Distributed multi-agent collaboration is an interactive algorithm that enables agents in a multi-agent system (MAS) to achieve pre-defined collaboration objective in a distributed manner, such as agreeing upon a common value (commonly referred as distributed consensus) or optimizing the aggregate cost of the MAS (commonly referred as distributed optimization).

Agents participating in a typical distributed multi-agent collaboration algorithm can lose privacy of their inputs (containing private information) to a passive adversary in two ways. The adversary can learn about agents' inputs either by corrupting some of the agents that are participating in the collaboration algorithm or by eavesdropping the communication links between the agents during an execution of the collaboration algorithm. Privacy of the agents' inputs in the former case is referred as internal privacy, and privacy of the agents' inputs in the latter case is referred as external privacy.

This dissertation proposes a protocol for preserving internal privacy in two particular distributed collaborations: distributed average consensus and distributed optimization. It is shown that the proposed protocol can preserve internal privacy of sufficiently well connected honest agents (agents that are not corrupted by the adversary) against adversarial agents (agents that are corrupted by the adversary), without affecting the collaboration objective.

This dissertation also investigates a model-based scheme, as an alternative to cryptographic encryptions, for external privacy in distributed collaboration algorithms that can be modeled as linear time-invariant networked control systems. It is demonstrated that the model-based scheme preserves external privacy, without affecting the collaboration objective, if the system parameters of the networked control system, that equivalently models the distributed collaboration algorithm, satisfy certain conditions. Unlike cryptographic encryptions, the model-based scheme does not rely on secure generation and distribution of keys amongst the agents for guaranteeing external privacy.