Stochastic optimal control for aircraft conflict resolution under wind uncertainty

As air traffic intensity increases and stochastic uncertainties, such as wind direction and speed, continue to impact air traffic controllers' workload significantly, airlines are increasingly pressured to reduce costs by flying via straighter/more direct trajectories. Due to these changes, it is important to search for new means/solutions for aircraft conflict resolution to ensure the required level of safety and rational flight trajectory. Such a solution could be the implementation of Dubin's method of flight trajectories. This paper aims to propose and deeply analyze a new mathematical model for two-aircraft conflict resolution where the Dubins method is applied in a dynamic conflict scenario. In this model, at a certain moment, the flight trajectory of one aircraft follows a path similar to a moving circle's tangential line. Upon that, the conflict detection and resolution (CDR) model considers wind uncertainty. The proposed CDR method could be applied when uncertainty such as wind direction and speed are inconstant (stochastic) throughout the simulation.

A method for conflict detection and resolution based on the parameterization of the aircraft intents is presented. The method is also based on the use of predefined trajectory patterns, which are in fact flight intents; these patterns include standard airline procedures and air traffic control regulations. The conflict resolution problem is formulated as a parametric optimization problem subject to constraints; the optimality criterium is defined so that the deviation from the intended (preferred) trajectories in the lateral profile is minimized. The resolution trajectory patterns take into account changes of the nominal waypoints (vectoring) and changes of the aircraft speeds. The method is applied to the case of multiple conflicts among commercial transport aircraft in converging traffic in the terminal area; different scenarios are considered, which include locked aircraft, that is, aircraft whose trajectories are known and fixed. The conflict detection and resolution algorithm relies on a kinetic trajectory predictor (nonlinear point-mass model with variable mass), which is accurate, flexible, and transparent, and provides the high-fidelity prediction required in the analysis of the demanding terminal area traffic. The cost of the global conflict resolution process is assessed, in terms of extra distance traveled, extra flight time, and extra fuel consumed for each aircraft.

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

ABSTRACTThis paper studies the optimal control of multi‐machine power systems with the excitation of fractional Gaussian noise (FGN) and applies the theory of quasi‐generalized Hamiltonian systems. First, a multi‐machine power system model is established based on the long‐range correlation of fractional Gaussian noise, which is transformed into a quasi‐generalized Hamiltonian system model. Next, according to the fractional path integral rules and the stochastic averaging method (SAM), the stochastic multi‐machine power system is reduced in dimension. Then, based on the averaged multi‐machine power system, the dynamic programming method of stochastic optimal control is utilized to propose a control strategy that maximizes the probability of the controlled system being in the desired region. Finally, the effectiveness of the proposed control strategy is verified through numerical simulations, and the superiority of the control methods has also been compared with the Linear Quadratic Regulator (LQR).

The time delay in active and semi-active controls is an important research subject. Many researches on the time-delay control for deterministic systems have been made (Hu and Wang 2002, Yang et al. 1990, Abdel-Mooty and Roorda 1991, Pu 1998, Cai and Huang 2002), while the study on that for stochastic systems is very limited. The effects of the time delay on the control of nonlinear systems under Gaussian white noise excitations have been studied by Bilello et al. (2002). The controlled linear systems with deterministic and random time delay subjected to Gaussian white noise excitations have been treated by Grigoriu (1997). Recently, a stochastic averaging method for quasi-integrable Hamiltonian systems with time delay has been proposed (Liu and Zhu 2007). In the present paper, a stochastic optimal time-delay control method for stochastically excited nonlinear structural systems is proposed based on the stochastic averaging method for quasi Hamiltonian systems with time delay and the stochastic dynamical programming principle. An example of stochastically excited and controlled hysteretic column is given to illustrate the proposed control method.

This paper presents a real-time coordinated ramp control approach in response to incident-induced traffic congestion on freeways. The proposed control methodology includes two major functions to alleviate in real time incident impact on multi-segment traffic flows of freeways, i.e. (1) identification of control zone-based congestion patterns, and (2) stochastic optimization of group-based ramp metering control. To reduce congestion, the modified generalized sequential probability ratio testing (M-GSPRT) technology together with stochastic optimal control methods are used, respectively, in the above two mechanisms. With the aid of the Paramics microscopic traffic simulator, numerical results obtained under various simulated incident-induced congestion conditions indicate the feasibility of the proposed method. Numerical test results indicate both the feasibility of the proposed ramp control method in responding to diverse lane-blocking incident conditions, and its efficiency, particularly in improving the averaged hourly throughput by 67.5% in medium-volume incident cases, compared with the no-control strategy.

