Improving CACC Robustness to Parametric Uncertainty via Plant Equivalent Controller Realizations

Cooperative Adaptive Cruise Control (CACC) enables vehicle platooning through inter-vehicle communication, improving traffic efficiency and safety. Conventional CACC relies on feedback linearization, assuming exact vehicle parameters; however, longitudinal vehicle dynamics are nonlinear and subject to parametric uncertainty. Applying feedback linearization with a nominal model yields imperfect cancellation, leading to model mismatch and degraded performance with off-the-shelf CACC controllers. To improve robustness without redesigning the CACC law, we explicitly model the mismatch between the ideal closed-loop dynamics assumed by the CACC design and the actual dynamics under parametric uncertainties. Robustness is formulated as an $\mathcal{L}_2$ trajectory-matching problem, minimizing the energy of this mismatch to make the uncertain system behave as closely as possible to the ideal model. This objective is addressed by optimizing over plant equivalent controller (PEC) realizations that preserve the nominal closed-loop behavior while mitigating the effects of parametric uncertainty. Stability and performance are enforced via linear matrix inequalities, yielding a convex optimization problem applicable to heterogeneous platoons. Experimental results demonstrate improved robustness and performance under parametric uncertainty while preserving nominal CACC behavior.

💡 Research Summary

The paper tackles a fundamental robustness issue in Cooperative Adaptive Cruise Control (CACC) systems that rely on feedback linearization. Traditional CACC designs assume exact knowledge of vehicle parameters (mass, aerodynamic drag, viscous friction, driveline time constant, etc.) in order to cancel nonlinearities and obtain a simple second‑order linear model. In practice, these parameters are uncertain and may vary over time due to payload changes, road conditions, or environmental factors. When the nominal model is used for linearization, the cancellation is imperfect, leaving a residual nonlinear term ϕ that causes a mismatch between the ideal closed‑loop dynamics assumed in the controller design and the true vehicle behavior. This mismatch degrades string stability, inter‑vehicle spacing accuracy, and overall performance.

The authors first present a comprehensive nonlinear longitudinal vehicle model that aggregates the various resistive forces into six parameter groups (p_j) (j = 1,…,6). Each group is expressed as a nominal value (p_{j|0}) plus an additive uncertainty (\Delta_j). By substituting these uncertain parameters into the acceleration dynamics, the model is rewritten as a nominal linear part plus a disturbance term that is linear in the uncertainties (equations (8)–(11)). The desired linearized vehicle model (9) is recovered when all (\Delta_j = 0).

The key contribution is the exploitation of Plant Equivalent Controller (PEC) realizations. A PEC is a different state‑space representation of the same nominal controller that yields identical input‑output behavior when the plant is exactly known, but whose internal dynamics can be tuned to attenuate the effect of parameter uncertainties. By applying a linear transformation (14) to the original controller state (\rho_i), new controller matrices (\bar A_c, \bar B_c, \bar E_c) are obtained (15). The transformation matrices (F_{i,i}) and (F_{i,i-1}) constitute the design variables. Importantly, the nominal closed‑loop response (i.e., when (\Delta = 0)) remains unchanged, while the mapping of the uncertainty term (\varphi_i) into the closed‑loop dynamics is altered through the product (F_{i,i} B_{\varphi}).

To make the problem tractable, the authors restrict attention to a two‑vehicle platoon (leader and follower) and focus on the follower’s dynamics. They show that, after the transformation, only a single scalar element of the PEC matrix (denoted (f_{2,3})) influences the propagation of the uncertainty, allowing the remaining degrees of freedom to be fixed (e.g., choosing (f_{1,2} = -\tau_i h_i) to eliminate dependence on the leader’s input).

The uncertain closed‑loop system is then expressed as a polytopic linear system, where the matrices depend affinely on the uncertainty vector (\Delta =