Control of complex systems with generalized embedding and empirical dynamic modeling

TL;DR

The paper addresses the challenge of controlling nonlinear, complex systems when explicit mathematical models are difficult to obtain. It introduces a data-driven, explainable model predictive control (MPC) framework built on generalized state-space embedding and empirical dynamic modeling (EDM), avoiding predefined dictionaries and heavy training. Demonstrated on an agent-based civil-disobedience model with 1200 agents, the approach uses cross-mapping and s-map to construct a predictive state space and quantify intervariable dependencies, yielding a high out-of-sample prediction accuracy of ${\rho} \approx 0.98$ and enabling a robust logistic controller that stabilizes the system under variable legitimacy. The work argues that this generalized embedding EDM framework provides interpretable, scalable MPC for complex systems and is applicable to any state-space-representable dynamics.

Abstract

Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows obtaining a satisfactory mathematical representation is increasingly difficult. Further, many data-driven approaches consist of abstract internal representations that may have no obvious connection to the underlying dynamics and control, or, require extensive model design and training. Here, we remove these constraints by demonstrating model predictive control from generalized state space embedding of the process dynamics providing a data-driven, explainable method for control of nonlinear, complex systems. Generalized embedding and model predictive control are demonstrated on nonlinear dynamics generated by an agent based model of 1200 interacting agents. The method is generally applicable to any type of controller and dynamic system representable in a state space.

Figures (10)

• Figure 1: Schematic of empirical dynamic modeling (EDM) processing.
• Figure 2: Schematic of state based control. A complex system generates time series observations modeled in state space. State space predictions inform a controller modulating a system or state variable. The predictions do not require an explicit mathematical or structural model.
• Figure 3: Agent-based model interface (top) and nominal results (bottom) for Epstiens model of civil disobedience with constant legitimacy and propaganda.
• Figure 4: a) EDM simplex out--of--sample prediction skill (Pearson $\rho$) of the agent--based model Active variable as a function of state space embedding dimension at different forecast intervals ($\mathrm{T_p}$). b) EDM simplex out--of--sample prediction skill (Pearson $\rho$) of the Active variable as a function of forecast interval at different state space embedding dimensions (E).
• Figure 5: a) Civil disobedience model output under a scenario of variable legitimacy and no control. Punctuated equilibrium dynamics transition to a trapped state of sustained rebellion. b) Model output under a scenario with variable legitimacy and propaganda control. The control prevents the trapped states and sustained rebellion.