Asset allocation for a DC pension fund with stochastic income and mortality risk: A multi-period mean–variance framework

Rotorcraft shipboard landing is one of the most challenging operations for rotorcraft pilots owing to the workload associated with the task, which can be attributed to a variety of environmental conditions like random ship motion, heavy sea states and unsteady aerodynamic conditions. This paper explores the effectiveness of Model Predictive Path Integral (MPPI) approach, a stochastic optimal control method, for parallel trajectory optimization as a guidance solution to the rotorcraft shipboard landing problem. Specifically, the computational efficiency for real time guidance solutions afforded by the MPPI approach in comparison to its sequential counterpart is evaluated. Furthermore, a sensitivity analysis of MPPI parameter selection on its performance is carried out. The performance of the developed MPPI algorithms for real time guidance in helicopter ship board landing is demonstrated using nonlinear model simulations of a helicopter executing a symmetric landing profile aligned with the ship deck centerline.

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

Innovative procedures for the stochastic optimal time-delay control and stabilization are proposed for a quasi-integrable Hamiltonian system subject to Gaussian white noises. First, the problem of stochastic optimal control with time delay is formulated. Then, the problem is converted into a stochastic optimal control without time delay, and the converted control problems are then solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The optimal time-delay stabilization of quasi-integrable Hamiltonian systems is formulated as an ergodic control with a cost function determined by minimizing the largest Lyapunov exponent of the controlled system. As an example, a two-degree-of-freedom quasi-integrable Hamiltonian system with time delay in feedback control forces is investigated in detail to illustrate the procedures and their effectiveness.KeywordsTime-delay feedback controlStochastic averaging methodStochastic optimal controlFeedback stabilization

Reliability-based stochastic optimal control of frame building under near-fault ground motions

A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

China has been gradually relaxing its ban on the use of low-altitude airspace across the country. To guarantee the high reliability of air traffic management (ATM), conflict detection and conflict resolution (CDR) approaches are indispensable to maintain safe separation between neighbouring small fixed-wing aircraft. In this study, we analyse a temporal and spatial integrated strategy for safety assessment purposes in opening the low-altitude urban airspace of Chinese pilot cities. First, we present a detailed mathematical description of the proposed algorithms based on a spatial grid partitioning system (SGPS). For our system, a conflict detection (CD) algorithm is designed to determine if two trajectories pass through the same grid space within overlapping time windows. A conflict resolution (CR) algorithm integrates a proposed time scheduling-based technique (TST) and vertical change-based technique (VCT), which operate under predetermined basic principles. Then, based on our novel CDR algorithms, a causal model is constructed in graphical modelling and analysis software (GMAS) to generate a state space that can provide a global perspective on scenario dynamics and better understanding of induced conflict occurrences. Finally, simulation results demonstrate that the proposed approach is practical and efficient.

Conflict detection algorithms can be broadly classified as state based and intent based algorithms. State based algorithms predict the path of aircraft by projecting their current position and velocity vectors. The path predictions are then used to determine if the aircraft are in conflict within a look ahead time. That is, if loss of separation occurs in the future. Intent based algorithm uses flight plans and other information, which usually resides in a flight management computer, to predict the path of aircraft. Algorithms that use intent information for conflict detection obtain the intent of other aircraft and broadcast their own intent via some type of communication link. Intent information that is exchanged among the aircraft is defined as explicit intent. A conflict detection algorithm can also make use of intent information based on aircraft nominal routes, corridors, published approaches, etc., and in this case, there is no information exchange between aircraft. This kind of intent is defined as implicit intent. Implicit intent can be used very effectively in conflict detection without the added cost and complexity of communication links. The use of implicit intent, in combination with state information, reduces false alarms over a state based conflict detection algorithm and therefore increases the effectiveness of the alerting system. In this paper, conflict detection using implicit intent information is described and its performance is compared with a state based conflict detection algorithm.

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.