Direct descent curvature optimal control with a modification algorithm and its application to nonlinear process.

This paper presents a direct descent second order or direct descent curvature algorithm with some modifications for the optimal control computations. This algorithm is compared with Hamiltonian methods in the literature. The proposed algorithm has generated numerically robust solutions with respect to conjugate points. The weighting matrix updating scheme was developed to improve the second-order optimal control algorithm, tested the performance of the algorithm, and shown on the benchmark and industrial process. The time-varying optimal feedback (TVOFB) gains are also generated along the trajectory as byproducts. If the trajectory deviates from the optimal trajectory for any reason (i.e., changing of system parameters, step disturbance into the plant, changing of initial conditions), it is held on the optimal trajectory by means of the optimal feedback. Simulations have been given for controlling the Van der Pol and bioreactor system, which are nonlinear benchmark systems.

Trajectory priming with dynamic fuzzy networks in nonlinear optimal control.

Fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods. The application of classical fuzzy logic (FL) technology to dynamic system control has been constrained by the nondynamic nature of popular FL architectures. Many difficulties include large rule bases (i.e., curse of dimensionality), long training times, etc. These problems can be overcome with a dynamic fuzzy network (DFN), a network with unconstrained connectivity and dynamic fuzzy processing units called "feurons." In this study, DFN as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints. The overall algorithm operates as an autotrainer for DFN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. For this, DFN encapsulates and generalizes the optimal control trajectories. By the algorithm, the time-varying optimal feedback gains are also generated along the trajectory as byproducts. This structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control. For this purpose, the direct-descent-curvature algorithm is used with some modifications [called modified-descend-controller (MDC) algorithm] for the nonlinear optimal control computations. The algorithm has numerically generated robust solutions with respect to conjugate points. The minimization of an integral quadratic cost functional subject to dynamic equality constraints (which is DFN) is considered for trajectory obtained by MDC tracking applications. The adjoint theory (whose computational complexity is significantly less than direct method) has been used in the training of DFN, which is as a quasilinear dynamic system. The updating of weights (identification of DFN parameters) are based on Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Simulation results are given for controlling a difficult nonlinear second-order system using fully connected three-feuron DFN.

Intelligent optimal control with dynamic neural networks.

The application of neural networks technology to dynamic system control has been constrained by the non-dynamic nature of popular network architectures. Many of difficulties are-large network sizes (i.e. curse of dimensionality), long training times, etc. These problems can be overcome with dynamic neural networks (DNN). In this study, intelligent optimal control problem is considered as a nonlinear optimization with dynamic equality constraints, and DNN as a control trajectory priming system. The resulting algorithm operates as an auto-trainer for DNN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. In this way, optimal control trajectories are encapsulated and generalized by DNN. The time varying optimal feedback gains are also generated along the trajectory as byproducts. Speeding up trajectory calculations opens up avenues for real-time intelligent optimal control with virtual global feedback. We used direct-descent-curvature algorithm with some modifications (we called modified-descend-controller-MDC algorithm) for the optimal control computations. The algorithm has generated numerically very robust solutions with respect to conjugate points. The adjoint theory has been used in the training of DNN which is considered as a quasi-linear dynamic system. The updating of weights (identification of parameters) are based on Broyden-Fletcher-Goldfarb-Shanno BFGS method. Simulation results are given for an intelligent optimal control system controlling a difficult nonlinear second-order system using fully connected three-neuron DNN.