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Mechanical Engineering Commons

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2002

Mechanical and Aerospace Engineering Faculty Research & Creative Works

Nonlinear Control Systems

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Full-Text Articles in Mechanical Engineering

A New Filtering Technique For A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan Jan 2002

A New Filtering Technique For A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In this paper, a new nonlinear filtering technique (θ-D filter) is presented. This filter is derived by constructing the dual of a new nonlinear regulator control technique, θ-D approximation which involves approximate solution to the Hamilton-Jacobi-Bellman equation. The structure of this filter is similar to the state dependent riccati equation filter (SDREF). However, this method does not need time-consuming online computation of the algebraic Riccati equation at each sample time compared with the SDREF. By manipulating the perturbation terms both the asymptotic stability and optimality properties can be obtained. A simple pendulum problem is investigated to demonstrate the effectiveness of ...


A New Method For Suboptimal Control Of A Class Of Nonlinear Systems, Ming Xin, S. N. Balakrishnan Jan 2002

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 ...