TY - JOUR
T1 - Compensator-based approximate optimal control for affine nonlinear systems with input constraints and unmatched disturbances
AU - Lu, Ke
AU - Liu, Chunsheng
AU - Sun, Jingliang
AU - Li, Chunhua
AU - Ma, Chengcheng
N1 - Publisher Copyright:
© The Author(s) 2020.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.
AB - This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.
KW - Adaptive dynamic programming (ADP)
KW - asymptotically stable
KW - auxiliary dynamic compensator
KW - input constraints
KW - unmatched disturbances
UR - http://www.scopus.com/inward/record.url?scp=85088293692&partnerID=8YFLogxK
U2 - 10.1177/0142331220940161
DO - 10.1177/0142331220940161
M3 - Article
AN - SCOPUS:85088293692
SN - 0142-3312
VL - 42
SP - 3024
EP - 3034
JO - Transactions of the Institute of Measurement and Control
JF - Transactions of the Institute of Measurement and Control
IS - 15
ER -