1. http://www.collator-systems.com Monte-Carlo based Expertise A powerful Tool for System Evaluation & Optimization  Introduction  Features  System Performance Evaluation  Optimal Control Design

2. http://www.collator-systems.com Introduction  In order to validate a system in a robust sense, it is not enough to rely on the results of a nominal System Simulation, only optimal for a single specific environment.  Robust design consists of searching for a product design that guarantees low variations in the performance level of the system due to uncontrolled environmental variations.  This approach leads to what is known as a system parameter optimization that tend to minimize the risk of getting poor performance when the environment changes.  This risk is evaluated by simulating the system over a range of environmental scenarios.

3. http://www.collator-systems.com Introduction (ctd.)  “Monte Carlo” (MC) is a method of calculation based on combining the operation of an automaton with the intentional injection of random data  The Monte Carlo method is, in certain practical cases, more efficient in arriving at correct answers than purely deterministic methods - since the random data represent real- life variables uncertainties

4. http://www.collator-systems.com Introduction (ctd.)  The Monte-Carlo (MC) Simulation Mode is a batch of System Simulation runs  Each run uses a different set of parameters and variables which reflect its uncertainties  Each MC run starts by selecting the constant parameters randomly from their distribution functions, whereas the time dependent processes are selected randomly during the run  The MC Mode purpose is to verify the design of a System and determine its performance in a statistical way to reach the goal of “Robust System”

5. http://www.collator-systems.com Features  Generic method: any type of application can use this method  Repeatability of parameter perturbations between the same run in all the applications using this method  Capability of reconstructing a particular discrete run without running the whole batch  can solve a family of problems, not just a single nominal case.  The Monte-Carlo method is a complete procedure that include intrinsically a number of other major applications, like optimization, parametric studies, sensitivity analyses, what-if analyses, etc.  It provides a natural link to experimentation and tests reconstruction.  That method is a technology that treat multi-disciplinary problems just as easily as simple problems.

6. http://www.collator-systems.com System Performance evaluation  CEP and SEP calculations  Sleeves of selected parameters  Safety Zones analysis  Statistical analysis

7. http://www.collator-systems.com System Performance evaluation Example: Typical UAV automatic landing scenario analyzed by Monte- Carlo

8. http://www.collator-systems.com Implementation Monte-Carlo based Optimal Control Design  finding the set of decision parameters that minimizes a performance index (i.e. cost function) of a static or dynamic system for a given application.  Monte-Carlo method enables to evaluate the spectrum of parameters of interest of a system, as determined by the incertitude /variation range of the system's physical parameters as well as sensor measurements, for a given set of decision parameters.  By connecting the Monte-Carlo process to an Optimization master module, one can find the optimal set of decision/control parameters over all the possible behaviors of any stochastic system, depending on the physical parameters fluctuation model (For example, an optimal automatic landing and take-off system will provide the minimum standard deviation of the touch down point. In the passengers transport domain, a train/bus/shuttle schedule management can be optimized to achieve the maximum passengers flow per time).

9. http://www.collator-systems.com Implementation Monte-Carlo based Optimal Control Design  This optimal control tool is based on a Conjugate Gradient Method algorithm that computes an updated decision vector at each iteration until the nearest local minimum of the performance index is reached. The algorithm handles equality and inequality constraints in the parameters of decision, by adding penalty functions to the desired performance index. The problem of finding local minimum versus absolute minimum is solved by trying different initial guess for each decision parameters.  The whole optimization process is illustrated in the following figure:

10. http://www.collator-systems.com Monte Carlo based Optimal Control OPTIMIZATION Module MONTE-CARLO Processor Decision / Control System Platform /system Physical Model Post-Run Analysis Updated control parameters Random variables SYSTEM SIMULATION Initial Guess Constraints Performance index