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## Full-Text Articles in Engineering

A New State Observer And Flight Control Of Highly Maneuverable Aircraft, S. N. Balakrishnan, Ming Xin

#### A New State Observer And Flight Control Of Highly Maneuverable Aircraft, S. N. Balakrishnan, Ming Xin

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, a new nonlinear observer (θ-D observer) is proposed to estimate the feedback states for optimal control of a highly maneuverable aircraft. This observer is derived by constructing the dual of a recently developed nonlinear optimal control technique-known as the θ-D technique. The θ-D optimal control approach provides an approximate closed-form solution to the Hamilton-Jacobi-Bellman (HJB) equation. An optimal flight controller using this technique is designed for a highly maneuverable aircraft operating at high angle of attack where the θ-D observer is employed to estimate the states for feedback. The structure of this observer is similar to the ...

Optimal Controller Synthesis Of Variable-Time Impulsive Problems Using Single Network Adaptive Critics, Xiaohua Wang, S. N. Balakrishnan

#### Optimal Controller Synthesis Of Variable-Time Impulsive Problems Using Single Network Adaptive Critics, Xiaohua Wang, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper presents a systematic approach to solve for the optimal control of a variable-time impulsive system. First, optimality condition for a variable-time impulsive system is derived using the calculus of variations method. Next, a single network adaptive critic technique is proposed to numerically solve for the optimal control and the detailed algorithm is presented. Finally, two examples-one linear and one nonlinear-are solved applying the conditions derived and the algorithm proposed. Numerical results demonstrate the power of the neural network based adaptive critic method in solving this class of problems.

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.

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 ...

Robust/Optimal Temperature Profile Control Of A High-Speed Aerospace Vehicle Using Neural Networks, Vivek Yadav, Radhakant Padhi, S. N. Balakrishnan

#### Robust/Optimal Temperature Profile Control Of A High-Speed Aerospace Vehicle Using Neural Networks, Vivek Yadav, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. a 1-D distributed parameter model of a fin is developed from basic thermal physics principles. ldquoSnapshotrdquo solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the ldquoproper orthogonal decompositionrdquo (POD) technique and the snapshot solutions. a low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. an ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with ...

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 ...

Optimal Impulse Control Of Systems With Control Constraints And Application To Hiv Treatment, Vivek Yadav, S. N. Balakrishnan

#### Optimal Impulse Control Of Systems With Control Constraints And Application To Hiv Treatment, Vivek Yadav, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, conditions for optimal impulse control of an impulsive system with constraints on control are derived. These hold for a system whose states can be changed instantaneously at discrete times with impulses while a continuous control is being applied between those times. The conditions derived are applied to the problem of optimal HIV treatment. Simulation results are presented to show the treatment procedure. The results obtained show that the intervention method developed leads to good results.

Optimal Management Of Beaver Population Using A Reduced-Order Distributed Parameter Model And Single Network Adaptive Critics, Radhakant Padhi, S. N. Balakrishnan

#### Optimal Management Of Beaver Population Using A Reduced-Order Distributed Parameter Model And Single Network Adaptive Critics, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired ...

Hierarchical Optimal Force-Position-Contour Control Of Machining Processes. Part Ii. Illustrative Example, Yan Tang, Robert G. Landers, S. N. Balakrishnan

#### Hierarchical Optimal Force-Position-Contour Control Of Machining Processes. Part Ii. Illustrative Example, Yan Tang, Robert G. Landers, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

There has been a tremendous amount of research in machine tool servomechanism control, contour control, and machining force control; however, to date these technologies have not been tightly integrated. This paper develops a hierarchical optimal control methodology for the simultaneous regulation of servomechanism positions, contour error, and machining forces. The contour error and machining force process reside in the top level of the hierarchy where the goals are to 1) drive the contour error to zero to maximize quality and 2) maintain a constant cutting force to maximize productivity. These goals are systematically propagated to the bottom level, via aggregation ...

Hierarchical Optimal Force-Position-Contour Control Of Machining Processes. Part I. Controller Methodology, Yan Tang, Robert G. Landers, S. N. Balakrishnan

#### Hierarchical Optimal Force-Position-Contour Control Of Machining Processes. Part I. Controller Methodology, Yan Tang, Robert G. Landers, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

There has been a tremendous amount of research in machine tool servomechanism control, contour control, and machining force control; however, to date these technologies have not been tightly integrated. This paper develops a hierarchical optimal control methodology for the simultaneous regulation of servomechanism positions, contour error, and machining forces. The contour error and machining force process reside in the top level of the hierarchy where the goals are to 1) drive the contour error to zero to maximize quality and 2) maintain a constant cutting force to maximize productivity. These goals are systematically propagated to the bottom level, via aggregation ...

