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Full-Text Articles in Engineering
Optimal Control Synthesis Of A Class Of Nonlinear Systems Using Single Network Adaptive Critics, Radhakant Padhi, Nishant Unnikrishnan, S. N. Balakrishnan
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 …
A New Method For Suboptimal Control Of A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan
A New Method For Suboptimal Control Of A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this paper, a new nonlinear control synthesis technique (θ - D approximation) is presented. This approach achieves suboptimal solutions to nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman (HJB) equation approximately by adding perturbations to the cost function. By manipulating the perturbation terms both semi-globally asymptotic stability and suboptimality properties can be obtained. The convergence and stability proofs are given. This method overcomes the large control for large initial states problem that occurs in some other Taylor expansion based methods. It does not need time-consuming online computations like the state dependent Riccati equation (SDRE) technique. …
A New Optimal Nonlinear Control Method And Its Application To Missile Guidance Law Design, Ming Xin, S. N. Balakrishnan
A New Optimal Nonlinear Control Method And Its Application To Missile Guidance Law Design, Ming Xin, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this paper, a new nonlinear control synthesis technique (q-D approximation) is discussed. By adding perturbations to the cost function this approach achieves a suboptimal solution to the Hamilton-Jacobi- Bellman (HJB) equation. By manipulating the perturbation terms both asymptotic stability and optimality properties are obtained. An application to the design of missile guidance law is presented and is compared with a similar technique (State Dependent Riccati Equation technique) used in problems of this class. © 2002 by the author(s).
Adaptive Critic Based Neuro-Observer, Xin Liu, S. N. Balakrishnan
Adaptive Critic Based Neuro-Observer, Xin Liu, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A new Neural Network (NN) based observer design method for nonlinear systems represented by nonlinear dynamics and linear/nonlinear measurement is proposed in this paper. In this new approach, as the first step, the observer design problem is changed into a "controller" design problem by establishing the error dynamics, and then the Adaptive Critic (AC) based approach is applied on this error dynamics to design a 'controller', such that the errors are driven to zero. The resulting observer has inherent robustness from the AC based design approach. Some simulations are presented to illustrate the effectiveness of this approach.
Adaptive Critic Based Neural Networks For Control (Low Order System Applications), S. N. Balakrishnan, Victor Biega
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 …