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Missouri University of Science and Technology

Dynamic Programming

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Full-Text Articles in Mechanical Engineering

Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis Aug 2008

Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called “adaptive critics” or “action-critic” networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in “model-free” development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse ...


Optimal Control Synthesis Of A Class Of Nonlinear Systems Using Single Network Adaptive Critics, Radhakant Padhi, Nishant Unnikrishnan, S. N. Balakrishnan Jan 2004

Optimal Control Synthesis Of A Class Of Nonlinear Systems Using Single Network Adaptive Critics, Radhakant Padhi, Nishant Unnikrishnan, S. N. Balakrishnan

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Adaptive critic (AC) neural network solutions to optimal control designs using dynamic programming has reduced the need of complex computations and storage requirements that typical dynamic programming requires. In this paper, a "single network adaptive critic" (SNAC) is presented. This approach is applicable to a class of nonlinear systems where the optimal control (stationary) equation is explicitly solvable for control in terms of state and costate variables. The SNAC architecture offers three potential advantages; a simpler architecture, significant savings of computational load and reduction in approximation errors. In order to demonstrate these benefits, a real-life micro-electro-mechanical-system (MEMS) problem has been ...


Approximate Dynamic Programming Based Optimal Neurocontrol Synthesis Of A Chemical Reactor Process Using Proper Orthogonal Decomposition, Radhakant Padhi, S. N. Balakrishnan Jan 2003

Approximate Dynamic Programming Based Optimal Neurocontrol Synthesis Of A Chemical Reactor Process Using Proper Orthogonal Decomposition, Radhakant Padhi, S. N. Balakrishnan

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The concept of approximate dynamic programming and adaptive critic neural network based optimal controller is extended in this study to include systems governed by partial differential equations. An optimal controller is synthesized for a dispersion type tubular chemical reactor, which is governed by two coupled nonlinear partial differential equations. It consists of three steps: First, empirical basis functions are designed using the "Proper Orthogonal Decomposition" technique and a low-order lumped parameter system to represent the infinite-dimensional system is obtained by carrying out a Galerkin projection. Second, approximate dynamic programming technique is applied in a discrete time framework, followed by the ...


Infinite Time Optimal Neuro Control For Distributed Parameter Systems, S. N. Balakrishnan, Radhakant Padhi Jan 2000

Infinite Time Optimal Neuro Control For Distributed Parameter Systems, S. N. Balakrishnan, Radhakant Padhi

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The conventional dynamic programming methodology for the solution of optimal control, despite having many desirable features, is severely restricted by its computational requirements. However, in recent times, an alternate formulation, known as the adaptive-critic synthesis, has given it a new perspective. In this paper, we have attempted to use the philosophy of adaptive-critic design to the optimal control of distributed parameter systems. An important contribution of this study is the derivation of the necessary conditions of optimality for distributed parameter systems, described in discrete domain, following the principle of approximate dynamic programming. Then the derived necessary conditions of optimality are ...


Convergence Analysis Of Adaptive Critic Based Optimal Control, S. N. Balakrishnan, Xin Liu Jan 2000

Convergence Analysis Of Adaptive Critic Based Optimal Control, S. N. Balakrishnan, Xin Liu

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Adaptive critic based neural networks have been found to be powerful tools in solving various optimal control problems. The adaptive critic approach consists of two neural networks which output the control values and the Lagrangian multipliers associated with optimal control. These networks are trained successively and when the outputs of the two networks are mutually consistent and satisfy the differential constraints, the controller network output produces optimal control. In this paper, we analyze the mechanics of convergence of the network solutions. We establish the necessary conditions for the network solutions to converge and show that the converged solution is optimal.


A Dual Neural Network Architecture For Linear And Nonlinear Control Of Inverted Pendulum On A Cart, S. N. Balakrishnan, Victor Biega Jan 1996

A Dual Neural Network Architecture For Linear And Nonlinear Control Of Inverted Pendulum On A Cart, S. N. Balakrishnan, Victor Biega

Mechanical and Aerospace Engineering Faculty Research & Creative Works

The use of a self-contained dual neural network architecture for the solution of nonlinear optimal control problems is investigated in this study. The network structure solves the dynamic programming equations in stages and at the convergence, one network provides the optimal control and the second network provides a fault tolerance to the control system. We detail the steps in design and solve a linearized and a nonlinear, unstable, four-dimensional inverted pendulum on a cart problem. Numerical results are presented and compared with linearized optimal control. Unlike the previously published neural network solutions, this methodology does not need any external training ...


Adaptive Critic Based Neural Networks For Control (Low Order System Applications), S. N. Balakrishnan, Victor Biega Jan 1995

Adaptive Critic Based Neural Networks For Control (Low Order System Applications), S. N. Balakrishnan, Victor Biega

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Dynamic programming is an exact method of determining optimal control for a discretized system. Unfortunately, for nonlinear systems the computations necessary with this method become prohibitive. This study investigates the use of adaptive neural networks that utilize dynamic programming methodology to develop near optimal control laws. First, a one dimensional infinite horizon problem is examined. Problems involving cost functions with final state constraints are considered for one dimensional linear and nonlinear systems. A two dimensional linear problem is also investigated. In addition to these examples, an example of the corrective capabilities of critics is shown. Synthesis of the networks in ...


A New Neural Architecture For Homing Missile Guidance, S. N. Balakrishnan, Victor Biega Jan 1995

A New Neural Architecture For Homing Missile Guidance, S. N. Balakrishnan, Victor Biega

Mechanical and Aerospace Engineering Faculty Research & Creative Works

We present a new neural architecture which imbeds dynamic programming solutions to solve optimal target-intercept problems. They provide feedback guidance solutions, which are optimal with any initial conditions and time-to-go, for a 2D scenario. The method discussed in this study determines an optimal control law for a system by successively adapting two networks - an action and a critic network. This method determines the control law for an entire range of initial conditions; it simultaneously determines and adapts the neural networks to the optimal control policy for both linear and nonlinear systems. In addition, it is important to know that the ...