Neural networks for control systems: a survey
Automatica (Journal of IFAC)
Direct training method for a continuous-time nonlinear optimal feedback controller
Journal of Optimization Theory and Applications
Universal approximation bounds for superpositions of a sigmoidal function
IEEE Transactions on Information Theory
Optimal control of terminal processes using neural networks
IEEE Transactions on Neural Networks
Identification and control of dynamical systems using neural networks
IEEE Transactions on Neural Networks
Centralized Indirect Control of an Anaerobic Digestion Bioprocess Using Recurrent Neural Identifier
AIMSA '08 Proceedings of the 13th international conference on Artificial Intelligence: Methodology, Systems, and Applications
Reinforcement learning and adaptive dynamic programming for feedback control
IEEE Circuits and Systems Magazine
A retrospective on adaptive dynamic programming for control
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Adaptive critic based redundancy resolution scheme for robot manipulators
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Neural network solution of optimal control problem with control and state constraints
ICANN'11 Proceedings of the 21st international conference on Artificial neural networks - Volume Part II
Neural networks solving free final time optimal control problem
TPNC'12 Proceedings of the First international conference on Theory and Practice of Natural Computing
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A neural network based optimal control synthesis approach is presented for systems modeled by partial differential equations. The problem is formulated via discrete dynamic programming and the necessary conditions of optimality are derived. For synthesis of the controller, we propose two sets of neural networks: the set of action networks captures the mapping between the state and control, while the set of critic networks captures the mapping between the state and costate. We illustrate the solution process with a parabolic equation involving a nonlinear term. For comparison, we consider the linear 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 control design of both linear and nonlinear distributed parameter systems.