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A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics with constant diffusion coefficient is considered. A fundamental solution form is obtained where the same solution can be used for a limited variety of terminal costs without re-solution of the problem. One may convert this fundamental solution form from a stochastic control problem form to a deterministic control problem form. This yields an equivalence between certain second-order (in space) Hamilton-Jacobi partial differential equations (HJ PDEs) and associated first-order HJ PDEs. This reformulation has substantial numerical implications.
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Distributed Control of Thermostatically Controlled Loads: Kullback-Leibler Optimal Control in Continuous Time
The paper develops distributed control techniques to obtain grid services from flexible loads. The Individual Perspective Design (IPD) for local (load level) control is extended to piecewise deterministic and diffusion models for thermostatically controlled load models.The IPD design is formulated as an infinite horizon average reward optimal control problem, in which the reward function contains a term that uses relative entropy rate to model deviation from nominal dynamics. In the piecewise deterministic model, the optimal solution is obtained via the solution to an eigenfunction problem, similar to what is obtained in prior work. For a jump diffusion model this simple structure is absent. The structure for the optimal solution is obtained, which suggests an ODE technique for computation that is likely far more efficient than policy- or value-iteration.
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- Award ID(s):
- 1646229
- PAR ID:
- 10211833
- Date Published:
- Journal Name:
- Conference on Decision and Control
- Page Range / eLocation ID:
- 7258 to 7265
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A class of nonlinear, stochastic staticization control problems (including minimization problems with smooth, convex, coercive payoffs) driven by diffusion dynamics and constant diffusion coefficient is considered. Using dynamic programming and tools from static duality, a fundamental solution form is obtained where the same solution can be used for a variety of terminal costs without re-solution of the problem. Further, this fundamental solution takes the form of a deterministic control problem rather than a stochastic control problem.more » « less
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We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding non-local path-dependent Hamilton-Jacobi-Bellman equation. This is the first well-posedness result for nonsmooth solutions of fully nonlinear non-local path-dependent partial differential equations.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC40024.2019.9029603
