Derive the relationship between the probability of an observation se$-$

quence, and the $$ and $$ variables of the Hidden Markov Model.

Utilize HMM$\_$CSTR$.$mlx and relevant script files to generate the following

datasets:

Dataset $1$ for $C_1$ as specified, ie$,$ for normal operation regime

Dataset $2$ for $20\%$ higher $C_1,$ ie$,$ for $1^{st}$ abnormal operation regime

Dataset $3$ for $20\%$ lower $C_1,$ ie$,$ for $2^{nd}$ abnormal operation regime

Next, train HMM agents, HMM$-1,$ HMM$-2$ and HMM$-3,$ respectively,

on Datasets $1,2$ and $3.$ Then from each dataset, randomly pick a 'test'

sequence, input it to each agent, and obtain the log likelihood. Plot

$log$ likelihood versus agent $($HMM$-1,$ HMM$-2$ and HMM$-3)$ for each

test sequence.

Finally, comment on the performance of HMM agents in identifying

the operation regime of test sequences.

The Matlab script ANFIS$\_$IMC.mlx uses ANFIS for inverse model con$-$

trol of a chemical process. Execute the script for $2,4$ and $6$ membership

functions with $200$ epochs each. Compare and comment on the results

thus obtained.

Use the Matlab script DDPG$.$mlx to train the reinforcement learning

agent for random set points in the range, $20C-25C$ with and without

parallel computing. Show the simulated experience in each case, and

comment on the results.