Bang-bang control and singular arcs in reservoir flooding

Zandvliet, Maarten; Bosgra, О.H.; Jansen, J.D.; Hof, Paul M.J. Van den; Kraaijevanger, J. F. B. M.

doi:10.1016/j.petrol.2006.12.008

Cited by 79 publications

(37 citation statements)

References 19 publications

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“…Results showed that the waterflooding optimization was a ''bang-bang'' control problem, where each control variable took either its minimum or maximum allowed values. Zandvliet et al (2007) further investigated why and under what conditions waterflooding problems had optimal solutions under bangbang control. They concluded that waterflooding optimization with simple boundary constraints sometimes had bang-bang optimal solutions, while problems with other general inequality or equality constraints would have a smooth optimal solution.…”

Section: Reservoir Production Optimizationmentioning

confidence: 99%

A review of closed-loop reservoir management

Hou

Zhou

Zhang³

et al. 2015

Pet. Sci.

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The closed-loop reservoir management technique enables a dynamic and real-time optimal production schedule under the existing reservoir conditions to be achieved by adjusting the injection and production strategies. This is one of the most effective ways to exploit limited oil reserves more economically and efficiently. There are two steps in closed-loop reservoir management: automatic history matching and reservoir production optimization. Both of the steps are large-scale complicated optimization problems. This paper gives a general review of the two basic techniques in closed-loop reservoir management; summarizes the applications of gradient-based algorithms, gradient-free algorithms, and artificial intelligence algorithms; analyzes the characteristics and application conditions of these optimization methods; and finally discusses the emphases and directions of future research on both automatic history matching and reservoir production optimization.

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Section: Reservoir Production Optimizationmentioning

confidence: 99%

A review of closed-loop reservoir management

Hou

Zhou

Zhang³

et al. 2015

Pet. Sci.

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“…This observation has been investigated also by Brouwer and Jansen (2004). According to Zandvliet et al (2007), if the objective functional is linear in the control and the only constraints are upper and lower bounds on the control, due to the particular structure, the problem will sometimes have bang-bang optimal solutions. The bang-bang control has a major practical advantage since it can be implemented with simple on-off valves and together with the switching time method it may have a promising beneficial application .…”

Section: Optimal Control Theorymentioning

confidence: 99%

Optimal switching time control of petroleum reservoirs

Hasan

Foss

2015

Journal of Petroleum Science and Engineering

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“…For this, we exploit the known bang-singular structure of maneuvers and parametrize a maneuver by the times at which the control inputs switch, and by the terminal time. This approach, commonly referred to as switching time optimization (STO, Zandvliet et al 2007), provides the significant advantage of requiring no initial guess of x a or c. Instead of requiring an initial guess of x a or c, it requires a guess of the switching times, which are easier to obtain, and which can lead to convergence from a much larger range of initial guesses.…”

Section: Algorithm For Calculation Of Time-optimal Maneuversmentioning

confidence: 99%

Performance benchmarking of quadrotor systems using time-optimal control

2012

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Frequently hailed for their dynamical capabilities, quadrotor vehicles are often employed as experimental platforms. However, questions surrounding achievable performance, influence of design parameters, and performance assessment of control strategies have remained largely unanswered. This paper presents an algorithm that allows the computation of quadrotor maneuvers that satisfy Pontryagin's minimum principle with respect to time-optimality. Such maneuvers provide a useful lower bound on the duration of maneuvers, which can be used to assess performance of controllers and vehicle design parameters. Computations are based on a two-dimensional first-principles quadrotor model. The minimum principle is applied to this model to find that time-optimal trajectories are bang-bang in the thrust command, and bang-singular in the rotational rate control. This paper presents a procedure allowing the computation of time-optimal maneuvers for arbitrary initial and final states by solving the boundary value problem induced by the minimum principle. The usage of the computed maneuvers as a benchmark is demonstrated by evaluating quadrotor design parameters, and a linear feedback control law as an example of a control strategy. Computed maneuvers are verified experimentally by applying them to quadrocopters in the ETH Zurich Flying Machine Arena testbed. Electronic supplementary materialThe online version of this article (

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Bang-bang control and singular arcs in reservoir flooding

Cited by 79 publications

References 19 publications

A review of closed-loop reservoir management

A review of closed-loop reservoir management

Optimal switching time control of petroleum reservoirs

Performance benchmarking of quadrotor systems using time-optimal control

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