}-G_{out}$. The matrix $A$ is a diagonal matrix of the given sequence of data points ${\lambda }_{i}\in \mathbb {C} (A=diag({\lambda }_{1},...,{\lambda }_{m})$

## The Data

Given: ‌ Initial sequence of data points in the complex plane ${\lambda }_{1},...,{\lambda }_{m}$ with ${\lambda }_{i}\in C_{+}{\widehat {=}}(s|Re(s)>0)$. ‌ Two sequences of row vectors containing distinct target points $u_{1},....,u_{m}$ with $u_{i}\in C^{q}$, and $v_{1},...,v_{m}$ with $v_{i}\in C^{p},i=1,...,m$.

## The LMI: Nevanlinna- Pick Interpolation with Scaling

First, implement a change of variables for $P=D^{\ast }D$ and $N=G_{in}-G_{out}$.
From this substitution it can be concluded that ${\gamma }_{opt}$ is the smallest positive ${\gamma }$ such that there exists a $P>0,P\in \mathbb {D}$ such that the following is true:
$A^{\ast }G_{in}+G_{in}A-U^{\ast }PU=0$,
$A^{\ast }G_{out}+G_{out}A-V^{\ast }PV=0$,
${\gamma }^{2}G_{in}-G_{out}\geq 0$

## Conclusion:

If the LMI constraints are met, then there exists a $H_{\infty }$ norm-bounded optimal gain ${\gamma }$ which satisfies the scaled Nevanlinna-Pick interpolation objective defined above in Problem (1).

## Implementation

Implementation requires YALMIP and Mosek. - MATLAB code for Nevanlinna-Pick Interpolation.

## Related LMIs

Nevalinna-Pick Interpolation

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* Generalized Interpolation in $H_{\infty }$.

## Return to Main Page:

LMIs in Control: https://en.wikibooks.org/wiki/LMIs_in_Control
# LMIs in Control/Matrix and LMI Properties and Tools/KYP Lemmas

      * Continuous Time
      * Discrete Time
# LMIs in Control/Matrix and LMI Properties and Tools/KYP Lemmas/Discrete Time

      * Discrete time Bounded Real Lemma
      * Discrete Time KYP Lemma for QSR Dissipative System
      * Discrete Time KYP Lemma with Feedthrough