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## Full-Text Articles in Mechanical Engineering

Stationkeeping Of An L₂ Libration Point Satellite With Θ-D Technique, Ming Xin, S. N. Balakrishnan, Henry J. Pernicka, Michael W. Dancer

#### Stationkeeping Of An L₂ Libration Point Satellite With Θ-D Technique, Ming Xin, S. N. Balakrishnan, Henry J. Pernicka, Michael W. Dancer

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A new method for L_{2} libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the L_{2} libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the "θ-D technique," based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual ...

Missile Longitudinal Autopilot Design Using A New Suboptimal Nonlinear Control Method, Ming Xin, S. N. Balakrishnan

#### Missile Longitudinal Autopilot Design Using A New Suboptimal Nonlinear Control Method, Ming Xin, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A missile longitudinal autopilot is designed using a new nonlinear control synthesis technique called the θ-D approximation. The particular θ-D methodology used is referred to as the θ-D H2 design. The technique can achieve suboptimal closed-form solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman equation approximately by adding perturbations to the cost function. An interesting feature of this method is that the expansion terms in the expression for suboptimal control are nothing but solutions to the state-dependent Riccati equations associated with this class of problems. The θ-D H2 design has the ...

Nonlinear H Infinity Missile Longitudinal Autopilot Design With Θ-D Method, Ming Xin, S. N. Balakrishnan

#### Nonlinear H Infinity Missile Longitudinal Autopilot Design With Θ-D Method, Ming Xin, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, a new nonlinear control synthesis technique, the theta- D method, is employed to design a missile longitudinal autopilot. The θ-D technique yields suboptimal solutions to nonlinear optimal control problems in the sense that it provides approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. Semi-global asymptotic stability can be achieved by manipulating the perturbation terms which are added to the cost function in developing a series solution. Furthermore, this method can be used to provide an approximate closed-form solution to the state dependent Riccati equation. The particular θ-D methodology adopted in this paper is referred to as θ-D H ...

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 ...

Cell Mapping Based Fuzzy Control Of Car Parking, Tea-Quin Kim, Ming-Chuan Leu

#### Cell Mapping Based Fuzzy Control Of Car Parking, Tea-Quin Kim, Ming-Chuan Leu

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper describes the development of a near-optimal fuzzy controller for maneuvering a car in a parking lot. To generate the rules of the fuzzy controller, a cell mapping method is utilized to systematically generate near-optimal trajectories for all possible initial states in the parking lot. Based on the input-output relations of these trajectories, which represent the states and controls of the corresponding cells, a set of fuzzy rules are generated automatically. In order to result in a small number of fuzzy rules from the large amount of numerical information generated by cell mapping, grouping of trajectories is proposed and ...

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 ...