Resilient Output Containment under Undisclosed Leader Dynamics and Actuator Attacks

Technical Summary: Resilient Output Containment under Undisclosed Leader Dynamics and Actuator Attacks

Problem Statement
This work addresses the problem of resilient output containment for heterogeneous linear multi-agent systems (MAS) operating over directed network topologies. The objective is to ensure that the physical outputs of a network of followers converge to the time-varying convex hull generated by multiple leaders. The problem is complicated by two critical constraints:

1. Undisclosed Leader Dynamics: Leaders generate bounded, locally absolutely continuous trajectories, but their dynamic models, velocity bounds, and motion envelopes are strictly undisclosed to the followers. This prevents the use of standard distributed observer designs that rely on reconstructing leader exosystem parameters.
2. Actuator Cyber-Attacks: Followers are subject to actuator compromises modeled as a combination of state-correlated attacks, input-correlated attacks, and bounded exogenous false-data injections. These attacks can corrupt the execution of containment commands and potentially propagate through the network.

Existing solutions face limitations: distributed observers violate nondisclosure constraints; sliding mode protocols often introduce chattering or require a priori knowledge of leader velocity bounds; and continuous adaptive protocols are typically restricted to undirected graphs or require full state measurements.

Methodology
The authors propose a continuous, two-layer adaptive control architecture designed to separate network-level command generation from local execution resilience.

1. Network Interface Layer (Command Generation):

   • This layer generates task-space commands ($\sigma_i$) using only neighbor-exchanged network-interface states and instantaneous leader signals (where available).
   • It employs a novel adaptive interaction protocol that does not require global graph knowledge (e.g., eigenvalues of the Laplacian) for tuning, nor does it require a priori bounds on leader velocities or motion envelopes.
   • The protocol utilizes a nonsmooth Lyapunov analysis to prove asymptotic containment of the command states ($\sigma_i$) to the leaders' convex hull, provided the graph contains a leader-rooted united spanning tree.

2. Local Virtual-Actuator Recovery Layer (Execution Resilience):

   • This layer ensures the physical follower tracks the generated command despite actuator attacks.
   • It utilizes a "virtual actuator" concept, inserting a recovery block between the nominal controller and the compromised actuator.
   • The design uses a stable local command filter to embed the task-space command into the follower's dynamics.
   • A continuous adaptive control law compensates for state-correlated, input-correlated, and bounded exogenous attacks. Crucially, this recovery mechanism relies only on partial state measurements (the external normal-form state $x_i$), avoiding the need for full state measurement (specifically the zero-dynamics state $\eta_i$).
   • The stability analysis employs a nonsmooth Lyapunov function and Riccati-based inequalities to guarantee asymptotic convergence of the local tracking errors.

Key Contributions

• Continuous Adaptive Protocol for Directed Graphs: The paper proposes a continuous adaptive protocol that achieves asymptotic command containment over general directed leader-rooted graphs without requiring leader-model reconstruction, known leader-motion bounds, or global graph parameters.
• Nonsmooth Lyapunov Analysis: A novel nonsmooth Lyapunov analysis is used to establish asymptotic results for the proposed protocol, avoiding the chattering issues associated with discontinuous sliding mode controls and the ultimate boundedness limitations of boundary-layer approximations.
• Partial-State Virtual Actuator Recovery: A continuous adaptive virtual-actuator layer is developed that asymptotically compensates for a broad class of actuator attacks (state-correlated, input-correlated, and exogenous) using only partial state measurements. This contrasts with existing results that often require full state measurements for asymptotic recovery.
• Practical Containment with Residual Analysis: The work distinguishes between command-level containment (asymptotic) and physical-output containment (practical). It provides a rigorous characterization of the residual error in physical outputs, attributing it to the mismatch between the moving command and the stable local command filter, rather than a failure of the containment protocol.

Simulation Results
The architecture was validated via numerical simulations involving a network of six heterogeneous quadrotors carrying cable-suspended loads (vector relative degree [4,4]) and three leaders generating complex, moving, rotating, and resizing convex hulls.

• Attack Scenario: Two followers were subjected to severe, persistent actuator attacks combining state-correlated, input-correlated, and exogenous components.
• Performance:
  • The network interface successfully drove the command states ($\sigma_i$) to the leaders' convex hull with negligible error ($< 10^{-6}$ m relative to hull diameter).
  • The local recovery layer maintained bounded signals and ensured the physical outputs remained within a small practical residual of the convex hull (maximum distance $\approx 7.23$ m, or $\approx 1\%$ of the hull diameter).
  • The dominant source of the physical residual was identified as the command-filter realization error (due to the inability of the stable filter to perfectly track arbitrary moving commands without higher-order derivatives), not the network containment error.
  • Comparisons with a non-resilient baseline showed that the proposed architecture effectively recovered from attacks, whereas the baseline failed to maintain containment.

Significance and Claims
The paper claims to fill a gap in the literature regarding continuous, asymptotic containment for heterogeneous MAS under undisclosed leader dynamics and actuator attacks. The significance lies in the ability to:

1. Operate without sensitive leader model information, enhancing security against adversarial synthesis of stealthy attacks.
2. Maintain resilience against complex actuator compromises without relying on discontinuous control actions that cause chattering.
3. Achieve asymptotic convergence of the coordination layer (commands) while providing a rigorous bound on the practical containment error of the physical layer.

The authors emphasize that the physical output containment is "practical" (converging to a residual) rather than asymptotic, a limitation inherent to the information pattern (lack of higher-order command derivatives) and the use of stable local filters, rather than a failure of the proposed control strategy. The work demonstrates that separating the network interface from the local execution layer effectively isolates actuator attacks, preventing them from propagating to the coordination layer.