This paper proposes rail-less trains, composed of electric buses which are coupled together. The dynamic model of the rail-less electric bus train (REBT) involves not only nonlinearities but also unknown and uncertain parameters, which pose significant challenges. To mitigate model nonlinearities and parameter uncertainties in practical REBT system, we develop centralized and distributed adaptive control laws based on high-order full actuation (HOFA) control. For developing the centralized adaptive control law, we propose a novel adaptive control method, integrating gamma-projection operators with sigma-modification in adaptive estimation. This method robustly constrains parameter estimates within the known set while suppressing drift and offering tradeoffs between the magnitudes of control signal and tracking performance. For developing the distributed adaptive control law, we propose a different adaptive control method, employing both autonomous and cooperative control actions and using again the gamma-projection. In addition, adaptive estimation is aided by an off-line least-squares (LS) algorithm that ensures the adaptive estimates to converge to the true system parameters under the persistent excitation condition, leading to asymptotic feedback linearization and global asymptotic stabilization. Disturbance rejection in the framework of -control is studied for the linearized REBT system. It is shown that the two proposed adaptive control laws ensure the -norm from the input disturbance to the output tracking errors for velocity and inter-EB-distance controls to be strictly smaller than any γ > 0, effectively suppressing energy bounded disturbances in the worst-case. The simulation study includes industrial-level simulators and validates the proposed adaptive control methods.
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