Optimal And Hierarchical Formation Control For Uav, Xiaohua Wang, S. N. Balakrishnan

#### Optimal And Hierarchical Formation Control For Uav, Xiaohua Wang, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this paper, optimal and hierarchical control concepts are investigated for cooperative formation flying of aircrafts. The airplanes are modeled as point mass and represented by double integrators. And all the planes are considered to be in a plane. For demonstration of the concepts, a task of forming a square from arbitrary initial conditions is presented to four airplanes. The final position that each airplane has to reach is unknown to them. The goal for the team is abstracted in the top layer. The system is modeled as a two layer hierarchical system in which the global information comes from ...

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 ...

Hierarchical Optimal Force-Position Control Of A Turning Process, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan

#### Hierarchical Optimal Force-Position Control Of A Turning Process, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Machining process control technologies are currently not well integrated into machine tool controllers and, thus, servomechanism dynamics are often ignored when designing and implementing process controllers. In this brief, a hierarchical controller is developed that simultaneously regulates the servomechanism motions and cutting forces in a turning operation. The force process and servomechanism system are separated into high and low levels, respectively, in the hierarchy. The high-level goal is to maintain a constant cutting force to maximize productivity while not violating a spindle power constraint. This goal is systematically propagated to the lower level and combined with the low-level goal to ...

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 ...

Optimal Beaver Population Management Using Reduced Order Distributed Parameter Model And Single Network Adaptive Critics, Radhakant Padhi, S. N. Balakrishnan

#### Optimal Beaver Population Management Using Reduced Order Distributed Parameter Model And Single Network Adaptive Critics, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control for a desired distribution of the animals is presented. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural network architecture. The objective of this research is to design an "optimal" beaver harvesting scheme for a region of interest.

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 ...

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 ...

Hierarchical Optimal Control Of A Turning Process - Linearization Approach, Anand Dasgupta, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan

#### Hierarchical Optimal Control Of A Turning Process - Linearization Approach, Anand Dasgupta, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Machining process control technologies are currently not well integrated into machine tool controllers and, thus, servomechanism dynamics are often ignored when designing and implementing process controllers. In this paper, a hierarchical controller is developed that simultaneously regulates the servomechanism positions and cutting forces in a lathing operation. The force process and servomechanism system are separated into high and low levels, respectively, in the hierarchy. The high level goal is to maintain a constant cutting force to maximize productivity while not violating a spindle power constraint. This goal is systematically propagated to the lower level and combined with the low level ...

Proper Orthogonal Decomposition Based Modeling And Experimental Implementation Of A Neurocontroller For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look, Radhakant Padhi

#### Proper Orthogonal Decomposition Based Modeling And Experimental Implementation Of A Neurocontroller For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look, Radhakant Padhi

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Experimental implementation of a dual neural network based optimal controller for a heat diffusion system is presented. Using the technique of proper orthogonal decomposition (POD), a set of problem-oriented basis functions are designed taking the experimental data as snap shot solutions. Using these basis functions in Galerkin projection, a reduced-order analogous lumped parameter model of the distributed parameter system is developed. This model is then used in an analogous lumped parameter problem. A dual neural network structure called adaptive critics is used to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship ...

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 ...

Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis Of Distributed Parameter Systems Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan

#### Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis Of Distributed Parameter Systems Using Neural Networks, Radhakant Padhi, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A new method for optimal control design of distributed parameter systems is presented in this paper. The concept of proper orthogonal decomposition is used for the model reduction of distributed parameter systems to form a reduced order lumped parameter problem. The optimal control problem is then solved in the time domain, in a state feedback sense, following the philosophy of ''adaptive critic'' neural networks. The control solution is then mapped back to the spatial domain using the same basis functions. Numerical simulation results are presented for a linear and nonlinear one-dimensional heat equation problem in an infinite time regulator framework.

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 ...

State-Constrained Agile Missile Control With Adaptive-Critic-Based Neural Networks, Dongchen Han, S. N. Balakrishnan

#### State-Constrained Agile Missile Control With Adaptive-Critic-Based Neural Networks, Dongchen Han, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

In this study, we develop an adaptive-critic-based controller to steer an agile missile that has a constraint on the minimum flight Mach number from various initial Mach numbers to a given final Mach number in minimum time while completely reversing its flightpath angle. This class of bounded state space, free final time problems is very difficult to solve due to discontinuities in costates at the constraint boundaries. We use a two-neural-network structure called "adaptive critic" in this study to carry out the optimization process. This structure obtains an optimal controller through solving optimal control-related equations resulting from a Hamiltonian formulation ...

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.

Convergence Analysis Of Adaptive Critic Based Optimal Control, S. N. Balakrishnan, Xin Liu

#### Convergence Analysis Of Adaptive Critic Based Optimal Control, S. N. Balakrishnan, Xin Liu

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Adaptive critic based neural networks have been found to be powerful tools in solving various optimal control problems. The adaptive critic approach consists of two neural networks which output the control values and the Lagrangian multipliers associated with optimal control. These networks are trained successively and when the outputs of the two networks are mutually consistent and satisfy the differential constraints, the controller network output produces optimal control. In this paper, we analyze the mechanics of convergence of the network solutions. We establish the necessary conditions for the network solutions to converge and show that the converged solution is optimal.