Integral Reinforcement Learning Control for a Class of High-Order Multivariable Nonlinear Dynamics With Unknown Control Coefficients

This paper develops an integral reinforcement learning (IRL) controller for a class of high-order multivariable nonlinear systems with unknown control coefficients (UCCs). A new long-term performance index is first presented, and then the critic neural network (NN) and the action NN are presented to estimate the unobtainable long-term performance index and the unknown drift of systems, respectively. By combining the critic and action NNs with Nussbaum-type functions, the IRL controllers for high-order, nonsquare multivariable systems are proposed to cope with the problem of UCCs. The analysis are given to illustrate that the stability of the closed-loop system can be obtained, and the signals of the closed-loop systems are semiglobally uniformly ultimately bounded (UUB). Finally, one simulation example is provided to show the effectiveness of the proposed IRL controllers.