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## Full-Text Articles in Engineering

Design Of A Linear Time-Varying Cross-Coupled Iterative Learning Controller, K. L. Barton, Douglas A. Bristow, Andrew G. Alleyne

#### Design Of A Linear Time-Varying Cross-Coupled Iterative Learning Controller, K. L. Barton, Douglas A. Bristow, Andrew G. Alleyne

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In many manufacturing applications contour tracking is more important than individual axis tracking. Many control techniques, including iterative learning control (ILC), target individual axis error. Because individual axis error only indirectly relates to contour error, these approaches may not be very effective for contouring applications. Cross-coupled ILC (CCILC) is a variation on traditional ILC that targets the contour tracking directly. In contour trajectories with rapid changes, high frequency control is necessary in order to meet tracking requirements. This paper presents an improved CCILC that uses a linear time-varying (LTV) filter to provide high frequency control for short durations. The improved ...

Weighting Matrix Design For Robust Monotonic Convergence In Norm Optimal Iterative Learning Control, Douglas A. Bristow

#### Weighting Matrix Design For Robust Monotonic Convergence In Norm Optimal Iterative Learning Control, Douglas A. Bristow

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper we examine the robustness of norm optimal ILC with quadratic cost criterion for discrete-time, linear time-invariant, single-input single-output systems. A bounded multiplicative uncertainty model is used to describe the uncertain system and a sufficient condition for robust monotonic convergence is developed. We find that, for sufficiently large uncertainty, the performance weighting can not be selected arbitrarily large, and thus overall performance is limited. To maximize available performance, a time-frequency design methodology is presented to shape the weighting matrix based on the initial tracking error. The design is applied to a nanopositioning system and simulation results are presented.

Optimal Neuro-Controller Synthesis For Variable-Time Impulse Driven Systems, Xiaohua Wang, S. N. Balakrishnan

#### Optimal Neuro-Controller Synthesis For Variable-Time Impulse Driven Systems, Xiaohua Wang, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper develops a systematic scheme to solve for the optimal controls of variable time impulsive systems. First, the optimality conditions for variable time impulse driven systems are derived using the calculus of variation. After wards, a neural network based adaptive critic method is proposed to numerically solve the two-point boundary value problems formulated based on the optimality conditions derived. Finally, two examples - one linear and one nonlinear - are presented to illustrate the conditions derived and to show the power of the neural network based adaptive critic method proposed.

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

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

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, a new nonlinear H 1 control technique, called μ¡D H 1 method, is employed to design a missile longitudinal autopilot. The μ ¡D H 1 design has the same structure as that of linear H 1 , except that the two Riccati equations that are part of the solution process are state dependent. The μ ¡D technique yields suboptimal solutions to nonlinear optimal control problems in the sense that it provides an approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation. It is also shown that this method can be used to provide an approximate closed-form solution to the ...

Optimal Neuro-Controller Synthesis For Impulse-Driven System, Xiaohua Wang, S. N. Balakrishnan

#### Optimal Neuro-Controller Synthesis For Impulse-Driven System, Xiaohua Wang, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper presents a new controller design technique for systems driven with impulse inputs. Necessary conditions for optimal impulse control are derived. A neural network structure to solve the resulting equations is presented. The solution concepts are illustrated with a few example problems that exhibit increasing levels of difficulty. Two linear problems-one scalar and one vector-and a benchmark nonlinear problem-Van Der Pol oscillator-are used as case studies. Numerical results show the efficacy of the new solution process for impulse driven systems. Since the theoretical development and the design technique are free from restrictive assumptions, this technique is applicable to many ...

An Optimal Dynamic Inversion Approach For Controlling A Class Of One-Dimensional Nonlinear Distributed Parameter Systems, Radhakant Padhi, S. N. Balakrishnan

#### An Optimal Dynamic Inversion Approach For Controlling A Class Of One-Dimensional Nonlinear Distributed Parameter Systems, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a ...

Neuroadaptive Model Following Controller Design For A Nonaffine Uav Model, Nishant Unnikrishnan, S. N. Balakrishnan

#### Neuroadaptive Model Following Controller Design For A Nonaffine Uav Model, Nishant Unnikrishnan, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper proposes a new model-following adaptive control design technique for nonlinear systems that are nonaffine in control. The adaptive controller uses online neural networks that guarantee tracking in the presence of unmodeled dynamics and/or parameter uncertainties present in the system model through an online control adaptation procedure. The controller design is carried out in two steps: (i) synthesis of a set of neural networks which capture the unmodeled (neglected) dynamics or model uncertainties due to parametric variations and (ii) synthesis of a controller that drives the state of the actual plant to that of a reference model. This ...

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 ...

