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Constrained optimal control of affine nonlinear discrete-time systems using GHJB method

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4 Author(s)
Lili Cui ; Sch. of Inf. Sci. & Eng., Northeastern Univ., Shenyang ; Huaguang Zhang ; Derong Liu ; Yongsu Kim

The infinite-horizon optimal control problem of nonlinear discrete-time systems with actuator saturation is considered in this paper. In order to deal with actuator saturation, a novel nonquadratic functional is introduced, and the constrained generalized Hamilton-Jacobi-Bellman (GHJB) equation and Hamilton-Jacobi-Bellman (HJB) equation for nonlinear discrete-time systems are derived in terms of non-quadratic functionals. The optimal saturated controller is obtained by a novel iterative algorithm based on the constrained GHJB equation, and a convergence proof is presented, where a neural network is used to approximate the value function. Finally, a nearly optimal saturated controller is obtained. The effectiveness of this algorithm is demonstrated by a numerical example.

Published in:

Adaptive Dynamic Programming and Reinforcement Learning, 2009. ADPRL '09. IEEE Symposium on

Date of Conference:

March 30 2009-April 2 2009