Groupe d’études et de recherche en analyse des décisions

Neural Networks for Feedback Control of Robots and Dynamical Systems

Frank L. Lewis

Practical industrial, robotic, and aerospace systems have unknown disturbances, unmodeled dynamics, actuator constraints, friction, and restricted availability of measurements. Such systems cannot easily be dealt with using standard adaptive or robust feedback control techniques. Over the past years we have developed a family of feedback controllers that can confront these systems using neural networks as the basic control block structure. The learning abilities of neural networks considered as Intelligent Systems allow these controllers to learn on-line and improve their performance through tuning of the weights. We will present a catalog of neural network controllers designed based on feedback linearization, backstepping, singular perturbations, and dynamic inversion techniques. These neural network controllers are all tuned on-line in real time based on the system errors. Then, we will present some recent results on \(H\)-infinity feedback control for constrained input nonlinear systems. The constraints on the input to the system are encoded via a quasi-norm that allows non-quadratic supply rates along with dissipativity theory to formulate the robust output feedback control problem using Hamilton-Jacobi-Isaac (HJI) equations. An iterative solution technique based on a game theoretic interpretation is presented. To provide a computationally tractable controller design method, the solution is approximated at each iteration with a neural network. The result is a closed-loop control based on a neural net that has been tuned a priori off-line.