scholarly journals An Optimal Control Study with Quantity of Additional food as Control in Prey-Predator Systems involving Inhibitory Effect

2021 ◽  
Vol 9 (1) ◽  
pp. 114-145
Author(s):  
V. S. Ananth ◽  
D. K. K. Vamsi

Abstract Additional food provided prey-predator systems have become a significant and important area of study for both theoretical and experimental ecologists. This is mainly because provision of additional food to the predator in the prey-predator systems has proven to facilitate wildlife conservation as well as reduction of pesticides in agriculture. Further, the mathematical modeling and analysis of these systems provide the eco-manager with various strategies that can be implemented on field to achieve the desired objectives. The outcomes of many theoretical and mathematical studies of such additional food systems have shown that the quality and quantity of additional food play a crucial role in driving the system to the desired state. However, one of the limitations of these studies is that they are asymptotic in nature, where the desired state is reached eventually with time. To overcome these limitations, we present a time optimal control study for an additional food provided prey-predator system involving inhibitory effect with quantity of additional food as the control parameter with the objective of reaching the desired state in finite (minimum) time. The results show that the optimal solution is a bang-bang control with a possibility of multiple switches. Numerical examples illustrate the theoretical findings. These results can be applied to both biological conservation and pest eradication.

Author(s):  
Jorn H. Baayen ◽  
Krzysztof Postek

AbstractNon-convex discrete-time optimal control problems in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often find solutions that are indistinguishable from global optima. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariant convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, optimality guarantees can be obtained, the exact nature of which depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.


Author(s):  
Nasser L. Azad ◽  
Pannag R. Sanketi ◽  
J. Karl Hedrick

In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon (HC) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe HC emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.


2011 ◽  
Vol 21 (1) ◽  
pp. 5-23 ◽  
Author(s):  
Navvab Kashiri ◽  
Mohammad Ghasemi ◽  
Morteza Dardel

An iterative method for time optimal control of dynamic systemsAn iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.


2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Ziwang Lu ◽  
Guangyu Tian ◽  
Simona Onori

Abstract The synchronization process takes up almost one half of the time of the gear-shifting process, and also influences the impacts between the sleeve and the gear ring. To avoid impacts and reduce time duration, a time-optimal control strategy with angle alignment is necessary for the synchronization process. Moreover, to be better accord with practice, the motor torque response process should be taken into account. The parameters in the torque response process depend on control commands, which makes the control problem a multistage one. To solve these issues, a rule-based control strategy is extracted from the dynamic programming (DP) solution of the multistage time-optimal control problem. To obtain this strategy, the dynamic model for the synchronization process with a modified Sigmoid model to precisely depict the torque response process is first solved. Then, the control problem is formulated as a multistage time-optimal control problem with three states and solved by DP. Based on the DP results, a three-stage and a four-stage rule-based control strategies are extracted for normal operation situation and startup situation, respectively. Finally, through comparative studies, the proposed rule-based control strategy can eliminate the speed difference and angle difference simultaneously with almost the same time of the bang–bang control, while the bang–bang control cannot obtain the zero terminals. Moreover, the proposed control strategy only takes 20 ms more than the pure speed synchronization control in the worst case. It would decrease when the initial speed difference increases.


Author(s):  
Abhishek Dhanda ◽  
Joshua Vaughan ◽  
William Singhose

The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on time-optimal control has concentrated on the rest-to-rest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibration-reducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bang-bang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.


Author(s):  
William J. O’Connor ◽  
David J. McKeown

This paper presents a new, robust, time-optimal control strategy for flexible manipulators controlled by acceleration-limited actuators. The strategy is designed by combining the well-known, open-loop, time-optimal solution with wave-based feedback control. The time-optimal solution is used to design a new launch wave input to the wave-based controller, allowing it to recreate the time-optimal solution when the system model is exactly known. If modeling errors are present or a real actuator is used, the residual vibrations, which would otherwise arise when using the time-optimal solution alone, are quickly suppressed due to the additional robustness provided by the wave-based controller. A proximal time-optimal response is still achieved. A robustness analysis shows that significant improvements can be achieved using wave-based control in conjunction with the time-optimal solution. The implications and limits are also discussed.


1991 ◽  
Vol 113 (3) ◽  
pp. 363-370 ◽  
Author(s):  
W. S. Newman ◽  
K. Souccar

A technique is presented for controlling second-order, nonlinear systems using a combination of bang-bang time-optimal control, sliding-mode control, and feedback linearization. Within the control loop, a state space evaluation of the system classifies the instantaneous dynamics into one of three regions, and one of three corresponding control algorithms is invoked. Using a prescribed generation of desirable sliding surfaces, the resulting combined controller produces nearly time-optimal performance. The combination controller is provably stable in the presence of model uncertainty. Experimental data are presented for the control of a General Electric GP132 industrial robot. The method is shown to achieve nearly time-optimal motion that is robust to modeling uncertainties. Representative transients compare favorably to bang-bang control and PD control.


2005 ◽  
Vol 128 (2) ◽  
pp. 379-390 ◽  
Author(s):  
J. Dong ◽  
J. A. Stori

The problem of generating an optimal feed-rate trajectory has received a significant amount of attention in both the robotics and machining literature. The typical objective is to generate a minimum-time trajectory subject to constraints such as system limitations on actuator torques and accelerations. However, developing a computationally efficient solution to this problem while simultaneously guaranteeing optimality has proven challenging. The common constructive methods and optimal control approaches are computationally intensive. Heuristic methods have been proposed that reduce the computational burden but produce only near-optimal solutions with no guarantees. A two-pass feedrate optimization algorithm has been proposed previously in the literature by multiple researchers. However, no proof of optimality of the resulting solution has been provided. In this paper, the two-pass feed-rate optimization algorithm is generalized and a proof of global optimality is provided. The generalized algorithm maintains computational efficiency, and supports the incorporation of a variety of state-dependent constraints. By carefully arranging the local search steps, a globally optimal solution is achieved. Singularities, or critical points on the trajectory, which are difficult to deal with in optimal control approaches, are treated in a natural way in the generalized algorithm. A detailed proof is provided to show that the algorithm does generate a globally optimal solution under various types of constraints. Several examples are presented to illustrate the application of the algorithm.


Author(s):  
J. Dong ◽  
J. A. Stori

The problem of generating an optimal feedrate trajectory has received a significant amount of attention in both the robotics and machining literature. The typical objective is to generate a minimum-time trajectory subject to constraints such as system limitations on actuator torques and accelerations. However, developing a computationally efficient solution to this problem while simultaneously guaranteeing optimality has proven challenging. The common constructive methods and optimal control approaches are computationally intensive. Heuristic methods have been proposed that reduce the computational burden but produce only near-optimal solutions with no guarantees. A two-pass feedrate optimization algorithm has been proposed previously in the literature by multiple researchers. However, no proof of optimality of the resulting solution has been provided. In this paper, the two-pass feedrate optimization algorithm is extended and generalized. The generalized algorithm maintains computationally efficiency, and supports the incorporation of a variety of state dependent constraints. By carefully arranging the local search steps, a globally optimal solution is achieved. Singularities, or critical points on the trajectory, which are difficult to deal with in optimal control approaches, are treated in a natural way in the generalized algorithm. A detailed proof is provided to show that the algorithm does generate a globally optimal solution under various types of constraints.


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