Linearly Solvable Stochastic Optimal Control for Infinite-Dimensional Systems

Theodorou, Evangelos A.; Boutselis, George I.; Bakshi, Kaivalya

doi:10.1109/cdc.2018.8618948

Cited by 4 publications

(9 citation statements)

References 14 publications

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“…The optimality of L * is verified in [32]. The statistical physics interpretation of inequality Equation ( 7) is that maximization of entropy results in a reduction in the available energy.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 84%

“…More information can be found in Appendix B. Define the free energy of cost function J(X) with respect to the uncontrolled path measure L and temperature ρ ∈ R as follows [32]:…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…where "<<" denotes absolute continuity [32]. The relationship between free energy and relative entropy was extended to a Hilbert space formulation in [32].…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…where "<<" denotes absolute continuity [32]. The relationship between free energy and relative entropy was extended to a Hilbert space formulation in [32]. Based on the free energy and generalized entropy definitions, Equation (1) with temperature T = 1 ρ becomes the so-called Legendre transformation, and takes the following form:…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…Essentially, there exist two different points of view on decision making under uncertainty that overlap for fairly general classes of stochastic systems, as depicted in Figure 1. These connections are extended to infinite-dimensional spaces [32] (see also Appendix F) and are leveraged in this letter to develop practical algorithms for distributed and boundary control of stochastic fields. Specifically, we develop a generic framework for control of stochastic fields that are modeled as semi-linear SPDEs.…”

Section: Introduction and Related Workmentioning

confidence: 99%

See 4 more Smart Citations

Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems

Boutselis

Evans

Pereira

et al. 2021

Entropy

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Stochastic spatio-temporal processes are prevalent across domains ranging from the modeling of plasma, turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by describing them as evolutionary processes on Hilbert spaces, and in doing so, derives a framework for spatio-temporal manipulation from fundamental thermodynamic principles. This approach yields a variational optimization framework for controlling stochastic fields. The resulting scheme is applicable to a wide class of spatio-temporal processes and can be used for optimizing parameterized control policies. Our simulated experiments explore the application of two forms of this approach on four stochastic spatio-temporal processes, with results that suggest new perspectives and directions for studying stochastic control problems for spatio-temporal systems.

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Section: Preliminaries and Problem Formulationmentioning

confidence: 84%

“…More information can be found in Appendix B. Define the free energy of cost function J(X) with respect to the uncontrolled path measure L and temperature ρ ∈ R as follows [32]:…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…where "<<" denotes absolute continuity [32]. The relationship between free energy and relative entropy was extended to a Hilbert space formulation in [32].…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Section: Introduction and Related Workmentioning

confidence: 99%

See 3 more Smart Citations

Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems

Boutselis

Evans

Pereira

et al. 2021

Entropy

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Stochastic spatio-temporal optimization for control and co-design of systems in robotics and applied physics

2021

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Spatio-Temporal Stochastic Optimization: Theory and Applications to Optimal Control and Co-Design

Evans¹,

Kendall²,

Boutselis³

et al. 2020

Preprint

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There is a rising interest in Spatio-temporal systems described by Partial Differential Equations (PDEs) among the control community. Not only are these systems challenging to control, but the sizing and placement of their actuation is an NP-hard problem on its own. Recent methods either discretize the space before optimziation, or apply tools from linear systems theory under restrictive linearity assumptions. In this work we consider control and actuator placement as a coupled optimization problem, and derive an optimization algorithm on Hilbert spaces for nonlinear PDEs with an additive spatio-temporal description of white noise. We study first and second order systems and in doing so, extend several results to the case of second order PDEs. The described approach is based on variational optimization, and performs joint RL-type optimization of the feedback control law and the actuator design over episodes. We demonstrate the efficacy of the proposed approach with several simulated experiments on a variety of SPDEs.

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Linearly Solvable Stochastic Optimal Control for Infinite-Dimensional Systems

Cited by 4 publications

References 14 publications

Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems

Leveraging Stochasticity for Open Loop and Model Predictive Control of Spatio-Temporal Systems

Stochastic spatio-temporal optimization for control and co-design of systems in robotics and applied physics

Spatio-Temporal Stochastic Optimization: Theory and Applications to Optimal Control and Co-Design

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