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Optimal service allocation among two heterogeneous traffic types with no queueing

Two communication traffic streams with Poisson statistics arrive at a network node. These are to be transmitted across a channel with a total bandwidth capacity of C slots. Messages not accepted at the node are assumed to be lost. Under the assumptions of exponential service time distributions, the problem of dynamic allocation of available channel bandwidth among the two traffic types is studied in order to minimize a weighted sum of blocking probabilities. Modeling the system as a two-dimensional Markov chain is studied to minimize a weighted sum of blocking probabilities. Modeling the system as a two-dimensional Markov chain, it is shown by an application of dynamic programming principles that the optimal policy has the form of a 'switching curve'.

Lambadaris, I.

Adaptive Stress Testing of Collision Avoidance Systems for Small UASs with Deep Reinforcement Learning

The next-generation Airborne Collision Avoidance System for smaller UASs (ACAS sXu) is currently being developed and tested by the Federal Aviation Administration (FAA) to provide detect-and-avoid capability for small unmanned aircraft operating beyond line-of-sight. Due to the complexity and safety-critical nature of the system, safety validation is important not only for the certification of the final system, but also for informing changes during the iterative development process. In this paper, we analyze a prototype of ACAS sXu in simulated aircraft encounters to discover scenarios of small near mid-air collisions (sNMACs), an important safety event in which two aircraft come closer than 50 feet horizontally and 15 feet vertically. Due to the size and complexity of the system as well as rarity of sNMAC events, traditional methods such as Monte Carlo testing often require informed setup and targeting to elicit failures. However, such a dependence on domain knowledge can be incompatible with the independent verification and validation (IV&V) process, the aim of which is to discover unforeseen issues. To address these challenges, we apply an accelerated validation method called adaptive stress testing (AST) to find the most likely sNMAC scenarios without reliance on system introspection. AST uses reinforcement learning to adapt the search towards the most promising areas of the search space as it progresses. We use a state-of-the-art deep reinforcement learning algorithm, proximate policy optimization, to more efficiently search the large and continuous state space. We find that this approach significantly improves the performance of AST compared to a prior approach based on Monte Carlo tree search. We perform experiments using AST to find sNMAC events under various encounter configurations, varying parameters pertaining to dynamics and coordination. Our experiments show AST to be very effective at finding sNMAC scenarios. We summarize our findings, presenting high-level categories of discovered sNMACs and specific examples of encounters in each category.

aircraft collision avoidance

Scheduling the NASA Deep Space Network with Deep Reinforcement Learning

With three complexes spread evenly across the Earth, NASA’s Deep Space Network (DSN) is the primary means of communications as well as a significant scientific instrument for dozens of active missions around the world. A rapidly rising number of spacecraft and increasingly complex scientific instruments with higher bandwidth requirements have resulted in demand that exceeds the network’s capacity across its 12 antennae. The existing DSN scheduling process operates on a rolling weekly basis and is time-consuming; for a given week, generation of the final baseline schedule of spacecraft tracking passes takes roughly 5 months from the initial requirements submission deadline, with several weeks of peer-to-peer negotiations in between. This paper proposes a deep reinforcement learning (RL) approach to generate candidate DSN schedules from mission requests and spacecraft ephemeris data with demonstrated capability to address real-world operational constraints. A deep RL agent is developed that takes mission requests for a given week as input, and interacts with a DSN scheduling environment to allocate tracks such that its reward signal is maximized. A comparison is made between an agent trained using Proximal Policy Optimization and its random, untrained counterpart. The results represent a proof-of-concept that, given a well-shaped reward signal, a deep RL agent can learn the complex heuristics used by experts to schedule the DSN. A trained agent can potentially be used to generate candidate schedules to bootstrap the scheduling process and thus reduce the turnaround cycle for DSN scheduling.

Wilson, Brian

Reinforcement Learning Approach to Flight Control Allocation with Distributed Electric Propulsion

The flight control system of the SUSAN Electrofan concept aircraft achieves attitude control using both conventional flight control surfaces and differential thrust through distributed electric propulsion (DEP) from sixteen wing-mounted electric engines. The introduction of eight pairs of wing fans for attitude control creates a highly actuated system. Such a system requires more sophisticated control to operate, especially in the presence of wingfan failures where the loss of a single wingfan can result in a thrust imbalance. This paper investigates the use of deep reinforcement learning (RL) using proximal policy optimization (PPO) to achieve attitude control through a combination of DEP and control surface deflections. First, the paper examines the aircraft undergoing a coordinated turn. Then, it examines the aircraft experiencing a wingfan failure during cruise conditions. It is shown that deep reinforcement learning can be a potential avenue for nonlinear flight control design.

Distributed Electric Propulsion

Optimal design and use of retry in fault tolerant real-time computer systems

A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.

Lee, Y. H.

