Direct training method for a continuous-time nonlinear optimal feedback controller

Infinite time optimal controllers have been designed for a dispersion type tubular reactor model by using the framework of adaptive critic optimal control design. For the reactor control problem, which is governed by two coupled nonlinear partial differential equations, an optimal controller synthesis is presented through two sets of neural networks. One set of neural networks captures the relationship between the states and the control, whereas the other set of networks captures the relationship between the states and the costates. This innovative approach embeds the solutions to the optimal control problem for a large number of initial conditions in the domain of interest. Although the main aim of this paper is to solve a process control problem, the methodology presented here can be viewed as a practical computational tool for many problems associated with nonlinear distributed parameter systems. Numerical results demonstrate the viability of the proposed method.

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“…By discretizing the state equation Eq. (14) and then using the necessary conditions of optimality (Eq. (7) and Eq.…”

Section: Discrete Formulationmentioning

confidence: 99%

“…They have been shown adequate to handle noisy and non-stationary environments. The synthesis of such nonlinear control laws has been demonstrated in a variety of applications as well [8,14,16,22,24,23,26,32].…”

Section: Introductionmentioning

confidence: 99%

Optimal Process Control Using Neural Networks

Padhi

Balakrishnan

2003

Asian Journal of Control

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“…It is the goal of this paper to extend the result in Edwards and Goh (1995) to nonlinear feedback optimal control problems subjected to further continuous state constraints. It is well-known that, even for computing open-loop optimal solutions, the state constrained optimal control problem is notoriously difficult.…”

Section: Introductionmentioning

confidence: 97%

“…In Edwards and Goh (1995), a direct training method is proposed for the synthesis of an optimal feedback controller in the form of a feedforward neural network for continuoustime nonlinear dynamical systems. The controller is independent of the system's initial condition provided that it arises from some bounded domain of the state space, and is not constricted by any fixed model structure for the dynamical system.…”

Section: Introductionmentioning

confidence: 99%

“…While there is no shortage of theoretical results in the form of necessary conditions for the constrained problem, practical methods for constructing the constrained solutions have been few. In this paper, we discuss two methods to transform a state-constrained problem into an unconstrained problem, and subsequently apply the method in Edwards and Goh (1995) to synthesize the optimal feedback controller for the resulting unconstrained problem.…”

Section: Introductionmentioning

confidence: 99%

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Feedback control of state constrained optimal control problems

Redfern

Goh

1996

System Modelling and Optimization

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Solutions to nonlinear optimal control problems are usually computed in open-loop form, especially if the problem is subjected to state constraints. Open-loop controls, however, are not very useful from a control perspective due to their lack of robustness. We discuss a couple of useful techniques which reduce a state-constrained problem into an unconstrained problem, and subsequently apply a technique to synthesize an optimal state feedback controller for the reduced problem. The controller is able to recover the openloop optimal state and control for arbitrary initial conditions arising from a nontrivial subset of the state space, while ensuring that the state constraint is satisfied at all time.

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Approximate Output Feedback Optimal Control of Higher-Order Dynamical Systems

Goh

Edwards

1997

Optim. Control Appl. Meth.

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Direct training method for a continuous-time nonlinear optimal feedback controller

Cited by 17 publications

References 9 publications

Optimal Process Control Using Neural Networks

Optimal Process Control Using Neural Networks

Feedback control of state constrained optimal control problems

Approximate Output Feedback Optimal Control of Higher-Order Dynamical Systems

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