Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics
طراحی مسیر راه اندازی بهینه برای تثبیت دینامیک خطای خطی متغیر خطی-2021
This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization. Consequently, the trajectory is designed such that the Linear Time-Varying (LTV) dynamic system, describing the controller’s error dynamics, is stable, while additionally the desired optimality criterion is optimized and all enforced constraints on the trajectory are fulfilled. This is achieved by means of a Lyapunov stability analysis of the LTV dynamics within the optimization problem using a time-dependent, quadratic Lyapunov function candidate. Special care is taken with regard to ensuring the correct definiteness of the ensuing matrices within the Lyapunov stability analysis, specifically considering a numerically stable formulation of these in the numerical optimization. The developed algorithm is applied to a trajectory design problem for which the LTV system is part of the path-following error dynamics, which is required to be stable. The main benefit of the proposed scheme in this context is that the designed trajectory trades-off the required stability and robustness properties of the LTV dynamics with the optimality of the trajectory already at the design phase and thus, does not produce unstable optimal trajectories the system must follow in the real application.
keywords: LTV error dynamics | LTV stability | Optimal control-based LTV stabilization | Path-following error controller | Trajectory generation | Trajectory optimization
Parsimonious shooting heuristic for trajectory design of connected automated traffic part II: Computational issues and optimization
تیراندازی پارسییمونیک مکاشفه ای برای طراحی مسیر ترافیک خودکار متصل شده بخش دوم: مسائل محاسباتی و بهینه سازی-2017
Advanced connected and automated vehicle technologies enable us to modify driving be havior and control vehicle trajectories, which have been greatly constrained by human lim its in existing manually-driven highway traffic. In order to maximize benefits from these technologies on highway traffic management, vehicle trajectories need to be not only con trolled at the individual level but also coordinated collectively for a stream of traffic. As one of the pioneering attempts to highway traffic trajectory control, Part I of this study (Zhou et al., 2016) proposed a parsimonious shooting heuristic (SH) algorithm for con structing feasible trajectories for a stream of vehicles considering realistic constraints in cluding vehicle kinematic limits, traffic arrival patterns, car-following safety, and signal op erations. Based on the algorithmic and theoretical developments in the preceding paper, this paper proposes a holistic optimization framework for identifying a stream of vehicle trajectories that yield the optimum traffic performance measures on mobility, environment and safety. The computational complexity and mobility optimality of SH is theoretically an alyzed, and verifies superior computational performance and high solution quality of SH. A numerical sub-gradient-based algorithm with SH as a subroutine (NG-SH) is proposed to simultaneously optimize travel time, a surrogate safety measure, and fuel consumption for a stream of vehicles on a signalized highway section. Numerical examples are conducted to illustrate computational and theoretical findings. They show that vehicle trajectories gen erated from NG-SH significantly outperform the benchmark case with all human drivers at all measures for all experimental scenarios. This study reveals a great potential of trans formative trajectory optimization approaches in transportation engineering applications. It lays a solid foundation for developing holistic cooperative control strategies on a general transportation network with emerging technologies.
Keywords: Connected vehicles | Automated vehicles | Traffic smoothing | Trajectory optimization | Traffic signal | Shooting heuristic | Customized numerical-gradient heuristic | Expedited objective evaluation
New reference trajectory optimization algorithm for a flight management system inspired in beam search
الگوریتم بهینه سازی مسیر جامع جدید برای یک سیستم مدیریت پرواز الهام گرفته از جستجوی پرتو-2017
With the objective of reducing the flight cost and the amount of polluting emissions released in the atmosphere, a new optimization algorithm considering the climb, cruise and descent phases is presented for the reference vertical flight trajectory. The selection of the reference vertical navigation speeds and altitudes was solved as a discrete combinatory problem by means of a graphtree passing through nodes using the beam search optimization technique. To achieve a compromise between the execution time and the algorithm’s ability to find the global optimal solution, a heuristic methodology introducing a parameter called ‘‘optimism coefficient was used in order to estimate the trajectory’s flight cost at every node. The optimal trajectory cost obtained with the developed algorithm was compared with the cost of the optimal trajectory provided by a commercial flight management system(FMS). The global optimal solution was validated against an exhaustive search algorithm(ESA), other than the proposed algorithm. The developed algorithm takes into account weather effects, step climbs during cruise and air traffic management constraints such as constant altitude segments, constant cruise Mach, and a pre-defined reference lateral navigation route. The aircraft fuel burn was computed using a numerical performance model which was created and validated using flight test experimental data
KEYWORDS : Beam search | Commercial aircraft | Flight time | Flight management system | Fuel burn | FMS | Trajectory optimization
Effects of linear holding for reducing additional flight delays without extra fuel consumption
اثرات برگزاری خطی برای کاهش تاخیر پرواز های اضافی و بدون مصرف سوخت اضافی-2017
This paper presents an approach to implement linear holding (LH) for flights initially sub ject to ground holding, in the context of Trajectory Based Operations. The aim is to neutral ize additional delays raised from the lack of coordination between various traffic management initiatives (TMIs) and without incurring extra fuel consumption. Firstly, motivated from previous works on the features of LH to absorb delays airborne, a potential applicability of LH to compensate part of the fixed ground holding is proposed. Then, the dynamic adjustment of LH in response to TMIs-associated tactical delays is formulated as a multi-stage aircraft trajectory optimization problem, addressing both pre- and post departure additional delays. Results suggest that additional delays of 25 mins in a typical case study can be totally recovered at no extra fuel cost. A notable extent of delay reduction observed from the computational experiments further supports the benefits of LH for reducing different combinations of additional delays without consuming extra fuel.
Keywords: Air transportation | Linear holding | Speed reduction | Trajectory optimization | Air traffic flow management
Optimal Aircraft Trajectories to Minimize the Radiative Impact of Contrails and CO2
مسیرهای بهینه هواپیما برای به حداقل رساندن تاثیر تابشی Contrails و CO2-2017
The rapid growth of air traffic in the Asia Pacific region in the last decade has brought about the need for more sustainable modes of flight. A key initiative is the development of a Next Generation Air Traffic Management (NG-ATM) system which allows aircraft to fly optimal trajectories. Besides fuel- and time-related costs, other considerations for optimal routing include emissions, noise and contrails. Multi-Objective Trajectory Optimisation (MOTO) allows the generation of optimal trajectories with regards to these objectives, with dynamic weights depending on the phase of flight. Contrails are a major contributor to aviation’s total Radiative Forcing (RF), being more significant than that of CO2. In particular, when formed in areas of low temperature and high relative humidity, contrails are known to persist for hours, spreading and eventually transitioning into cirrus clouds. Contrails trap heat by reflecting the long-wave infra-red radiation emitted by the earth back to its surface, producing positive RF. However, the albedo of contrails also reflects the incoming shortwave radiation from the sun, resulting in a negative component of RF. The impact of contrails, quantified by its associated RF, is thus not merely a function of environmental parameters but also a function of time. In this paper, a MOTO algorithm is used to generate optimal trajectories that minimize the radiative impact of contrails and CO2, while minimizing flight time and fuel burn. A case study of a transcontinental flight from Paris to Beijing is presented to demonstrate the feasibility of such an algorithm in providing strategic and tactical trajectory optimization capabilities.
Keywords: Contrail modelling | trajectory optimisation | sustainable aviation