Stability Certificates for Receding Horizon Games: Ensuring Reliable and Resilient Control of Multi-Agent Systems
แนวคิดหลัก
Receding Horizon Games (RHG) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This work presents the first formal stability analysis for RHG controllers, deriving LMI-based certificates that ensure asymptotic stability and are numerically verifiable.
บทคัดย่อ
This paper presents a stability analysis for Receding Horizon Games (RHG), an emerging control methodology for multi-agent systems. RHG generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion, allowing it to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process.
The key contributions of this work are:
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Derivation of LMI-based stability certificates that ensure asymptotic stability of the closed-loop system under the RHG feedback law. These certificates are valid for non-potential games and can be numerically verified.
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Demonstration that the numerical verification can be performed in a scalable manner if the agents have decoupled dynamics.
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Provision of tuning guidelines for the agents' cost function weights to fulfill the stability certificates and ensure closed-loop stability.
The stability analysis is based on viewing the RHG closed-loop system as a feedback interconnection of an LTI system and a static nonlinearity. By leveraging dissipativity theory and monotone operator theory, the authors derive sufficient conditions for asymptotic stability that can be checked by solving a convex optimization problem.
The paper also includes an analysis of a simplified 1-dimensional case, which provides insights into how the agents can modify their local subsystems to ensure stability. Finally, the effectiveness of the stability certificates and tuning guidelines is validated through a case study on a battery charging scenario.
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Stability Certificates for Receding Horizon Games
สถิติ
The system dynamics are described by the linear time-invariant (LTI) model:
xt+1 = A xt + Σv∈V Bv uv
t
The stage cost for each agent v is given by:
ℓv(xt, uv
t, u-v
t) = xt⊤ Wv xt + (wv)⊤ xt + ℓv
u(uv
t, u-v
t)
The agents' local input constraints are:
uv
t ∈ Uv
And the coupling constraint is:
(uv
t, u-v
t) ∈ C
คำพูด
"Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion."
"This control paradigm has recently received an increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process."
สอบถามเพิ่มเติม
How can the stability certificates be extended to handle unstable LTI systems or non-linear dynamics
To extend the stability certificates to handle unstable LTI systems or non-linear dynamics, we can explore different Lyapunov function candidates that are suitable for analyzing the stability of such systems. For unstable LTI systems, we can consider using input-to-state stability (ISS) Lyapunov functions, which can capture the system's behavior in the presence of disturbances or uncertainties. By incorporating ISS Lyapunov functions into the stability analysis, we can assess the system's stability properties even when the open-loop dynamics are unstable.
For non-linear dynamics, we can leverage tools from dissipativity theory and passivity-based control to develop Lyapunov functions that account for the non-linearities in the system. By formulating appropriate energy functions or storage functions that capture the system's behavior, we can establish stability conditions that account for the non-linear dynamics. Additionally, we can explore techniques such as small-gain theorems to handle non-linearities and ensure stability in the closed-loop system.
What are the implications of relaxing the strong monotonicity assumption on the pseudo-gradient mapping, and how can the stability analysis be adapted to handle more general game structures
Relaxing the strong monotonicity assumption on the pseudo-gradient mapping can have implications on the stability analysis of the system. When the strong monotonicity condition is relaxed, the stability analysis may need to consider weaker forms of monotonicity, such as cocoercivity or quasimonotonicity. These weaker forms of monotonicity can still provide insights into the system's behavior and stability properties, albeit with potentially different convergence guarantees.
To adapt the stability analysis to handle more general game structures with relaxed monotonicity assumptions, we can explore alternative stability criteria based on variational inequalities or generalized Nash equilibrium concepts. By incorporating these concepts into the stability analysis, we can develop stability certificates that are applicable to a broader class of games with varying degrees of monotonicity in the pseudo-gradient mapping. Additionally, we can consider robust stability analysis techniques to account for uncertainties or variations in the system dynamics.
Can the stability analysis be further refined to provide tighter bounds on the region of attraction or the convergence rate of the closed-loop system under the RHG feedback law
To provide tighter bounds on the region of attraction or the convergence rate of the closed-loop system under the RHG feedback law, we can employ advanced stability analysis techniques such as input-to-state stability (ISS) or incremental stability analysis. By utilizing ISS Lyapunov functions, we can quantify the system's convergence properties and establish tighter bounds on the region of attraction around the equilibrium point. Additionally, incremental stability analysis can help characterize the system's convergence rate and provide insights into the system's transient behavior.
Furthermore, we can explore optimization-based methods to optimize the Lyapunov functions and improve the system's stability properties. By formulating optimization problems that maximize the region of attraction or minimize the convergence time, we can tailor the stability analysis to achieve specific performance objectives. These refined stability analyses can offer a more detailed understanding of the system's behavior under the RHG feedback law and provide valuable insights for system design and control.
