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## Full-Text Articles in Engineering

Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis

#### Issues On Stability Of Adp Feedback Controllers For Dynamical Systems, S. N. Balakrishnan, Jie Ding, F. L. Lewis

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called “adaptive critics” or “action-critic” networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in “model-free” development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse ...

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.

Output Feedback Controller For Operation Of Spark Ignition Engines At Lean Conditions Using Neural Networks, Jonathan B. Vance, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

#### Output Feedback Controller For Operation Of Spark Ignition Engines At Lean Conditions Using Neural Networks, Jonathan B. Vance, Brian C. Kaul, Jagannathan Sarangapani, J. A. Drallmeier

*Electrical and Computer Engineering Faculty Research & Creative Works*

Spark ignition (SI) engines operating at very lean conditions demonstrate significant nonlinear behavior by exhibiting cycle-to-cycle bifurcation of heat release. Past literature suggests that operating an engine under such lean conditions can significantly reduce NO emissions by as much as 30% and improve fuel efficiency by as much as 5%-10%. At lean conditions, the heat release per engine cycle is not close to constant, as it is when these engines operate under stoichiometric conditions where the equivalence ratio is 1.0. A neural network controller employing output feedback has shown ability in simulation to reduce the nonlinear cyclic dispersion ...

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 ...

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 ...

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 ...

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 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 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 ...

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 ...

Experimental Implementation Of Adaptive-Critic Based Infinite Time Optimal Neurocontrol For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look

#### Experimental Implementation Of Adaptive-Critic Based Infinite Time Optimal Neurocontrol For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Recently the synthesis methodology for the infinite time optimal neuro-controllers for PDE systems in the framework of adaptive-critic design has been developed. In this paper, first we model an experimental setup representing one dimensional heat diffusion problems. Then we synthesize and implement an adaptive-critic based neuro-controller for online temperature profile control of the experimental setup.

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.

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.

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 ...

Robust Adaptive Critic Based Neurocontrollers For Systems With Input Uncertainties, S. N. Balakrishnan, Zhongwu Huang

#### Robust Adaptive Critic Based Neurocontrollers For Systems With Input Uncertainties, S. N. Balakrishnan, Zhongwu Huang

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A two-neural network approach to solving optimal control problems is described in this study. This approach called the adaptive critic method consists of two neural networks: one is called the supervisor or critic, and the other is called an action network or controller. The inputs to both these networks are the current states of the system to be controlled. Each network is trained through an output of the other network and the conditions for optimal control. When their outputs are mutually consistent, the controller network output is optimal. The optimality is limited to the underlying model. Hence, we develop a ...

Online Identification And Control Of Aerospace Vehicles Using Recurrent Networks, Zhenning Hu, S. N. Balakrishnan

#### Online Identification And Control Of Aerospace Vehicles Using Recurrent Networks, Zhenning Hu, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

Methods for estimating the aerospace system parameters and controlling them through two neural networks are presented in this study. We equate the energy function of Hopfield neural network to integral square of errors in the system dynamics and extract the parameters of a system. Parameter convergence is proved. For control, we equate the equilibrium status of a "modified" Hopfield neural network to the steady state Riccati solution with the system parameters as inputs. Through these two networks, we present the online identification and control of an aircraft using its nonlinear dynamics.

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

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

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

We investigate the use of an `adaptive critic' based controller to steer an agile missile with a constraint on the angle of attack from various initial Mach numbers to a given final Mach number in minimum time while completely reversing its flightpath angle. We use neural networks with a two-network structure called `adaptive critic' to carry out the optimization process. This structure obtains an optimal controller through solving Hamiltonian equations. This approach needs no external training; each network along with the optimality equations generates the output for the other network. When the outputs are mutually consistent, the controller output is ...

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 ...

Robustness Analysis Of Hopfield And Modified Hopfield Neural Networks In Time Domain, Jie Shen, S. N. Balakrishnan

#### Robustness Analysis Of Hopfield And Modified Hopfield Neural Networks In Time Domain, Jie Shen, S. N. Balakrishnan

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

A variant of the Hopfield network, called the modified Hopfield network is formulated. This network which consists of two mutually recurrent networks has more free parameters than the well-known Hopfield network. Stability analysis of this network is presented. The analysis is carried out in the time domain with an application of the Lyapunov method and robust control Lyapunov function. The current flow in the network is treated as a "control". This "controller" is shown to guarantee "a practically stabilizing control". Analysis of the Hopfield network is also included for completion.

Adaptive Critic Based Neurocontroller For Autolanding Of Aircraft With Varying Glideslopes, Gaurav Saini, S. N. Balakrishnan

#### Adaptive Critic Based Neurocontroller For Autolanding Of Aircraft With Varying Glideslopes, Gaurav Saini, S. N. Balakrishnan

*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' networks 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 in the presence of wind disturbances and gusts using elevator deflection as the control for glideslope and flare modes. The performance of the neurocontroller is compared to that of a conventional PID controller. Neurocontroller ...

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 ...

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 ...

A New Neural Architecture For Homing Missile Guidance, S. N. Balakrishnan, Victor Biega

#### A New Neural Architecture For Homing Missile Guidance, S. N. Balakrishnan, Victor Biega

*Mechanical and Aerospace Engineering Faculty Research & Creative Works*

We present a new neural architecture which imbeds dynamic programming solutions to solve optimal target-intercept problems. They provide feedback guidance solutions, which are optimal with any initial conditions and time-to-go, for a 2D scenario. The method discussed in this study determines an optimal control law for a system by successively adapting two networks - an action and a critic network. This method determines the control law for an entire range of initial conditions; it simultaneously determines and adapts the neural networks to the optimal control policy for both linear and nonlinear systems. In addition, it is important to know that the ...

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 ...