Statistical methodologies for the control of dynamic remapping

Following an initial mapping of a problem onto a multiprocessor machine or computer network, system performance often deteriorates with time. In order to maintain high performance, it may be necessary to remap the problem. The decision to remap must take into account measurements of performance deterioration, the cost of remapping, and the estimated benefits achieved by remapping. We examine the tradeoff between the costs and the benefits of remapping two qualitatively different kinds of problems. One problem assumes that performance deteriorates gradually, the other assumes that performance deteriorates suddenly. We consider a variety of policies for governing when to remap. In order to evaluate these policies, statistical models of problem behaviors are developed. Simulation results are presented which compare simple policies with computationally expensive optimal decision policies; these results demonstrate that for each problem type, the proposed simple policies are effective and robust.

Saltz, J. H.

On the determination of optimal costly measurement strategies for linear stochastic systems.

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of prediction accuracy and accumulated observation cost is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. It is shown that the optimal measurement policy and the associated matched Kalman-type filter can be precomputed.

Athans, M.

A Decision-Theoretic Approach to Autonomous Planetary Rover Control

The report discusses the: Decentralized Control of Markov Decision Processes. Study the complexity of decentralized control of Markov decision processes, and develop algorithms for finding optimal control policies. Scheduling Contract Algorithms. Develop an optimal method for scheduling runs of a contract anytime algorithm (one that takes the deadline as input) in situations where the deadline is unknown, multiple problem instances must be solved, and a multi-processor machine is available. Planetary Rover Control as a Markov Decision Process.Use the Markov decision process framework to formalize and solve problems in planetary rover control. Adaptive Peer Selection. Use reinforcement learning to maximize the expected down-load speed for a client in a peer-to-peer file sharing system.

Zilberstein, Shlomo

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.

Using Markov Models of Fault Growth Physics and Environmental Stresses to Optimize Control Actions

A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.

Bole, Brian

Proof of quasi-adaptivity for the m-measurement feedback class of stochastic control policies

Bounds on expected performance are established which show that the m-measurement feedback (mM) policy for nonlinear stochastic control performs as well or better than the open-loop optimal control policy, and thus is quasi-adaptive in the sense of Witenhausen (1966). The chain of performance inequalities indicate a tendency for the mM policy performance to improve with increasing m. It is suggested that the present analytical method, based on the construction of artificial control sequences denoted as utility controls, can be used to establish performance bounds on other well-known policies, avoiding the extensive Monte Carlo simulations necessary in comparing stochastic control policies.

Bayard, David S.

DTS: Building custom, intelligent schedulers

DTS is a decision-theoretic scheduler, built on top of a flexible toolkit -- this paper focuses on how the toolkit might be reused in future NASA mission schedulers. The toolkit includes a user-customizable scheduling interface, and a 'Just-For-You' optimization engine. The customizable interface is built on two metaphors: objects and dynamic graphs. Objects help to structure problem specifications and related data, while dynamic graphs simplify the specification of graphical schedule editors (such as Gantt charts). The interface can be used with any 'back-end' scheduler, through dynamically-loaded code, interprocess communication, or a shared database. The 'Just-For-You' optimization engine includes user-specific utility functions, automatically compiled heuristic evaluations, and a postprocessing facility for enforcing scheduling policies. The optimization engine is based on BPS, the Bayesian Problem-Solver (1,2), which introduced a similar approach to solving single-agent and adversarial graph search problems.

Hansson, Othar

Combined optimal control and estimation.

Combined optimization problem, equivalent to dual control problem, considering determination of optimal control policies for plant under random disturbances, using iterative equations

CONTROL SYSTEM

Guidance analysis of the aeroglide plane change maneuver as a turning point problem

The development of guidance approximations for the atmospheric (aeroglide) portion of the minimum fuel, orbital plane change, trajectory optimization problem is described. Asymptotic methods are used to reduce the two point, boundary value, optimization problem to a turning point problem from the bank angle control. The turning point problem solution, which yields an approximate optimal control policy, is given in terms of parabolic cylinder functions, which are tabulated, and integral expressions, which must be numerically computed. Comparisons of the former, over their region of validity, with optimal control solutions show good qualitative agreement. Additional work and analysis is needed to compute the guidance approximation work.

Gracey, Christopher

Optimal startup control of a jacketed tubular reactor.

The optimal startup policy of a jacketed tubular reactor, in which a first-order, reversible, exothermic reaction takes place, is presented. A distributed maximum principle is presented for determining weak necessary conditions for optimality of a diffusional distributed parameter system. A numerical technique is developed for practical implementation of the distributed maximum principle. This involves the sequential solution of the state and adjoint equations, in conjunction with a functional gradient technique for iteratively improving the control function.

Hahn, D. R.

Stochastic ordering properties and optimal routing control for a class of finite capacity queueing systems

The problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities is considered. Stochastic ordering and weak majorization properties on critical performance measures are established by means of event-driven inductions. In particular, it is shown that the intuitive 'join the shortest non-full queue' (SNQ) policy is optimal with respect to an overall function that accounts for holding and blocking costs. Moreover, the buffer allocation problem is solved by proving the intuitive result that, for a fixed total buffer capacity, the optimal allocation scheme is the one in which the difference between the maximum and minimum queue capacities is minimized, i.e., becomes either 0 or 1.

Towsley, Don