Infinite dimensional control of doubly stochastic Jump Diffusions

Bakshi, Kaivalya; Theodorou, Evangelos A.

doi:10.1109/cdc.2016.7798421

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…Recall the terminal conditions for the value function (43) and for optimal costate function ( 17) implies for all p(T ) satisfying the conditions (T1) through (T4)…”

Section: Dpp For the Infinite Dimensional Value Function And Relation...mentioning

confidence: 99%

“…Direct application would require generating samples over the entire time horizon starting from each space time grid point. Instead, we use an iteratively backpropagated costate (IBC) algorithm [43], the key ingredient for which is derived below. By Dynkin's formula, Theorem 7.1, chapter 7 of [15] for QMJD process (1), applied to π(t, x) ∈ C 1,2 c ([0, T ] × R nx ) which satisfies ( 16), (17)…”

Section: Sampling Based Algorithm For Pdf Control Of Qmjd Processesmentioning

confidence: 99%

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Open-loop Deterministic Density Control of Marked Jump Diffusions

Bakshi,

Theodorou

2020

Preprint

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The standard practice in modeling dynamics and optimal control of a large population, ensemble, multi-agent system represented by it's continuum density, is to model individual decision making using local feedback information. In comparison to a closed-loop optimal control scheme, an open-loop strategy, in which a centralized controller broadcasts identical control signals to the ensemble of agents, mitigates the computational and infrastructure requirements for such systems. This work considers the open-loop, deterministic and optimal control synthesis for the density control of agents governed by marked jump diffusion stochastic diffusion equations. The density evolves according to a forward-intime Chapman-Kolmogorov partial integro-differential equation and the necessary optimality conditions are obtained using the infinite dimensional minimum principle (IDMP). We establish the relationship between the IDMP and the dynamic programming principle as well as the IDMP and stochastic dynamic programming for the synthesized controller. Using the linear Feynman-Kac lemma, a sampling-based algorithm to compute the control is presented and demonstrated for agent dynamics with non-affine and nonlinear drift as well as noise terms.

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“…Recall the terminal conditions for the value function (43) and for optimal costate function ( 17) implies for all p(T ) satisfying the conditions (T1) through (T4)…”

Section: Dpp For the Infinite Dimensional Value Function And Relation...mentioning

confidence: 99%

Section: Sampling Based Algorithm For Pdf Control Of Qmjd Processesmentioning

confidence: 99%

Open-loop Deterministic Density Control of Marked Jump Diffusions

Bakshi,

Theodorou

2020

Preprint

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“…Dynamics and control of multi-agent populations consisting of a large number of identical and non-cooperative agents are of interest in various applications including robotic swarms, macro-economics, traffic and neuroscience. Prior works on optimal open-loop or closed-loop ensemble (broadcast) control consider several copies of a particular deterministic [1] or stochastic ( [2], [3], [4]) systems and have applications in quantum control [5] and neuroscience [6]. A standard idea in engineering, economics and biology is regulation using local feedback information, which is used to model decision making in large-size populations of rational agents with limited information.…”

Section: Introductionmentioning

confidence: 99%

Schrödinger Approach to Optimal Control of Large-Size Populations

Bakshi,

Fan,

Theodorou

2018

Preprint

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Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the problem of designing mean-field type optimal state-feedback controllers which guarantee closed-loop stability of the stationary density of such agents with nonlinear Langevin dynamics, under the action of their individual steady state controls.We represent the corresponding optimality system which consists of coupled forward-backward PDEs as decoupled Schrödinger equations, by introducing a novel variable transform. Spectral properties of the Schrödinger operator which underlie the stability analysis are used to obtain explicit control design constraints, in the case that the agents do not interact explicitly via density dependent dynamics or cost function. Our interpretation of the Schrödinger potential as the cost function of a closely related optimal control problem motivates a quadrature based algorithm to compute the finite time optimal control 1 . We show the deep connection between the nonlinear Schrödinger equation and Mean Field Games for agents with nonlinear Langevin dynamics and explicit interactions.

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Global inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes

Duc¹

2021

Robotica

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This paper formulates and solves a new problem of global practical inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes with unknown characteristics. The control design is based on a new inverse optimal control design for nonlinear systems driven by Lévy processes and ensures global practical exponential stability almost surely and in the pth moment for the path-tracking errors. Moreover, it minimizes cost function that penalizes tracking errors and control torques without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jaccobi–Isaacs equation.

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Infinite dimensional control of doubly stochastic Jump Diffusions

Cited by 6 publications

References 18 publications

Open-loop Deterministic Density Control of Marked Jump Diffusions

Open-loop Deterministic Density Control of Marked Jump Diffusions

Schrödinger Approach to Optimal Control of Large-Size Populations

Global inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes

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