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The convergence and stability of a value-iteration-based adaptive dynamic programming (ADP) algorithm are considered for discrete-time nonlinear systems accompanied by a discounted quadric performance index. More importantly than sufficing to achieve a good approximate structure, the iterative feedback control law must guarantee the closed-loop stability. Specifically, it is firstly proved that the iterative value function sequence will precisely converge to the optimum. Secondly, the necessary and sufficient condition of the optimal value function serving as a Lyapunov function is investigated. We prove that for the case of infinite horizon, there exists a finite horizon length of which the iterative feedback control law will provide stability, and this increases the practicability of the proposed value iteration algorithm. Neural networks (NNs) are employed to approximate the value functions and the optimal feedback control laws, and the approach allows the implementation of the algorithm without knowing the internal dynamics of the system. Finally, a simulation example is employed to demonstrate the effectiveness of the developed optimal control method.

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A new concept of LTS/HTS hybrid conductor was recently proposed. However, little theoretical and experimental research has been done in aspects of its stability. Based on the electromagnetic model of the hybrid conductors, current redistribution between LTS and HTS is numerically investigated in transient process. Furthermore, temperature distribution, quench velocity and minimum quench energy are also simulated by solving thermal-magnetic coupling equivalent equations. Comparing with conventional superconducting conductor, the simulated results show that the stability of the hybrid conductor can be greatly improved and it has potential application in large scale and conduction cooled superconducting magnet.