Temporal Finite-Time Adaptation in Controlling Quantized Nonlinear Systems Amidst Time-Varying Output Constraints

Journal article, 2024

Using the backstepping technique, this paper formulates innovative adaptive finite-time stabilizing controllers for uncertain nonlinear systems featuring nonuniform input quantization and asymmetric, time-varying output constraints. These novel controllers leverage the consistent characteristics of both hysteresis quantizers and logarithmic quantizers. Quantization errors, when consistent, become unbounded and contingent on control input, rendering them incompatible with the growth conditions of nonlinear systems. Consequently, the developed adaptive controllers eliminate the reliance on growth conditions, effectively addressing the impact of unbounded quantization errors on finite-time stability. This adaptability allows the controllers to function effectively with systems employing either hysteresis quantizers or logarithmic quantizers. The paper establishes the convergence of these controllers through the finite-time Lyapunov stability theorem. It also provides a comprehensive guideline for tuning settling time, enabling fine-grained control over finite-time convergence and adjustable tracking error performance. Additionally, the controllers rigorously maintain system output within predefined limits. Their effectiveness and low computational burden are demonstrated through three comparative numerical simulations and a practical simulation in collision-free trajectory tracking control of an autonomous vehicle platoon using the vehicle motion software CarSim. These simulations confirm the advanced performance of the adaptive controllers. Note to Practitioners—This paper introduces an innovative approach to control uncertain nonlinear systems encountering intricate input quantization and output constraints. Employing the sophisticated backstepping technique, the authors present adaptive finite-time-stabilizing controllers engineered to address nonuniform input quantization and asymmetric, time-varying output restrictions. What distinguishes these controllers is their reliance on the consistent behavior exhibited by hysteresis and logarithmic quantizers. This unique feature equips them to effectively counteract unbounded quantization errors influenced by control input. Most notably, these controllers eliminate the conventional growth conditions typically demanded by nonlinear systems. As a result, they extend their applicability to a broad spectrum of systems employing either hysteresis or logarithmic quantizers. The research also provides practitioners with a valuable guideline for precisely adjusting settling time. This enables the attainment of desired convergence rates while permitting adaptable tracking error performance. Additionally, these controllers guarantee that the system’s output adheres to predefined limits. The practical significance of this study is highlighted through three comparative numerical simulations and a real-world application simulation. This real-world simulation involves collision-free trajectory tracking control of an autonomous vehicle platoon, executed using the vehicle motion software CarSim. These simulations unequivocally demonstrate the effectiveness and low computational burden of the developed controllers, thereby establishing them as a valuable resource for practitioners facing complex control challenges in various domains.