On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

Parzani, Céline; Puechmorel, Stéphane

doi:10.1002/oca.2389

Cited by 16 publications

(14 citation statements)

References 35 publications

(59 reference statements)

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“…Khardi used the HJB approach to minimize aircraft noise, fuel consumption, and air pollution around airports [30]. Parzani and Puechmorel applied the HJB approach to generate a conflict-free minimum-time aircraft trajectory [31].…”

Section: Introductionmentioning

confidence: 99%

A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

2021

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4D flight trajectory optimization is an essential component to improve flight efficiency and to enhance air traffic capacity. this technique not only helps to reduce the operational costs, but also helps to reduce the environmental impact caused by the airliners. This study considers Dynamic Programming (DP), a well-established numerical method ideally suited to solve 4D flight Trajectory Optimization Problems (TOPs). However, it bears some shortcomings that prevent the use of DP in many practical real-time implementations. This paper proposes a Modified Dynamic Programming (MDP) approach that reduces the computational effort and overcomes the drawbacks of the traditional DP. In this paper, two numerical examples with fixed arrival times are presented, where the proposed MDP approach is successfully implemented to generate optimal trajectories that minimize aircraft fuel consumption and emissions. Then the obtained optimal trajectories are compared with the corresponding reference commercial flight trajectory for the same route in order to quantify the potential benefit of reduction of aircraft fuel consumption and emissions.

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Section: Introductionmentioning

confidence: 99%

A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

2021

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“…Hamilton-Jacobi (HJ) analysis is a method for solving optimal control and differential game problems, by formulating an HJ partial differential equation (PDE) which encodes the dynamics and the cost [2]- [7]. It has been widely utilized in a variety of fields, including autonomous driving [8], [9], air traffic [10], [11], robotics [12], economics [13], and finance [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Hamilton-Jacobi Formulation for State-Constrained Optimal Control and Zero-Sum Game Problems

Lee

Keimer

Bayen

et al. 2020

2020 59th IEEE Conference on Decision and Control (CDC)

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This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ partial differential equations, the computational complexity is exponential in the dimension of the continuous state. To manage this computational complexity, methods based on Lax-Hopf theory have been developed for the state-unconstrained optimal control problem under certain assumptions, such as affine dynamics and state-independent stage cost. Based on the Lax formula [2], this paper proposes an HJ formula for the stateconstrained optimal control problem for nonlinear systems. We call this formula the generalized Lax formula for the optimal control problem. The HJ formula provides both the optimal cost and an optimal control signal. We also provide an efficient computational method for a class of problems for which the dynamics is affine in the state, and for which the stage and terminal cost, as well as the state constraints, are convex in the state. This class of problems does not require affine dynamics and convex stage cost in the control. This paper also provides three practical examples.

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“…A powerful tactic for solving a stochastic control problem, especially that based on a system of SDEs, is finding an appropriate solution to a Hamilton‐Jacobi‐Bellman (HJB) equation, which is a degenerate parabolic partial differential equation to determine the optimal control of the system. Both analytical and numerical approaches have been employed for solving HJB equations. In the research areas of environment and ecology, HJB equations are modern mathematical tools for effective system management .…”

Section: Introductionmentioning

confidence: 99%

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Yoshioka

2019

Optim Control Appl Methods

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An optimization problem of controlling a dam installed in a river is analyzed based on a stochastic control formalism of a diffusion process under model ambiguity: a new mathematical approach to this issue. The diffusion process is a pathwise unique solution to a water balance equation considering the inflow, outflow, water loss in the reservoir, and direct rainfall. Finding the optimal reservoir operation policy reduces to solving a degenerate parabolic partial differential equation: a Hamilton-Jacobi-Bellman-Isaacs equation. A monotone finite difference scheme is constructed for discretization of the equation, successfully generating nonoscillatory and reasonably accurate numerical solutions. Stability analysis of the resulting water balance dynamics is finally carried out for both environmentally friendly and not friendly reservoir operations. KEYWORDS finite difference scheme, Hamilton-Jacobi-Bellman-Isaacs equation, reservoir operation, stochastic control, viscosity solution INTRODUCTIONThis paper contributes to providing a mathematical framework for modeling and control of reservoirs created in rivers.Since the problem has an engineering background, it is first presented, and then, the issues to be addressed and our contributions are explained.Many rivers have dams serving as central infrastructures to supply essential water resources for human lives. 1-3 The stored water in the reservoir created by a dam is utilized for multiple purposes, such as drinking water, irrigation, and hydropower generation. 4 Several dams are used for flood mitigation as well. 5,6 On the other hand, controlling a dam critically affects its downstream river environment because the original flow regime is altered. 7-9 Sediment transport and attached algae population dynamics in dam downstream experience significant changes because dams trap sediment and the algae growth is highly flow-dependent. 10 Dam operation is thus desired to be environmentally friendly such that its impacts on the downstream are minimized, while it should be fit-for-purpose at the same time.Management of environment and ecology in rivers has been a long-standing engineering problem, 11-13 and mathematical tools and concepts for their modeling, analysis, and control are still developing. Several researchers considered river management problems based on stochastic process models such as stochastic differential equations (SDEs) 14 that can naturally consider stochasticity involved in environmental and ecological processes. 15 Interactions between aquatic species, such as riparian vegetation and fishes, and river discharges have been described with SDEs. 16 Miyamoto and Kimura 17 analyzed seedling, growth, and mortality dynamics of riparian trees subject to stochastic flood disturbances. Vesipa et al 18 764

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On a Hamilton‐Jacobi‐Bellman approach for coordinated optimal aircraft trajectories planning

Cited by 16 publications

References 35 publications

A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

A Modified Dynamic Programming Approach for 4D Minimum Fuel and Emissions Trajectory Optimization

Hamilton-Jacobi Formulation for State-Constrained Optimal Control and Zero-Sum Game Problems

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

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