## Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach.(English)Zbl 1087.49022

Summary: The Hamilton-Jacobi-Bellman (HJB) equation corresponding to constrained control is formulated using a suitable nonquadratic functional. It is shown that the constrained optimal control law has the largest region of asymptotic stability (RAS). The value function of this HJB equation is solved by solving a sequence of cost functions satisfying a sequence of Lyapunov equations (LE). A neural network is used to approximate the cost function associated with each LE using the method of least-squares on a well-defined region of attraction of an initial stabilizing controller. As the order of the neural network is increased, the least-squares solution of the HJB equation converges uniformly to the exact solution of the inherently nonlinear HJB equation associated with the saturating control inputs. The result is a nearly optimal constrained state feedback controller that has been tuned a priori off-line.

### MSC:

 49L20 Dynamic programming in optimal control and differential games 93C10 Nonlinear systems in control theory 92B20 Neural networks for/in biological studies, artificial life and related topics
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### References:

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