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## Full-Text Articles in Engineering

Formation Control Of Car-Like Mobile Robots: A Lyapunov Function Based Approach, S. A. Panimadai Ramaswamy, S. N. Balakrishnan

#### Formation Control Of Car-Like Mobile Robots: A Lyapunov Function Based Approach, S. A. Panimadai Ramaswamy, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In literature leader - follower strategy has been used extensively for formation control of car-like mobile robots with the control law being derived from the kinematics. This paper takes it a step further and a nonlinear control law is derived using Lyapunov analysis for formation control of car-like mobile robots using robot dynamics. Controller is split into two parts. The first part is the development of a velocity controller for the follower from the error kinematics (linear and angular). The second part involves the use of the dynamics of the robot in the development of a torque controller for both the ...

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 Control Of Class Of Non-Linear Plants Using Artificial Immune Systems: Application Of The Clonal Selection Algorithm, S. A. Panimadai Ramaswamy, Ganesh K. Venayagamoorthy, S. N. Balakrishnan

#### Optimal Control Of Class Of Non-Linear Plants Using Artificial Immune Systems: Application Of The Clonal Selection Algorithm, S. A. Panimadai Ramaswamy, Ganesh K. Venayagamoorthy, S. N. Balakrishnan

*Electrical and Computer Engineering Faculty Research & Creative Works*

The function of natural immune system is to protect the living organisms against invaders/pathogens. Artificial Immune System (AIS) is a computational intelligence paradigm inspired by the natural immune system. Diverse engineering problems have been solved in the recent past using AIS. Clonal selection is one of the few algorithms that belong to the family of AIS techniques. Clonal selection algorithm is the computational implementation of the clonal selection principle. The process of affinity maturation of the immune system is explicitly incorporated in this algorithm. This paper presents the application of AIS for the optimal control of a class of ...

Reinforcement Learning Based Output-Feedback Control Of Nonlinear Nonstrict Feedback Discrete-Time Systems With Application To Engines, Peter Shih, Jonathan B. Vance, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

#### Reinforcement Learning Based Output-Feedback Control Of Nonlinear Nonstrict Feedback Discrete-Time Systems With Application To Engines, Peter Shih, Jonathan B. Vance, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

*Electrical and Computer Engineering Faculty Research & Creative Works*

A novel reinforcement-learning based output-adaptive neural network (NN) controller, also referred as the adaptive-critic NN controller, is developed to track a desired trajectory for a class of complex nonlinear discrete-time systems in the presence of bounded and unknown disturbances. The controller includes an observer for estimating states and the outputs, critic, and two action NNs for generating virtual, and actual control inputs. The critic approximates certain strategic utility function and the action NNs are used to minimize both the strategic utility function and their outputs. All NN weights adapt online towards minimization of a performance index, utilizing gradient-descent based rule ...

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 ...

Near Optimal Output-Feedback Control Of Nonlinear Discrete-Time Systems In Nonstrict Feedback Form With Application To Engines, Peter Shih, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

#### Near Optimal Output-Feedback Control Of Nonlinear Discrete-Time Systems In Nonstrict Feedback Form With Application To Engines, Peter Shih, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

*Electrical and Computer Engineering Faculty Research & Creative Works*

A novel reinforcement-learning based output-adaptive neural network (NN) controller, also referred as the adaptive-critic NN controller, is developed to track a desired trajectory for a class of complex nonlinear discrete-time systems in the presence of bounded and unknown disturbances. The controller includes an observer for estimating states and the outputs, critic, and two action NNs for generating virtual, and actual control inputs. The critic approximates certain strategic utility function and the action NNs are used to minimize both the strategic utility function and their outputs. All NN weights adapt online towards minimization of a performance index, utilizing gradient-descent based rule ...

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 ...

Neural Network-Based Output Feedback Controller For Lean Operation Of Spark Ignition Engines, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier, Jonathan B. Vance, Pingan He

#### Neural Network-Based Output Feedback Controller For Lean Operation Of Spark Ignition Engines, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier, Jonathan B. Vance, Pingan He

*Electrical and Computer Engineering Faculty Research & Creative Works*

Spark ignition (SI) engines running at very lean conditions demonstrate significant nonlinear behavior by exhibiting cycle-to-cycle dispersion of heat release even though such operation can significantly reduce NOx emissions and improve fuel efficiency by as much as 5-10%. A suite of neural network (NN) controller without and with reinforcement learning employing output feedback has shown ability to reduce the nonlinear cyclic dispersion observed under lean operating conditions. The neural network controllers consists of three NN: a) A NN observer to estimate the states of the engine such as total fuel and air; b) a second NN for generating virtual input ...

