⚡ electrical engineering

Security-Aware Planning and Control of Multi-Agent Systems with LTL Tasks

This paper proposes a secure-by-construction framework for multi-agent systems that integrates security constraints against passive intruders directly into linear temporal logic (LTL) synthesis to formally guarantee both task satisfaction and the protection of sensitive information regarding task execution and agent identity.

Original authors: Georgios Mitsos, Dimos V. Dimarogonas, Siyuan Liu

Published 2026-05-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Georgios Mitsos, Dimos V. Dimarogonas, Siyuan Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a team of drones flying around a city, tasked with a complex mission: one needs to scan the air, another needs to send the data, and a third needs to visit a secure repair station. They have to do this in a specific order, forever, while avoiding bad weather zones.

Now, imagine there is a "spy" watching them. This spy can't see the drones' internal computers or their exact GPS coordinates. The spy can only see which general neighborhood a drone is in (e.g., "North District" or "South District"). The spy is trying to figure out two things:

Did a drone visit a secret, sensitive location? (e.g., a high-security repair station).
Which specific drone did it?

This paper presents a "security-by-design" framework. Instead of planning the flight path first and then trying to hide the tracks later, the authors build the security rules directly into the planning process. They ensure that no matter what the spy sees, the spy can never be 100% sure if a secret mission happened or who did it.

Here is how they do it, using simple analogies:

1. The Two Types of "Cover Stories"

The authors introduce two ways to protect the drones, which they call Type-A and Type-B security.

Type-A Security (The "Ghost" Strategy):
Imagine a spy sees a drone enter a secret red zone. To satisfy Type-A security, the system must be able to say, "Actually, that drone could have been in a normal blue zone at the same time, and the spy would have seen the exact same thing."
- The Analogy: It's like a magician making a rabbit disappear. The audience (the spy) sees the magician's hand move, but they can't tell if the rabbit is actually gone or just hidden in a different pocket that looks identical from the outside. The system creates a "copy path" (a fake history) that looks exactly the same to the spy but involves no secret visits.
Type-B Security (The "Confusion" Strategy):
Imagine the spy sees a drone in a secret zone. To satisfy Type-B security, the system ensures that another drone is also in a zone that looks exactly the same to the spy.
- The Analogy: It's like a group of people wearing identical masks. If the spy sees "Person A" doing something suspicious, they can't be sure if it was Person A or Person B, because both were in the same "masked" area at the same time. The spy sees the action but can't identify the culprit.

2. The "Digital Twin" Game

To make this work, the computer doesn't just plan one flight path. It plans two paths simultaneously:

The Real Path: What the drones actually do.
The Copy Path: A fake version of the mission that looks identical to the spy but avoids the secrets (or swaps the agents around).

The system checks every possible move. If a move allows the spy to say, "Aha! I know for a fact Drone 1 is in the secret zone because no other drone could have been there," that move is deleted. The system only keeps the moves where the spy is always confused.

3. From Math to Real Flight

The paper describes a three-step process to turn these confusing math rules into real flying drones:

Step 1: The Map (Abstraction): The real world is a continuous space (infinite points). The computer breaks this down into a grid of "rooms" (polytopes). It turns the complex physics of flying into a simple board game where you just move from Room A to Room B.
Step 2: The Security Filter: The computer builds a "Secure Board Game." It removes any move that breaks the Type-A or Type-B rules. It also checks if the drones can physically make the jump between rooms without crashing or running out of battery (using something called "Control Barrier Functions," which act like invisible walls keeping the drones inside their current room until they are ready to switch).
Step 3: The Mission Planner: The computer uses a logic tool (Linear Temporal Logic, or LTL) to find the best path through the Secure Board Game that fulfills the mission (scan, encode, transmit) while staying safe and secure.

4. The Result: The Two-Drone Test

The authors tested this with two drones:

Drone 1 scans air quality and encodes data.
Drone 2 transmits the data and visits a secure diagnostics station.

The Secret: The "secure diagnostics station" and the "sensitive data zone" are secret.
The Spy: Can only see if a drone is in the "North" or "South" half of the sky.

The Outcome:
When Drone 1 flies into the secret zone to encode data, the system simultaneously generates a "Copy Path" where Drone 1 is in a non-secret zone that looks the same to the spy. At the same time, Drone 2 is also in a zone that matches the spy's view.

Result: The spy sees the drones moving, but they can never prove Drone 1 visited the secret spot, nor can they be sure which drone did it. The drones successfully complete their mission, avoid obstacles, and keep their secrets safe.

Summary

This paper is about teaching robots how to play "hide and seek" with a spy while doing their jobs. By planning the "fake" story alongside the "real" story from the very beginning, the system guarantees that the spy remains confused, ensuring that sensitive tasks and the identities of the agents performing them remain hidden.

Technical Summary: Security-Aware Planning and Control of Multi-Agent Systems with LTL Tasks

Problem Statement

The paper addresses the challenge of planning and controlling multi-agent systems (MAS) operating in continuous workspaces under Linear Temporal Logic (LTL) specifications, while simultaneously ensuring information security against a passive intruder.

Existing methods for LTL-based planning often abstract continuous dynamics into finite-state models to synthesize discrete plans, which are then refined into continuous trajectories. However, these approaches typically neglect information security. In critical applications like drone swarms or intelligent transportation systems, task correctness must be balanced with confidentiality. The specific problem is to synthesize a controller for agents with linear affine dynamics such that the resulting continuous trajectory satisfies a global LTL task while preventing a malicious observer (with partial observations of agent positions) from inferring:

Whether a "secret" task (visiting a designated secret region) has been executed.
Which specific agent is responsible for executing that secret task.

