Action-dependent updated terminal cost receding horizon control for discrete-time linear systems

In case of linear quadratic regulator (LQR), the updated terminal cost receding horizon control (UTC-RHC) enhances the standard RHC in terms of the stability and the convergence to the optimal solution. Based on the action-dependent (AD) value functions, known as Q-function, this paper proposes two modified RHC methods, AD-RHC and AD-UTC-RHC and proves the stability and convergence by using the matrix equivalence of the established control schemes. Additionally, in case of the horizon size N = 1, as like UTC-RHC is connected with heuristic dynamic programming (HDP), we shows the connection between the AD-UTC-RHC and ADHDP which has the learning abilities of the optimal solution without using the explicit descriptions of the system dynamics.