Optimal Management of Beaver Population using a Reduced-Order Distributed Parameter Model and Single Network Adaptive Critics

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 distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a single network adaptive critic (SNAC) neural-network architecture

Approximate Dynamic Programming Based Optimal Neurocontrol Synthesis of a Chemical Reactor Process Using Proper Orthogonal Decomposition

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 use of a dual neural network structure called adaptive critics, to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship between the state variables and the control, whereas the other set captures the relationship between the state and the costate variables. Third, the lumped parameter control is then mapped back to the spatial dimension using the same basis functions to result in a feedback control. Numerical results are presented that illustrate the potential of this approach. It should be noted that the procedure presented in this study can be used in synthesizing optimal controllers for a fairly general class of nonlinear distributed parameter systems

Infinite Time Optimal Neuro Control for Distributed Parameter Systems

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 used to synthesize infinite time optimal neuro-controllers in the framework of adaptive-critic design. A motivating example that follows clearly shows the potential of the adaptive critic procedure

Proper Orthogonal Decomposition Based Feedback Optimal Control Synthesis of Distributed Parameter Systems Using Neural Networks

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 \u27\u27adaptive critic\u27\u27 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

An Optimal Dynamic Inversion Approach for Controlling a Class of One-Dimensional Nonlinear Distributed Parameter Systems

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 real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile

Optimal Control of a Class of One-Dimensional Nonlinear Distributed Parameter Systems with Discrete Actuators

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 \u27\u27approximate-then-design\u27\u27 and \u27\u27design-then-approximate\u27\u27 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. Numerical results are presented which show that the desired temperature profile can be achieved starting from any initial temperature profile

Development and Analysis of a Feedback Treatment Strategy for Parturient Paresis of Cows

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 out before the condition of a patient deteriorates, the proposed continuous medication process may be initiated at any time. Moreover the proposed on-line continuous infusion strategy never leads to severe hypercalcemic problems, thereby avoiding an associated disastrous consequence of cardiac arrest. A comparison study with linear quadratic regulator theory brings out the advantages of the nonlinear control synthesis approach

An Optimal Control Based Treatment Strategy for Parturient Paresis Using Neural Networks

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

Optimal Beaver Population Management Using Reduced Order Distributed Parameter Model and Single Network Adaptive Critics

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