Lyapunov method in the synthesis of intelligent adaptive systems

Abstract

The development of intelligent adaptive systems has become increasingly significant in control engineering and artificial intelligence. These systems require robust mathematical tools to ensure stability and performance under uncertain and dynamically changing environments. This paper presents the Lyapunov method as a fundamental theoretical approach in the synthesis of intelligent adaptive systems. The method provides a rigorous framework to analyze and guarantee the stability of nonlinear and time-varying systems. We focus on the integration of Lyapunov-based stability analysis with modern adaptive algorithms, such as neural networks and fuzzy logic systems. Applications in robotics, autonomous vehicles, and environmental monitoring are discussed to demonstrate the effectiveness of this approach. By ensuring uniform asymptotic stability, the Lyapunov method plays a critical role in designing intelligent systems that are both adaptive and reliable. The study concludes that Lyapunov-based design significantly improves system performance, adaptability, and resilience to disturbances and parameter uncertainties.