I will restrict my attention to (1) studies published only in the last 5-6 years (since 2008), and (2) solely to the scope and limits of your question, namely effects on sleep in patients with Alzheimer's Disease:

In several studies, melatonin was found to enhancee sleep duration, as well as positively modulate sleep–wake cycle disturbances, and reduce sundowning and night activity in Alzheimer's Disease patients [1-3].

Furthermore, a long-term, large-scale randomized controlled trial [4] found that exposure to a continuous (all-day) ceiling-mounted light plus melatonin moderate dose melatonin (2.5 mg at bedtime) improved several sleep parameters such as sleep latency, total sleep time, duration of uninterrupted sleeping hours, and sleep efficiency.

In addition, a recent literature review [5] found that 5 double blind, randomized placebo-controlled trials and 1 open-label retrospective study (total N = 651) all confirmed that treatment with daily evening melatonin improved both sleep quality and cognitive performance in minimal cognitive impairment (MCI), an early phase of Alzheimer's Disease (AD).

REFERENCES

1. de JA, Korevaar JC, van Munster BC, et al. Effectiveness of melatonin treatment on circadian rhythm disturbances in dementia. Are there implications for delirium? A systematic review. Int J Geriatr Psychiatry 2010;25:1201–1208.

2. Riemersma-van der Lek RF, Swaab DF, Twisk J, et al. Effect of bright light and melatonin on cognitive and noncognitive function in elderly residents of group care facilities: a randomized controlled trial. JAMA 2008;299:2642–2655.

3. Bourne RS, Mills GH, Minelli C. Melatonin therapy to improve nocturnal sleep in critically ill patients: Encouraging results from a small randomised controlled trial. Crit Care 2008;12:R52.

4. der Lek RF Riemersma-van, Swaab DF, Twisk J, et al. Effect of bright light and melatonin on cognitive and noncognitive function in elderly residents of group care facilities: a randomized controlled trial. JAMA. 2008;299(22):2642–55.

5. Cardinali DP, Furio AM, Brusco LI. The use of chronobiotics in the resynchronization of the sleep/wake cycle. Therapeutical application in the early phases of Alzheimer's disease. Recent Pat Endocr Metab Immune Drug Discov 2011; 5(2):80-90.

Thank you very much for your reply. I greatly appreciate it.

See these two recent reviews:

Sleep and Alzheimer's disease.

Peter-Derex L, Yammine P, Bastuji H, Croisile B.

Sleep Med Rev. 2015 Feb;19:29-38. doi: 10.1016/j.smrv.2014.03.007.

Pharmacotherapies for sleep disturbances in Alzheimer's disease.

McCleery J, Cohen DA, Sharpley AL.

Cochrane Database Syst Rev. 2014 Mar 21;3:CD009178. doi: 10.1002/14651858.CD009178.pub2.