Energy-Efficient Adaptive Control for Nonlinear Dynamic Systems

This paper focuses on the optimal control of dynamic systems, particularly considering the optimization of reaching target states and minimizing energy consumption. The primary methods employed are Jacobian matrix linearization and state iteration for modeling. Based on this foundation, the paper attempts to solve the optimal control of dynamic systems using optimization problems. Subsequently, the optimization problem is improved by introducing adaptive step sizes and additional constraints to align it more closely with practical applications. The feasibility of these methods is verified from a mathematical perspective. Additionally, the paper examines the impact of constraints on the control problem and the issues that arise when the system approaches boundaries. Through mathematical derivations, the conditions under which constraints prevent the system from converging to the target state are investigated. Overall, this paper presents a novel algorithm for controlling dynamic systems while minimizing energy use. Additionally, it contributes by deriving specific conditions for system convergence under constraints, proposing a trade-off scheme between energy saving and target state achievement, and providing a comprehensive mathematical verification of the methods feasibility.