Inverse Optimal Planning for Air Traffic Control

We envision a system that concisely describes the rules of air traffic control, assists human operators and supports dense autonomous air traffic around commercial airports. We develop a method to learn the rules of air traffic control from real data as a cost function via maximum entropy inverse reinforcement learning. This cost function is used as a penalty for a search-based motion planning method that discretizes both the control and the state space. We illustrate the methodology by showing that our approach can learn to imitate the airport arrival routes and separation rules of dense commercial air traffic. The resulting trajectories are shown to be safe, feasible, and efficient

Computing the minimum-time interception of a moving target

In this paper, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where the plant with a given state equation has to approach the moving target whose trajectory is known as a priory. Our framework employs the analytical description of the distance from an arbitrary point to the reachable set of the plant. The proposed algorithm is always convergent and cannot be improved without loss of completeness for arbitrary Lipschitz-continuous trajectories of the moving target. An analytical description of the distance to the reachable set is hard to obtain in practice for the sophisticated state equation of the plant. Nevertheless, it can be obtained for some widely used models such as the Dubins car. Finally, we illustrate the generality and effectiveness of the proposed framework for simple motions and Dubins' model

Minimum-time lateral interception of a moving target by a Dubins car

This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation, every one of them is a continuous function of time. The optimal trajectory planning problem of constructing minimum-time trajectories for a Dubins car in the presence of a priory known time-dependent wind vector field is a special case of the presented problem. Using the properties of the three-dimensional reachable set of a Dubins car, it is proved that the optimal interception point belongs to a part of an analytically described surface in the three-dimensional space. The analytical description of the surface makes it possible to obtain 10 algebraic equations for calculating parameters of the optimal control that implements the minimum-time lateral interception. These equations are generally transcendental and can be simplified for particular cases of target motion (e.g. resting target, straight-line uniform target motion). Finally, some particular cases of the optimal lateral interception validate developments of the paper and highlight the necessity to consider each of 10 algebraic equations in general case.Comment: 16 pages, 19 figure

Optimal steering for kinematic vehicles with applications to spatially distributed agents

The recent technological advances in the field of autonomous vehicles have resulted in a growing impetus for researchers to improve the current framework of mission planning and execution within both the military and civilian contexts. Many recent efforts towards this direction emphasize the importance of replacing the so-called monolithic paradigm, where a mission is planned, monitored, and controlled by a unique global decision maker, with a network centric paradigm, where the same mission related tasks are performed by networks of interacting decision makers (autonomous vehicles). The interest in applications involving teams of autonomous vehicles is expected to significantly grow in the near future as new paradigms for their use are constantly being proposed for a diverse spectrum of real world applications. One promising approach to extend available techniques for addressing problems involving a single autonomous vehicle to those involving teams of autonomous vehicles is to use the concept of Voronoi diagram as a means for reducing the complexity of the multi-vehicle problem. In particular, the Voronoi diagram provides a spatial partition of the environment the team of vehicles operate in, where each element of this partition is associated with a unique vehicle from the team. The partition induces, in turn, a graph abstraction of the operating space that is in a one-to-one correspondence with the network abstraction of the team of autonomous vehicles; a fact that can provide both conceptual and analytical advantages during mission planning and execution. In this dissertation, we propose the use of a new class of Voronoi-like partitioning schemes with respect to state-dependent proximity (pseudo-) metrics rather than the Euclidean distance or other generalized distance functions, which are typically used in the literature. An important nuance here is that, in contrast to the Euclidean distance, state-dependent metrics can succinctly capture system theoretic features of each vehicle from the team (e.g., vehicle kinematics), as well as the environment-vehicle interactions, which are induced, for example, by local winds/currents. We subsequently illustrate how the proposed concept of state-dependent Voronoi-like partition can induce local control schemes for problems involving networks of spatially distributed autonomous vehicles by examining different application scenarios.PhDCommittee Chair: Tsiotras Panagiotis; Committee Member: Egerstedt Magnus; Committee Member: Feron Eric; Committee Member: Haddad Wassim; Committee Member: Shamma Jef

On behavioral Arrow Pratt risk process with applications to risk pricing, stochastic cash flows, and risk control

We introduce a closed form behavioural stochastic Arrow-Pratt risk process, decomposed into discrete asymmetric risk seeking and risk averse components that run on different local times in ϵ-disks centered at risk free states. Additionally, we embed Arrow-Pratt (“AP”) risk measure in a simple dynamic system of discounted cash flows with constant volatility, and time varying drift. Signal extraction of Arrow-Pratt risk measure shows that it is highly nonlinear in constant volatility for cash flows. Robust identifying restrictions on the system solution confirm that even for small time periods constant volatility is not a measure of AP risk. By contrast, time-varying volatility measures aspects of embedded AP risk. Whereupon maximal AP risk measure is obtained from a convolution of input volatility and idiosyncratic shocks to the system. We provide four applications for our theory. First, we find that Engle, Ng and Rothschild (1990) Factor-ARCH model for risk premia is misspecified because the factor price of risk is time varying and unstable. Our theory predicts that a hyper-ARCH correction factor is required to remove the Factor-ARCH specification. Second, when applied to analysts beliefs about interest rates and volatility, we find that AP risk measure is a feedback control over stochastic cash flows. Whereupon increased risk aversion to negative shocks to earnings increases volatility. Third, we use an oft cited example of Benes, Shepp and Witsenhausen (1980) to characterize a controlled AP diffusion for a conservative investor who wants to minimize the AP risk process for an asset. Fourth, we recover stochastic differential utility functional from the AP risk process and show how it is functionally equivalent to Duffie and Epstein’s (1992) parametrization.behavioural Arrow-Pratt risk process; asymmetric risk decomposition; asset pricing; Markov process; local martingale; local time change

A New Algorithm for Optimizing Dubins Paths to Intercept a Moving Target

This paper is concerned with determining the shortest path for a pursuer aiming to intercept a moving target travelling at a constant speed. We introduce an intuitive and efficient mathematical model outlined as an optimal control problem to address this challenge. The proposed model is based on Dubins path where we concatenate two possible paths: a left-circular curve or a right-circular curve followed by a straight line. We develop and explore this model, providing a comprehensive geometric interpretation, and design an algorithm tailored to implement the proposed mathematical approach efficiently. Extensive numerical experiments involving diverse target positions highlight the strength of the model. The method exhibits a remarkably high convergence rate in finding solutions. For experiment purposes, we utilized the modelling software AMPL, employing a range of solvers to solve the problem. Subsequently, we simulated the obtained solutions using MATLAB, demonstrating the efficiency of the model in intercepting a moving target. The proposed model distinguishes itself by employing fewer parameters and making fewer assumptions, setting the model simplifies the complexities, and thus, makes it easier for experts to design optimal path plans

Theory of Stochastic Optimal Economic Growth

This paper is a survey of the theory of stochastic optimal economic growth.International Development,