Novel Discounted Optimal Tracking Design Under Offline and Online Formulations for Asymmetric Constrained Systems

In this thesis, we construct improved value iteration (VI) and online VI structures, in a bid to tackle the optimal tracking control problem for discrete-time nonlinear systems. Note that asymmetric control restraints and the discount factor are considered. First, related properties are discussed for novel VI, involving the monotonicity of the iterative cost function sequence and the admissibility of the iterative tracking control policy. Second, the stability condition for the discount factor is provided to ensure the stability of all iterative tracking control policies, which are created by stabilizing VI. Third, by combining novel VI and stabilizing VI, an improved VI algorithm is developed, where iterative cost function sequences are monotonically nondecreasing and nonincreasing during novel VI and stabilizing VI stages, respectively. Fourth, with the appropriate discount factor, an online VI algorithm is proposed by integrating the attraction domain with improved VI. Also, under the online VI structure, the asymptotic stability proof is performed for the tracking error system. Finally, regarding theoretical contributions are illustrated by a simulation case.