Optimal control of unknown nonaffine nonlinear discrete-time systems based on adaptive dynamic programming

• Published in: Automatica (Oxford) Vol. 48; no. 8; pp. 1825 - 1832
• Main Authors: Wang, Ding, Liu, Derong, Wei, Qinglai, Zhao, Dongbin, Jin, Ning
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2012; Elsevier
• Subjects: Adaptive control systems; Adaptive critic designs; Adaptive dynamic programming; Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximate dynamic programming; Computer science; control theory; systems; Computer simulation; Control system synthesis; Control systems; Control theory. Systems; Cost function; Dynamical systems; Exact sciences and technology; Globalized dual heuristic programming; Intelligent control; Neural network; Nonlinear dynamics; Nonlinearity; Optimal control; Theoretical computing; Adaptive dynamic programming; Globalized dual heuristic programming; Optimal control; Approximate dynamic programming; Neural network; Adaptive critic designs; Intelligent control; Control system analysis; Adaptive algorithm; Adaptive system; Control program; Non linear control; Iterative method; Fork join problem; Adaptive method; Heuristic programming; Efficiency; Cost function; Dynamic programming; Optimal control (mathematics); Generic programming; Numerical convergence; Non linear system; Cost control; Discrete time
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.05.049

An intelligent-optimal control scheme for unknown nonaffine nonlinear discrete-time systems with discount factor in the cost function is developed in this paper. The iterative adaptive dynamic programming algorithm is introduced to solve the optimal control problem with convergence analysis. Then, the implementation of the iterative algorithm via globalized dual heuristic programming technique is presented by using three neural networks, which will approximate at each iteration the cost function, the control law, and the unknown nonlinear system, respectively. In addition, two simulation examples are provided to verify the effectiveness of the developed optimal control approach.