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Lyapunov Based Stable Neuro-Adaptive Nonlinear Model Predictive Control

This research presents a Nonlinear Model Predictive Control (NMPC) with adaptive neuro-modelling for redundant robotic manipulators. Using NMPC, the end-effector of robotic manipulator tracks a predefined geometry path in the Cartesian space without colliding with obstacles in the workspace and avoiding singular configurations of the robot. A model of the system is needed for prediction in MPC. In this research, a Multilayer Perceptron (MLP) is used for modelling nonlinear dynamics of the robot in MPC. Using neural network for model prediction, no knowledge about system parameters is needed and system robustness against change in parameters is obtained.

 

The neural networks used for model prediction are trained both offline and online .The neural networks are trained offline first using the data gathered form the system. The main reason for this is that the weights of NNs are initialized with random numbers; hence, without any offline training the robot might collide with obstacles. The offline training does not need to be very accurate; just a rough familiarity of NNs with the robot behaviour to avoid large initial tracking error and/or collision with obstacles suffices. It should be noted that the online training of NNs can cope with all changes in robot parameters, including the mass of links, the friction of joints and parameters of servomotors.



Also, the stability analysis for adaptive nonlinear model predictive control is considered. Stability of model predictive control (MPC) is addressed in many researches. These works are based on modifying the optimization problem employed in MPC. Works related to stability of MPC can be classified in two groups. First groups are based on adding constraints in optimization problem and the second groups are based on adding a term in cost function of optimization problem in such a way that closed-loop stability is guaranteed. It is shown that adding Lyapunov function as a terminal penalty in cost function, grantees the stability of NMPC. However, obtaining global Lyapunov function for nonlinear systems is rarely possible; Therefore, a local Lyapunov function is implemented. Moreover, adding constraints results in remarkable increase of the computational time. As a result, all the previous works show the stability of linear MPC and local stability of nonlinear MPC. In this research, the global stability of nonlinear adaptive neuro-MPC is established. To this aim, a Lyapunov function based on control goals and identification error of neural networks is defined. Then, the adaptation laws for weights of the neural network in prediction model are obtained in such a way that the stability of closed loop systems is guaranteed based on Lyapunov’s direct method.

 



Papers:


  • Ashkan Jasour, M. Farrokhi, ”Fuzzy Improved Adaptive Neuro-NMPC for On-Line Path Tracking and Obstacle Avoidance of Redundant Robotic Manipulators”, International Journal of Automation and Control (IJAAC), Vol. 4, No.2, pp. 177-200, 2010