Adaptive-critic based optimal neuro control synthesis for distributed parameter systems

A neural network based optimal control synthesis approach is presented for systems modeled by partial differential equations. The problem is formulate d via discrete dynamic programming and the necessary conditions of optimali ty are derived. For synthesis of the controller. we propose two sets of neu ral networks: the set of action networks captures the mapping between the s tate and control, while the set of critic networks captures the mapping bet ween the state and costate. We illustrate the solution process with a parab olic equation involving a nonlinear term. For comparison, we consider the l inear quadratic regulator problem for the diffusion equation, for which the Ricatti-operator based solution is known. Results show that this adaptive- critic based systematic approach holds promise for obtaining the optimal co ntrol design of both linear and nonlinear distributed parameter systems. (C ) 2001 Published by Elsevier Science Ltd.