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In this brief, an online robust adaptive dynamic programming algorithm is proposed for two-player zero-sum games of continuous-time unknown linear systems with matched uncertainties, which are functions of system outputs and states of a completely unknown exosystem. The online algorithm is developed using the policy iteration (PI) scheme with only one iteration loop. A new analytical method is proposed for convergence proof of the PI scheme. The sufficient conditions are given to guarantee globally asymptotic stability and suboptimal property of the closed-loop system. Simulation studies are conducted to illustrate the effectiveness of the proposed method.

Regarding two-player zero-sum games of continuous-time nonlinear systems with completely unknown dynamics, this paper presents an online adaptive algorithm for learning the Nash equilibrium solution, i.e., the optimal policy pair. First, for known systems, the simultaneous policy updating algorithm (SPUA) is reviewed. A new analytical method to prove the convergence is presented. Then, based on the SPUA, without using a priori knowledge of any system dynamics, an online algorithm is proposed to simultaneously learn in real time either the minimal nonnegative solution of the Hamilton-Jacobi-Isaacs (HJI) equation or the generalized algebraic Riccati equation for linear systems as a special case, along with the optimal policy pair. The approximate solution to the HJI equation and the admissible policy pair is reexpressed by the approximation theorem. The unknown constants or weights of each are identified simultaneously by resorting to the recursive least square method. The convergence of the online algorithm to the optimal solutions is provided. A practical online algorithm is also developed. Simulation results illustrate the effectiveness of the proposed method.

Most adaptive control algorithms for nonlinear discrete time systems become invalid when the controlled systems have non-minimum phase properties and large uncertainties. In this paper, an intelligent control method using multiple models and neural networks (NN) is developed to deal with those problems. The proposed control method includes a set of fixed controllers, a re-initialized neural network (NN) adaptive controller and a free-running NN adaptive controller. The bounded-input-bounded-output (BIBO) stability and performance convergence of the system are guaranteed by the free-running adaptive controller, while the multiple fixed controllers and the re-initialized adaptive controller are used to improve the transient response. Simulation results are presented to demonstrate the effectiveness of the proposed method.

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