Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions

An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs

“…Next, we change the utility function into a nonquadratic form in [34] with modifications, where the utility function is expressed as…”

Neural-network-based adaptive optimal tracking control scheme for discrete-time nonlinear systems with approximation errors

“…To overcome the difficulty, many approximation methods are proposed to obtain optimal tracking control law [2][3][4][5]. Among these approximate approaches, adaptive dynamic programming (ADP) algorithm, proposed by Werbos [6,7], has played an important role in seeking approximate solutions of dynamic programming problems as a way to solve the computational issue forward-in-time [8][9][10][11][12][13][14]. There are several synonyms used for ADP including "adaptive critic designs" [15], "adaptive dynamic programming" [16,17], "approximate dynamic programming" [18,19], "neural dynamic programming" [20], "neuro-dynamic programming" [21], and "reinforcement learning" [22].…”

Nonlinear neuro-optimal tracking control via stable iterative Q-learning algorithm

“…Iterative method is a primary tool in ADP to obtain the solution of HJB equation indirectly. In general, there are policy and value iterations according to the differences of the iteration procedures [9,25,33,36,38,40,[42][43][44]. In value iteration algorithms, the initial value iteration algorithm is generally set to zero [1,10].…”