Adaptive Critic Tracking Design for Data-Based Nonaffine Predictive Control

In recent years, model predictive control (MPC) is widely utilized to address the tracking problem of the practical industrial processes. In this paper, in terms of the advantages of adaptive dynamic programming (ADP), the adaptive critic trajectory tracking predictive control (ACTTPC) framework is designed to tackle tracking predictive control problems for unknown nonaffine systems. First, the unknown system dynamics are approximated by the established model network. Meanwhile, the feedforward steady control is considered to assist with accomplishing the tracking mission. Further, in each prediction horizon, the adaptive critic learning method is utilized to solve the open-loop optimization problem satisfying some conditions. Afterwards, the Lyapunov stability of the augmented error system is fully proved, and the convergence of the ACTTPC algorithm is analyzed in detail. Finally, a nonaffine system and a torsional pendulum plant are applied to validate the effectiveness of the presented approach in solving the tracking problems.
Note to Practitioners
—Many industrial processes are nonlinear nonaffine systems, which causes a great challenge to solve Hamilton-Jacobi-Bellman (HJB) equations for nonlinear MPC (NMPC). Therefore, it is quite valuable to solve the NMPC problem by using the advantages of ADP in addressing nonlinear HJB equations. In this paper, the ACTTPC algorithm is designed to guide the trajectory tracking predictive control for unknown system dynamics in the practical industrial processes. Generally speaking, the mathematical model of complex industrial systems is difficultly established. Hence, the model network is built via selecting a batch of data and it is seen as the prediction model. The introduced feedforward steady control can not only assist realizing trajectory tracking but also maintain stable tracking effect. Meanwhile, the feedback predictive control input is solved via the ACTTPC algorithm. The simulation experiments are conducted to prove the effectiveness of the presented algorithm. Moreover, the pseudo-code and the relevant experimental parameters are given. For different systems and reference trajectories, the practitioners can realize tracking tasks via modulating the related parameters.