Adaptive Robust Formation Tracking of Euler–Lagrange Systems Under RCRT-Based Secure Communication

Abstract

This paper studies privacy-aware formation tracking for multiple Euler–Lagrange systems over open channels subject to eavesdropping risk and residue-level bit-flip errors. A redundant Chinese remainder theorem (RCRT)-based private encoding mechanism is developed under a pre-shared-parameter threat model. One redundant modulus enables single-residue corruption detection, with rejected packets handled by holding the latest valid relative reconstruction. A command-filtered adaptive robust controller accommodates uncertain EL dynamics and bounded disturbances. A composite Lyapunov analysis establishes an invariant admissible set that preserves unambiguous relative decoding and bounds the quantization and hold-induced residuals. The resulting conditions relate the encoding scale, modulus range, and sampling period to the ultimate formation-error bounds and establish semiglobal uniform ultimate boundedness for prescribed compact sets of initial augmented errors. Monte Carlo, ablation, and enlarged-initial-condition simulations illustrate the tracking accuracy, robustness, and implementation tradeoffs of the proposed framework. Note to Practitioners—This paper provides a distributed formation-tracking architecture for Euler–Lagrange agents communicating over non-ideal digital links. The communication layer uses one redundant modulus to detect single-residue corruption. The scaling, translation, and modulus parameters are pre-shared through an authenticated setup, and the RCRT layer provides lightweight state obfuscation and corruption detection under the stated threat model. After a corrupted packet is rejected, a zero-order hold keeps the controller operating and converts the communication fault into a bounded residual. The adaptive regressor compensates for the parameterized nonlinear EL dynamics, while the smooth robust term attenuates bounded lumped disturbances; the communication-induced reconstruction residuals enter the command-filtered augmented error dynamics through the reconstructed relative deviations. The communication model allows residue corruptions to occur simultaneously on multiple directed links, while each scalar component on each link is subject to the single-residue corruption condition. Additional redundant moduli extend detection to multiple-residue corruption when all moduli are pairwise coprime and each redundant modulus exceeds every information modulus. The simulations show the resulting tradeoff among tracking accuracy, control variation, communication overhead, and fault tolerance.