Online optimal control of unknown discrete-time nonlinear systems by using time-based adaptive dynamic programming

Nearly dynamic programming NN‐approximation–based optimal control for greenhouse climate: A simulation study

“…This implies that the weight update laws (21), (40), and (50) of the 3 NN identifiers can guarantee the asymptotical convergence of the closed-loop system and the UUB performance of the tracking error e k .…”

“…However, greenhouse climate dynamics are very complex, and using a simple static model to predict the inside temperature, as done in Pucheta's method, may be insufficient. Since the nearly dynamic programming neural network approximation (NNOC) has been widely used to solve optimal control problems of nonlinear systems in recent years, we are inspired to develop a new optimal control approach for greenhouse climate based on NNOC and a greenhouse climate dynamics model to solve the greenhouse climate multivariable coupling optimal control problem. In the proposed approach, an NN is introduced to perform online estimation of the uncertainties to compensate as the unmodeled dynamics of the system, and the optimal controller is first designed to yield a set of virtual control inputs, which represent the required heat and mass fluxes to guarantee the convergence of the closed system.…”

Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs

“…Adaptive/Approximate Dynamic Programming (ADP) [1][2][3][4][5][6][7][8][9][10][11][12][13] has received attention due to its learning capacity, which can provide a solution to optimal control problems. As is known, traditional dynamic programming method with computation in backward-in-time manner may result in the curse of dimensionality.…”

“…The PI algorithm converges to the optimal control and the optimal value function if it starts with an initial admissible control, which was proved by Abu-Khalaf in [1], then the solution to the HJB equation can be obtained indirectly by the PI algorithm. Afterwards, [3,5,6,8,9] made contributions to online computation for infinite horizon optimal control. In [3], the online algorithm was implemented by using actor-critic NNs structure.…”

Data‐driven optimal tracking control for a class of affine non‐linear continuous‐time systems with completely unknown dynamics

“…Zhang et al [3] introduced the VI algorithm to solve the infinite‐time OTCP for a class of DT non‐linear systems with completely knowledge of system dynamics, and Zhang et al [5] attempted to consider a more complicate situation which contains time‐delay in system dynamics. To deal with the unknown systems, the authors [27–29] attempted to reconstruct the system model by an added neural network (NN), and then implement the ADP algorithm to solve the optimal control. The authors [6, 7] followed the idea and proposed methods to solve the OTCP with unknown dynamics by reconstructing system model.…”