Minimum-fuel Powered Descent in the Presence of Random Disturbances

Ridderhof, Jack; Tsiotras, Panagiotis

doi:10.2514/6.2019-0646

Cited by 21 publications

(19 citation statements)

References 15 publications

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“…In future work we plan to apply iCS to problems in entry, descent, and landing (EDL) with nonlinear dynamics, such as entry and powered descent [21]. Another extension to this work would be the addition of time-varying chance constraints that are satisfied for all time, rather than for each time, while not being overly conservative.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear Uncertainty Control with Iterative Covariance Steering

Ridderhof

Okamoto

Tsiotras

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An algorithm is developed to solve this problem by iteratively solving an approximate linearized problem as a convex program. This method, which we call iterative covariance steering (iCS), is numerically demonstrated by controlling a double integrator with quadratic drag force subject to additive Brownian noise while satisfying probabilistic path constraints.

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Section: Discussionmentioning

confidence: 99%

Nonlinear Uncertainty Control with Iterative Covariance Steering

Ridderhof

Okamoto

Tsiotras

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…Fortunately, there exist excellent monographs and survey papers on this topic; see [202,203,92,242,5,243,185]. The range of applications has also increased exponentially; we mention quality control, industrial manufacturing, vehicle path planning [205,206], image processing [23], computer graphics [226,227,229,230,231,150], machine learning [228,9,174], and econometrics [109], among others. We shall only briefly review some concepts and results that are relevant to the topics of this paper.…”

Section: Kantorovichmentioning

confidence: 99%

Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Chen¹,

Georgiou²,

Pavon³

2021

SIAM Rev.

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Schr\" odinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schr\" odinger's problem represents an early example of a fundamental inference method, the so-called maximum entropy method, having roots in Boltzmann's work and being developed in subsequent years by Jaynes, Burg, Dempster, and Csisz\' ar. The problem, known as the Schr\" odinger bridge problem (SBP) with ``uniform"" prior, was more recently recognized as a regularization of the Monge--Kantorovich optimal mass transport (OMT) problem, leading to effective computational schemes for the latter. Specifically, OMT with quadratic cost may be viewed as a zerotemperature limit of the problem posed by Schr\" odinger in the early 1930s. The latter amounts to minimization of Helmholtz's free energy over probability distributions that are constrained to possess two given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called Sinkhorn algorithm, which appears as a special case of an algorithm first studied in the more challenging continuous space setting by the French analyst Robert Fortet in 1938--1940 specifically for Schr\" odinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation of the optimal solution by iteratively solving the so-called Schr\" odinger system. Convergence of the iteration is guaranteed by contraction along the steps in suitable metrics, such as Hilbert's projective metric.In both the continuous as well as the discrete time and space settings, stochastic control provides a reformulation of and a context for the dynamic versions of general Schr\" odinger bridge problems and of their zero-temperature limit, the OMT problem. These problems, in turn, naturally lead to steering problems for flows of one-time marginals which represent a new paradigm for controlling uncertainty. The zero-temperature problem in the continuous-time and space setting turns out to be the celebrated Benamou--Brenier characterization of the McCann displacement interpolation flow in OMT. The formalism and techniques behind these control problems on flows of probability distributions have attracted significant attention in recent years as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, and network routing as well as in computer and data science. This multifaceted and versatile framework, intertwining SBP and OMT, provides the substrate for the historical and technical overview \ast

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“…This relaxation makes the terminal state less distributed than the target distribution. In many real-world applications [10] it may be preferable to achieve smaller uncertainty in the terminal state.…”

Section: Input-constrained Ocs Problemmentioning

confidence: 99%

“…Such a situation occurs in many real-world scenarios. For example, in aircraft [8] or spacecraft [10] control problems the control command values have physical restrictions such as minimum/maximum thrust.…”

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, input hard constraints have not been discussed in the framework of OCS, while input soft constraints have been investigated by several prior works. These include the incorporation of a maximum value of the expectation of quadratic functions of the control inputs [4,5], and the maximum probability of control constraint violation [10]. Our formulation of the input constraint is different than these approaches, in the sense that we directly impose hard constraints on the input.…”

Section: Introductionmentioning

confidence: 99%

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Input Hard Constrained Optimal Covariance Steering

Okamoto

Tsiotras

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We address the optimal covariance steering (OCS) problem for stochastic discrete linear systems with additive Gaussian noise under state chance constraints and input hard constraints. Because the system state can be unbounded due to the unbounded noise, the state constraints are formulated as probabilistic (chance) constraints, i.e., the maximum probability of constraint violation is constrained. In contrast, because it is hard to interpret the appropriate control action when the control command violates the constraints, probabilistically formulating the control constraints are difficult, and deterministic hard constraints are preferable. In this work we introduce an OCS approach subject to simultaneous state chance constraints and input hard constraints and validate the approach using numerical simulations.

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Minimum-fuel Powered Descent in the Presence of Random Disturbances

Cited by 21 publications

References 15 publications

Nonlinear Uncertainty Control with Iterative Covariance Steering

Nonlinear Uncertainty Control with Iterative Covariance Steering

Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schrödinger Bridge

Input Hard Constrained Optimal Covariance Steering

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