Numerical techniques for stochastic optimization
Numerical techniques for stochastic optimization
Universal approximation using radial-basis-function networks
Neural Computation
Regularization theory and neural networks architectures
Neural Computation
A receding-horizon regulator for nonlinear systems and a neural approximation
Automatica (Journal of IFAC)
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
Applications of Automatic Control Concepts to Traffic Flow Modeling and Control
Applications of Automatic Control Concepts to Traffic Flow Modeling and Control
Bounds on rates of variable-basis and neural-network approximation
IEEE Transactions on Information Theory
Comparison of worst case errors in linear and neural network approximation
IEEE Transactions on Information Theory
Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems
IEEE Transactions on Neural Networks
Tight Bounds on Rates of Neural-Network Approximation
ICANN '01 Proceedings of the International Conference on Artificial Neural Networks
Fault diagnosis for nonlinear systems using a bank of neural estimators
Computers in Industry - Special issue: Soft computing in industrial applications
Efficient sampling in approximate dynamic programming algorithms
Computational Optimization and Applications
Automatica (Journal of IFAC)
Smooth Optimal Decision Strategies for Static Team Optimization Problems and Their Approximations
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
A decision theoretic approach to Gaussian sensor networks
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Computational Optimization and Applications
Functional Optimization Through Semilocal Approximate Minimization
Operations Research
Stable hybrid control based on discrete-event automata and receding-horizon neural regulators
Automatica (Journal of IFAC)
Suboptimal Solutions to Team Optimization Problems with Stochastic Information Structure
SIAM Journal on Optimization
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Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional setting, involving for instance several tens of state variables.