| 1. |
- Bergeling, Carolina, et al.
(författare)
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Closed-form H-infinity optimal control for a class of infinite-dimensional systems
- 2020
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098. ; 117
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Tidskriftsartikel (refereegranskat)abstract
- H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.
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| 2. |
- Pates, Richard, et al.
(författare)
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On the Optimal Control of Relaxation Systems
- 2020
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Ingår i: 2019 IEEE 58th Conference on Decision and Control, CDC 2019. - 0743-1546 .- 2576-2370. - 9781728113999 - 9781728113982 ; 2019-December, s. 6068-6073
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Konferensbidrag (refereegranskat)abstract
- The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple H-infinity type optimal control problems. The resulting controllers are also relaxation systems, and often sparse. This makes them ideal candidates for applications in large-scale problems, which we demonstrate by designing simple, sparse, electrical circuits to optimally control large inductive networks and to solve linear regression problems.
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| 3. |
- RYU, ERNEST K., et al.
(författare)
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Operator splitting performance estimation : Tight contraction factors and optimal parameter selection
- 2020
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Ingår i: SIAM Journal on Optimization. - 1052-6234. ; 30:3, s. 2251-2271
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Tidskriftsartikel (refereegranskat)abstract
- We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computerassisted proofs to prove tight analytical contraction factors for Douglas-Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs.
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