Innovative Discounted Optimal Control Design via Offline and Online Formulations for Affine Systems

This paper develops a novel value iteration (VI) scheme and an online VI algorithm, to address the discounted optimal control problems of affine discrete-time nonlinear systems. First, we provide the derivation of the novel VI. Second, we analyze the convergence and monotonicity of the iterative value function sequence, as well as the admissibility of the iterative control. Third, based on the theory of the attraction domain and the novel VI scheme, an online VI algorithm is proposed to implement the stability analysis of the controlled system. It is worth noting that the current control during the online control stage is determined by the location of the current state. Finally, a simulation example is involved to demonstrate the performance of the developed algorithms.