The authors note that while opacity-based security has been explored for single-agent systems and some discrete multi-agent systems, there is a gap in handling systems with continuous dynamics, input constraints, and complex LTL specifications simultaneously.

Methodology

The proposed framework follows a "secure-by-construction" approach, integrating security constraints directly into the synthesis procedure. The methodology proceeds in four main stages:

1. Abstraction and Security Modeling

System Model: The workspace is partitioned into non-overlapping polytopes. Agent dynamics are abstracted into Weighted Transition Systems (WTS). A Global WTS (gWTS) is formed via the synchronous product of individual agent WTSs.
Security Definitions: Two complementary security notions are introduced based on the intruder's observation capabilities ( $H_i$ $H_{i}$ ):
- Type-A Security: Prevents the intruder from inferring if any agent visited a secret state. This is achieved by ensuring that for every "real" path where a secret visit occurs, there exists an indistinguishable "copy" path where the agent visits a non-secret state with the same observation.
- Type-B Security: Prevents the intruder from identifying which agent visited a secret state. This requires that if Agent $i$ visits a secret state, at least one other Agent $k$ produces the same observation at that time step.
Secure Abstractions: To enforce these properties, the authors construct:
- Twin-gWTS: A product system capturing pairs of indistinguishable global states.
- Secure Twin-gWTS: A refinement of the Twin-gWTS that removes state pairs where both the real and copy agents are in secret states simultaneously.
- Type-B gWTS: A restriction of the global state space ensuring that secret visits are "masked" by other agents' observations.

2. Transition Feasibility Verification

Before applying LTL synthesis, the framework verifies if discrete transitions in the secure abstractions are dynamically feasible in the continuous workspace.

Control Barrier Functions (CBFs): The authors use CBFs to guarantee that agents remain within their assigned polytopes (forward invariance) and cross boundaries at specific times.
Quadratic Programming (QP): For each discrete transition, a centralized QP is solved to find control inputs that drive agents between region centroids while satisfying dynamics, input bounds, and CBF constraints. If no solution exists, the transition is discarded from the abstract model.

3. LTL Synthesis

Product Büchi Automaton (PBA): The secure gWTS is synchronized with a Nondeterministic Büchi Automaton (NBA) derived from the LTL specification.
Path Search: The algorithm searches for a prefix-suffix path in the PBA that minimizes a cost function (balancing prefix and suffix costs). This path represents a discrete plan that satisfies both the LTL task and the security constraints.

4. Continuous Trajectory Generation

The optimal discrete path is refined into a continuous trajectory by concatenating the feasible trajectory segments computed in the QP stage. Formal guarantees are provided that the resulting continuous trajectory satisfies the LTL formula and the security properties.

Key Contributions

The paper claims the following contributions:

New Security Notions: The introduction of Type-A and Type-B security for multi-agent systems, which relax existing opacity definitions to improve scalability while maintaining strong security guarantees (plausible deniability and agent anonymity).
Continuous Dynamics Framework: A planning framework directly applicable to multi-agent systems with continuous affine dynamics and input constraints. The authors state this is, to their knowledge, the first such framework handling general LTL tasks alongside these security constraints, whereas prior work focused on finite-state models.
Complexity Reduction: The proposed discrete planning algorithm achieves significantly lower computational complexity compared to existing multi-agent security-aware methods (specifically citing a reduction from $(2|Q|)^{2M^2+M}$ states to $|Q|^{2M}$ states for the search space).

Results and Case Study

The framework is validated through a case study involving two drones:

Scenario: Drone 1 scans air quality and encodes data; Drone 2 relays data and visits a diagnostics station. Both must avoid an obstacle region.
Task: An LTL formula requiring a repeating sequence of scanning, encoding, and transmitting, plus an eventual inspection, while avoiding obstacles.
Security: Two regions are designated as secret (sensitive data collection and the diagnostics station). The system must satisfy Type-A/B security against an intruder observing the drones' general location (North/South zones).
Outcome: The algorithm successfully synthesized a trajectory where:
- When Drone 1 visits the secret region, a "copy" path shows it in a non-secret region with the same observation (satisfying Type-A).
- Drone 2 is positioned such that it produces the same observation as Drone 1 during the secret visit, preventing the intruder from identifying the responsible agent (satisfying Type-B).
Performance: The complete algorithm (including abstraction, QP solving, and path search) ran in approximately 70 seconds on a MacBook Air M2.

Significance and Claims

The paper positions its work as a significant step toward secure-by-construction strategies for autonomous cyber-physical systems. The authors claim that by integrating security constraints directly into the LTL synthesis procedure, they provide formal guarantees that the resulting behavior satisfies both global mission specifications and confidentiality requirements.

The significance lies in bridging the gap between high-level logical planning and low-level continuous control in a security-aware manner. The authors emphasize that their approach is the first to handle continuous dynamics and input constraints directly within this security-aware LTL synthesis context, offering a scalable solution that outperforms existing discrete-only methods in terms of computational complexity.

The paper concludes modestly, noting that future work could extend the framework to nonlinear dynamics and investigate hierarchical architectures to further improve scalability for larger multi-agent systems.