Optimal Control Of A Class Of One-Dimensional Nonlinear Distributed Parameter Systems With Discrete Actuators, Radhakant Padhi, S. N. Balakrishnan

#### Optimal Control Of A Class Of One-Dimensional Nonlinear Distributed Parameter Systems With Discrete Actuators, 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 with a finite number of actuators in the spatial domain. Unlike the existing ''approximate-then-design'' and ''design-then-approximate'' techniques, this approach does not use any approximation either of the system dynamics or of the resulting controller. The formulation has more practical significance because one can implement a set of discrete controllers with relative ease. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved through simulations ...

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 ...

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 ...

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

#### 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 ...

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 ...

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.

An Optimal Control Based Treatment Strategy For Parturient Paresis Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan

#### An Optimal Control Based Treatment Strategy For Parturient Paresis Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

An optimal online feedback treatment strategy is developed for the parturient paresis of cows, based on nonlinear optimal control theory. A limitation in the development of an existing mathematical model for calcium homeostasis is addressed and the model is extended to incorporate control inputs. An optimal feedback controller is synthesized for the nonlinear system using neural networks. Though the main aim of this paper is to solve the biomedical control problem, the methodology presented in this paper is a general computational tool, which can be applied to solve a fairly general class nonlinear optimal control problems.

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.

Stability Analysis Of Nonlinear Machining Force Controllers, Robert G. Landers, Yen-Wen Lu

#### Stability Analysis Of Nonlinear Machining Force Controllers, Robert G. Landers, Yen-Wen Lu

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Model parameters vary significantly during a normal operation, thus, adaptive techniques have predominately been used. However, model-based techniques that carefully account for changes in the force process have again been examined due to the reduced complexity afforded by such techniques. In this paper, the effect of model parameter variations on the closed-loop stability for two model-based force controllers is examined. It was found that the stability boundary in the process parameter space can be exactly determined for force control systems designed for static force processes. For force control systems designed for first-order force processes, it was found that the stability ...

A Class Of Modified Hopfield Networks For Control Of Linear And Nonlinear Systems, Jie Shen, S. N. Balakrishnan

#### A Class Of Modified Hopfield Networks For Control Of Linear And Nonlinear Systems, Jie Shen, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper presents a class of modified Hopfield neural networks (MHNN) and their use in solving linear and nonlinear control problems. This class of networks consists of parallel recurrent networks which have variable dimensions that can be changed to fit the problems under consideration. It has a structure to implement an inverse transformation that is essential for embedding optimal control gain sequences. Equilibrium solutions are discussed. Numerical results for a motivating aircraft control problem (linear) are presented. Furthermore, we formulate the state-dependent Riccati equation method (SDRE) for a class of nonlinear dynamical system and show how MHNN provides the solution ...

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

#### 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

#### 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 ...

Decoupled Dynamics For Control And Estimation, S. N. Balakrishnan

#### Decoupled Dynamics For Control And Estimation, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Decoupling of the dynamical equations in polar coordinates is used to develop a control scheme for use in target-intercept problems with passive measurements. By defining a pseudo control variable in the radial coordinate, the radial dynamics is made independent of the transverse dynamics. After solving for the radial control, the transverse control is determined through solutions to a two-point boundary value problem. Numerical results from a six degree-of-freedom simulation which used the decoupled control indicate that it is better than the completely Cartesian coordinate control for most of the cases considered. Decoupled control, though, is obtained iteratively through a two-point ...

Robust Nonlinear Control Of Brushless Dc Motors In The Presence Of Magnetic Saturation, N. Hemati, J. S. Thorp, Ming-Chuan Leu

#### Robust Nonlinear Control Of Brushless Dc Motors In The Presence Of Magnetic Saturation, N. Hemati, J. S. Thorp, Ming-Chuan Leu

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A robust control law is derived and examined for a direct-drive robot arm driven by a brushless DC motor (BLDCM). The complete dynamics of the motor and its interaction with the robot arm are accounted for. This is important, since in a direct-drive servo system the torque generated by the motor is directly transmitted to the load. Effects of magnetic saturation as well as reluctance variations are accounted for, in order to ensure accuracy. The effectiveness of the method is examined through computer simulations. The computational complexity of the overall control scheme is such that it can be readily used ...