On the Equivalence of Discrete Systems in Time-Optimal Control

1963 ◽  
Vol 85 (2) ◽  
pp. 204-210 ◽  
Author(s):  
E. Polak
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Pulse Width ◽  
Discrete System ◽  
Discrete Systems ◽  
Order Linear Differential Equation ◽  
Optimal Control Strategy ◽  
Pulse Width Modulated ◽  
Time Optimal ◽  
Linear Differential

It is shown in this paper that under a transformation which maps the state space of a system onto a sequence space in a one-to-one manner, time-optimal discrete regulator systems with different dynamics and modulators can be brought to equivalence and that this fact may be used to construct an optimal control strategy for one system from the known optimal control strategy of another one. In particular, the optimal control strategy for a pulse-width-modulated discrete system with a plant described by an nth order linear differential equation is derived in this manner.

Real-Time Optimal Power Management for Hybrid Electric Vehicle Based on Prediction of Trip Information

2013 ◽  
Vol 321-324 ◽  
pp. 1539-1547 ◽  
Author(s):  
Li Cun Fang ◽  
Gang Xu ◽  
Tian Li Li ◽  
Ke Min Zhu
Keyword(s):  
Optimal Control ◽  
Real Time ◽  
Power Management ◽  
Fuel Economy ◽  
Control Strategy ◽  
Hybrid Electric Vehicle ◽  
Driving Cycle ◽  
Moving Window ◽  
Optimal Control Strategy ◽  
Time Optimal

Power management of hybrid electric vehicle (HEV) is an important operational factor for HEV to enhance fuel economy and reduce emissions. Optimal control for HEV requires the knowledge of entire driving cycle and elevation profile to obtain the optimal control strategy over fixed driving cycle. In this paper, the traffic knowledge extracted from intelligent transportation systems (ITSs),global positioning systems (GPSs) and geographical information systems (GISs) is used for predicting the knowledge of the future driving cycle, and the real-time optimal control strategy based on dynamic programming in a moving window is investigated in order to minimize fuel consumption. A simulation study was conducted for two driving cycles, and the results showed significant improvement in fuel economy compared with a rule-based control. Furthermore, the results showed that the distance of the moving window has obvious effect on the fuel economy.

Optimal vaccination policy and cost analysis for epidemic control in resource-limited settings

Kybernetes ◽  
2015 ◽  
Vol 44 (3) ◽  
pp. 475-486 ◽  
Author(s):  
Kuan Yang ◽  
Ermei Wang ◽  
Yinggao Zhou ◽  
Kai Zhou
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Mass Action ◽  
Sir Epidemic Model ◽  
Epidemic Control ◽  
Optimal Control Strategy ◽  
Content Type ◽  
Total Cost ◽  
Time Optimal ◽  
The Impact

Purpose – The purpose of this paper is to use analytical method and optimization tools to suggest time-optimal vaccination program for a basic SIR epidemic model with mass action contact rate when supply is limited. Design/methodology/approach – The Lagrange Multiplier Method and Pontryagin’s Maximum Principle are used to explore optimal control strategy and obtain analytical solution for the control system to minimize the total cost of disease with boundary constraint. The numerical simulation is done with Matlab using the sequential linear programming method to illustrate the impact of parameters. Findings – The result highlighted that the optimal control strategy is Bang-Bang control – to vaccinate with maximal effort until either all of the resources are used up or epidemic is over, and the optimal strategies and total cost of vaccination are usually dependent on whether there is any constraint of resource, however, the optimal strategy is independent on the relative cost of vaccination when the supply is limited. Practical implications – The research indicate a practical view that the enhancement of daily vaccination rate is critical to make effective initiatives to prevent epidemic from out breaking and reduce the costs of control. Originality/value – The analysis of the time-optimal application of outbreak control is of clear practical value and the introducing of resource constraint in epidemic control is of realistic sense, these are beneficial for epidemiologists and public health officials.

Observer-based time-optimal control of an aerobic SBR for chemical and petrochemical wastewater treatment

2000 ◽  
Vol 42 (5-6) ◽  
pp. 163-170 ◽  
Author(s):  
A. Vargas ◽  
G. Soto ◽  
J. Moreno ◽  
G. Buitrón
Keyword(s):  
Optimal Control ◽  
Reaction Time ◽  
Control Strategy ◽  
Optimal Operation ◽  
Time Optimal Control ◽  
Nonlinear Observer ◽  
Synthetic Wastewater ◽  
Optimal Control Strategy ◽  
Time Optimal ◽  
High Concentrations

The present study implements a time-optimal control strategy for a discontinuous aerobic bioreactor, used to treat highly concentrated toxic wastewater present in some effluents of the chemical and petrochemical industries, using respirometric techniques. The control strategy regulates the feed rate to maintain a constant optimal substrate concentration in the reactor, which in turn minimizes the reaction time. Since this control requires on-line knowledge of unmeasurable variables, an Extended Kalman Filter is used as a nonlinear observer. The experimental setup was a 7 litre laboratory bioreactor used to treat synthetic wastewater with high concentrations of 4-chlorophenol. The controller consisted of a personal computer with data acquisition hardware and real-time software tools, peristaltic pumps and an electronic oxygen meter. Three experiments were performed: one to obtain parameters and calibrate the observer, another one to validate the time-optimal strategy and a final one to evaluate theperformance of a fully automated time-optimal operation. When well calibrated, the observer provided good enough estimates and the controller worked as expected, reducing reaction time and increasing the overall efficiency of the bioreactor, when compared with the usual SBR-type operation.

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