Tenant yelling on other tenants in house and is behind on rent

[Viney Khera]

Hello all, thank you for reading, I need advice on how to deal with this situation.

I have a single-family house rented per room to different tenants. One of the tenants is way behind his rent and has registered for a county program to pay his 6 month's rent, the program is yet to pay me, waiting for govt funding. After the program cutoff, he is paying rent but not fully, missing months or partial payments in between. He also has the lowest rent among others and is living for 5-6 yrs. I am unable to increase the rent as he is behind and says he can't afford it.

He is the same trouble tenant for me, who doesn't go well with some other tenants in the home. He creates problems quite often. 1-2 tenants have left previously because of him, one has called the police on him as well once for harassment. This same tenant who has called the police on this trouble tenant once keeps telling me once a month at least that he tries to stay away from this person but this guy is mentally sick and keeps yelling at him for no reason or keeps hearing him shouting alone in his room. If I would ask this trouble tenant, he will bring up his side of the story and give some reason why he yelled at other tenant. 

How should I deal with this troubled tenant? Shall I go with the eviction process - start with a letter to improve behavior towards other tenants irrespective of rent? But i know, if i start any process, he will stop paying rent during the process and don't know how long the court will take to give eviction. Also, how would it affect past rent pending from a county program? Or other ways to deal with this situation?

TIA