Development And Analysis Of A Feedback Treatment Strategy For Parturient Paresis Of Cows, Radhakant Padhi, S. N. Balakrishnan

#### Development And Analysis Of A Feedback Treatment Strategy For Parturient Paresis Of Cows, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

An intelligent on-line feedback treatment strategy based on nonlinear optimal control theory is presented for the parturient paresis of cows. A limitation in the development of an existing nonlinear mathematical model for the homogeneous system is addressed and further modified to incorporate a control input. A neural network based optimal feedback controller is synthesized for the treatment of the disease. Detailed studies are used to analyze the effectiveness of a feedback medication strategy and it is compared with the current "impulse" strategy. The results show that while the current practice may fail in some cases, especially if it is carried ...

Development And Implementation Of New Nonlinear Control Concepts For A Ua, Vijayakumar Janardhan, Derek Schmitz, S. N. Balakrishnan

#### Development And Implementation Of New Nonlinear Control Concepts For A Ua, Vijayakumar Janardhan, Derek Schmitz, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A reconfigurable flight control method is developed to be implemented on an Unmanned Aircraft (UA), a thirty percent scale model of the Cessna 150. This paper presents the details of the UAV platform, system identification, reconfigurable controller design, development, and implementation on the UA to analyze the performance metrics. A Crossbow Inertial Measurement Unit provides the roll, pitch and yaw accelerations and rates along with the roll and pitch. The 100400 mini-air data boom from spaceage control provides the airspeed, altitude, angle of attack and the side slip angles. System identification is accomplished by commanding preprogrammed inputs to the control ...

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 ...

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

#### 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 ...

Adaptive Critic-Based Neural Network Controller For Uncertain Nonlinear Systems With Unknown Deadzones, Pingan He, Jagannathan Sarangapani, S. N. Balakrishnan

#### Adaptive Critic-Based Neural Network Controller For Uncertain Nonlinear Systems With Unknown Deadzones, Pingan He, Jagannathan Sarangapani, S. N. Balakrishnan

*Electrical and Computer Engineering Faculty Research & Creative Works*

A multilayer neural network (NN) controller in discrete-time is designed to deliver a desired tracking performance for a class of nonlinear systems with input deadzones. This multilayer NN controller has an adaptive critic NN architecture with two NNs for compensating the deadzone nonlinearity and a third NN for approximating the dynamics of the nonlinear system. A reinforcement learning scheme in discrete-time is proposed for the adaptive critic NN deadzone compensator, where the learning is performed based on a certain performance measure, which is supplied from a critic. The adaptive generating NN rejects the errors induced by the deadzone whereas a ...

Robust State Dependent Riccati Equation Based Guidance Laws, S. N. Balakrishnan, Ming Xin

#### Robust State Dependent Riccati Equation Based Guidance Laws, S. N. Balakrishnan, Ming Xin

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A robust state dependent Riccati equation based guidance/control is investigated in this study. In order to have a better design tool in terms of required interceptor accelerations, the target intercept geometry is formulated in a set of polar coordinates. With this formulation, we formulate a cost function with state dependent weights. In this study, we investigate the effects of such cost functions on the levels of interceptor accelerations. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the target acceleration. In this manner, we will not need target acceleration estimation explicitly ...

Robust State Dependent Riccati Equation Based Robot Manipulator Control, Ming Xin, S. N. Balakrishnan, Zhongwu Huang

#### Robust State Dependent Riccati Equation Based Robot Manipulator Control, Ming Xin, S. N. Balakrishnan, Zhongwu Huang

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

We present a new optimal control approach to robust control of robot manipulators in the framework of state dependent Riccati equation (SDRE) technique. To treat this highly nonlinear control system, we formulate it as a nonlinear optimal regulator problem. SDRE technique was used to synthesize an optimal controller to this class of robot control problem. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the parameter uncertainties. A typical two-link robot position control problem was studied to show the effectiveness of SDRE approach and robust extra control design to robotic application.

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

#### 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 ...

Adaptive Critic Based Neurocontroller For Autolanding Of Aircrafts, S. N. Balakrishnan, Gaurav Saini

#### Adaptive Critic Based Neurocontroller For Autolanding Of Aircrafts, S. N. Balakrishnan, Gaurav Saini

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, adaptive critic based neural networks have been used to design a controller for a benchmark problem in aircraft autolanding. The adaptive critic control methodology comprises successive adaptations of two neural networks, namely action and critic network (which approximate the Hamiltonian equations associated with optimal control theory) until closed loop optimal control is achieved. The autolanding problem deals with longitudinal dynamics of an aircraft which is to be landed in a specified touchdown region (within acceptable ranges of speed, pitch angle and sink rate) in the presence of wind disturbances and gusts using elevator deflection as the control ...

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 ...

Approximate Analytical Guidance Schemes For Homing Missiles, S. N. Balakrishnan, Donald T. Stansbery

#### Approximate Analytical Guidance Schemes For Homing Missiles, S. N. Balakrishnan, Donald T. Stansbery

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Closed form solutions for the guidance laws are developed using modern control techniques. The resulting two-point boundary value problem is solved through the use of the state transition matrix of the intercept dynamics. Results are presented in terms of a design parameter.