Robust Nonlinear Data-Driven Predictive Control for Mixed Vehicle Platoons via Koopman Operator and Reachability Analysis

TL;DR

This work proposes RNDDPC, a robust nonlinear data-driven predictive control framework for mixed vehicle platoons containing CAVs and HDVs. It combines a Koopman-based deep EDMD lifting to linearize nonlinear dynamics in a high-dimensional space with a data-driven, zonotope-based reachability analysis to bound modeling errors, disturbances, and adversarial attacks. The online RNDDPC solves a receding-horizon convex optimization that enforces safety via over-approximated reachable sets, yielding improved tracking accuracy and safety across comprehensive, emergency, time-delay attack, and scalable platoon-size scenarios. The results demonstrate substantial performance gains over linear and nonlinear MPC, DeePC, and ZPC baselines, with real-time feasibility and scalable applicability to larger platoons. This approach advances robust, data-driven control for realistic mixed-traffic conditions and paves the way for field validations and extensions to delays and dynamic platoon topologies.

Abstract

Mixed vehicle platoons, comprising connected and automated vehicles (CAVs) and human-driven vehicles (HDVs), hold significant potential for enhancing traffic performance. However, most existing control strategies assume linear system dynamics and often ignore the impact of adverse factors such as noise, disturbances, and attacks, which are inherent to real-world scenarios. To address these limitations, we propose a Robust Nonlinear Data-Driven Predictive Control (RNDDPC) framework that ensures safe and optimal control under uncertain and adverse conditions. By utilizing Koopman operator theory, we map the system's nonlinear dynamics into a higher-dimensional space, constructing a Koopman-based model that approximates the behavior of the original nonlinear system. To mitigate modeling errors associated with this predictor, we introduce a data-driven reachable set analysis technique that performs secondary learning using matrix zonotope sets, generating a reachable set predictor for over-approximation of the future states of the underlying system. Then, we formulate the RNDDPC optimization problem and solve it in a receding horizon manner for robust control inputs. Extensive simulations demonstrate that the proposed framework significantly outperforms baseline methods in tracking performance under noise, disturbances, and attacks.

Figures (9)

• Figure 1: The schematic of the mixed vehicle platoon consists of a leading CAV (red) and multiple following HDVs (blue), following behind a head vehicle (gray). The green box represents the mixed vehicle platoon. The disturbance originates from variations in the head vehicle's velocity. The noise and attacks affect the uplink and downlink of the cloud control platform, respectively.
• Figure 2: The schematic of the proposed RNDDPC method for mixed vehicle platoons. In the offline learning phase (blue), pre-collected data (yellow) is utilized to train a DNN that learns the state lifting function $z(k)$. Using $z(k)$, this phase then computes over-approximated matrix zonotope sets $\mathcal{M}_{\mathrm{ABHJ}}$ and $\mathcal{M}_{\mathrm{C}}$, corresponding to the Koopman system matrices $A~B~H~J$ and $C$, respectively. In the online control phase (green), the RNDDPC framework focuses on determining a robust optimal control input. Specifically, it utilizes the matrix zonotope sets $\mathcal{M}_{\mathrm{ABHJ}}$ and $\mathcal{M}_{\mathrm{C}}$ to perform an online recursive computation of the data-driven reachable set for the system state, represented as zonotope. To enhance computational efficiency, the zonotope-type reachable sets are approximated as interval-type reachable sets, providing straightforward upper and lower bounds for each state variable. Based on these interval bounds and predefined safety constraints, a convex optimization problem is formulated within the RNDDPC framework. This optimization problem is solved using a receding horizon control strategy, ensuring that the computed control input for the CAV maintains robust and safe operation in real-time.
• Figure 3: The overview of the Koopman deep neural network framework. The original state $x(k) \in \mathbb{R}^{2n}$ of the mixed vehicle platoon is lifted using both the state itself and an encoder network to obtain the lifted state $z(k) \in \mathbb{R}^{n_\mathrm{z}}$. The lifted state $z(k)$, along with the control input $u(k) \in \mathbb{R}$, disturbance input $\epsilon(k) \in \mathbb{R}$, and attack input $\vartheta(k) \in \mathbb{R}$ together construct a linear evolution in the lifted space, which generates the next lifted state $z(k+1) \in \mathbb{R}^{n_\mathrm{z}}$. The corresponding original state $x(k+1) \in \mathbb{R}^{2n}$ is then reconstructed from the lifted state space via the decoder network. The state lifting function $z(k)$ is derived through automated training of the network, guided by a well-designed loss function.
• Figure 4: Simulation scenario for mixed vehicle platoon control in PreScan simulation software. The CAV is highlighted in red, the HDVs in blue, and the head vehicle in gray, consistent with the representation in \ref{['Fig:MixedPlatoon']}.
• Figure 5: The velocity profiles for comprehensive simulations and emergency simulations.

Theorems & Definitions (18)

• Definition 1: Koopman Operator koopman1931hamiltonian
• Definition 2: Interval Set althoff2010reachability
• Definition 3: Zonotope Set kuhn1998rigorously
• Definition 4: Matrix Zonotope Set althoff2010reachability
• remark 1: General Form of Non–Time-Delay Attacks
• remark 2: Modeling Nonlinear Dynamics of Mixed Vehicle Platoons
• remark 3: Robustness Requirements in Mixed Vehicle Platoons
• remark 4: Challenges in Koopman Operator-Based Mixed Vehicle Platoon Control
• remark 5: Reliability of Mapping Physical State from the Lifted State
• Lemma 1: Over-Approximated System Model