TY - JOUR
T1 - Robust min–max optimal control design for systems with uncertain models
T2 - A neural dynamic programming approach
AU - Ballesteros, Mariana
AU - Chairez, Isaac
AU - Poznyak, Alexander
N1 - Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/5
Y1 - 2020/5
N2 - The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min–max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton–Jacobi–Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution.
AB - The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min–max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton–Jacobi–Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution.
KW - Approximate dynamic-programming
KW - Artificial neural networks
KW - Bellman function
KW - Hamilton–Jacobi–Bellman equation
KW - Sub-optimal controller
UR - http://www.scopus.com/inward/record.url?scp=85079836128&partnerID=8YFLogxK
U2 - 10.1016/j.neunet.2020.01.016
DO - 10.1016/j.neunet.2020.01.016
M3 - Artículo
C2 - 32097830
SN - 0893-6080
VL - 125
SP - 153
EP - 164
JO - Neural Networks
JF - Neural Networks
ER -