This paper presents a structural analysis of trust, risk, and security management (TRiSM) in agent-based multi-agent systems (AMAS) based on large-scale language models (LLMs). We investigate the conceptual foundations of agent AI, highlighting its structural differences from traditional AI agents, and apply and extend the AI TRiSM framework for agent AI centered on four core pillars: explainability, ModelOps, security, privacy, and governance. We propose a novel risk classification scheme to capture the unique threats and vulnerabilities of agent AI (ranging from failures of collaboration to prompt-based adversarial manipulation), and introduce two new metrics: component synergy score (CSS) and tool utilization effectiveness (TUE) to support practical evaluation of agent AI tasks. We also discuss strategies to improve the explainability of agent AI, and ways to enhance security and privacy through encryption, adversarial robustness, and regulatory compliance. Finally, we present a research roadmap for responsible development and deployment of agent AI, which provides important directions for aligning emerging systems with TRiSM principles for safe, transparent, and responsible operation.
