Decentralized Control of Linear Switched Nested Systems With $\ell_{2}$-Induced Norm Performance

Mishra, Anshuman; Langbort, Cédric; Dullerud, Geir E.

doi:10.1109/tcns.2015.2426753

Cited by 8 publications

(7 citation statements)

References 29 publications

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“…Now, we need a way to preserve the desired controller structure when applying Lemma 2. For this, we present the following lemma, which was proven in [21].…”

Section: B Elimination Lemmamentioning

confidence: 99%

“…We now use the factorization in (22) and corresponding change of variables to convert the inequalities in Lemma 6 to be linear in the new variables. (21). Then, the inequality ( 17) is equivalent to the following inequalities linear in variables…”

Section: Necessary Conditionsmentioning

confidence: 99%

“…Proof: Applying Lemma 20 in [21] to inequality (17), along with factorizations (22), leads to inequality (24).…”

Section: Necessary Conditionsmentioning

confidence: 99%

“…Proof: (⇐) Let there be {Z a i, , Z b i, , Z c i, } i∈J , ∈A L+H satisfying (26). We can then use relations in (21) to obtain corresponding positive-definite matrices {Z i, } i∈J , ∈A L+H . Now, using definitions (23) and the transformation…”

Section: B Uniform Performance Boundsmentioning

confidence: 99%

“…The results in [19] were further extended in [20] to allow the controller access to a finite number of future modes. The synthesis results for a decentralized controller for nested systems with finite memory were presented in [21]. The decentralized controller synthesis was extended to include access to finite future modes in [22], and path-dependent performance bounds were considered in [23]; these papers form the basis for the theoretical work presented here.…”

Section: Introductionmentioning

confidence: 99%

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Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

Jansch-Porto

Dullerud²

2022

IEEE Trans. Contr. Syst. Technol.

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In this article, we develop synthesis methods for decentralized control of switched systems with mode-dependent (more generally, path-dependent) performance specifications and apply them to an experimental vehicular testbed. This specification flexibility is important when achievable system performance varies greatly between modes, as a mode-independent specification will lead to designs that do not extract all the system performance available in each mode. More specifically, under these specifications, we derive exact conditions for the existence of block lower triangular path-dependent controllers with 2 -induced-norm performance. The synthesis conditions are given in the form of a semidefinite program (SDP) for both uniform and path-dependent performance bounds. Building on previous results, we also introduce a basis-based approach that allows computational complexity to be more carefully controlled. We apply the resulting design methods to a group of miniature quadcopters, illustrating different features of the presented methods, along with some practical engineering considerations.

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“…Now, we need a way to preserve the desired controller structure when applying Lemma 2. For this, we present the following lemma, which was proven in [21].…”

Section: B Elimination Lemmamentioning

confidence: 99%

Section: Necessary Conditionsmentioning

confidence: 99%

“…Proof: Applying Lemma 20 in [21] to inequality (17), along with factorizations (22), leads to inequality (24).…”

Section: Necessary Conditionsmentioning

confidence: 99%

Section: B Uniform Performance Boundsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

Jansch-Porto

Dullerud²

2022

IEEE Trans. Contr. Syst. Technol.

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Stability analysis and output-feedback synthesis of hybrid systems affected by piecewise constant parameters via dynamic resetting scalings

Holicki

Scherer

2019

Nonlinear Analysis: Hybrid Systems

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Modeling and maximizing power in wind turbine arrays

Buccafusca

Beck

Dullerud

2017

2017 IEEE Conference on Control Technology and Applications (CCTA)

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This work considers a specific application domain, that of wind turbine arrays, and explores algorithms for determining individual axial induction factors that optimize overall energy extraction. Large wind turbine arrays, or wind farms, can be viewed as large coupled networks, for which the application of traditional optimization techniques are impractical. A brief discussion on wind farm models and traditional optimization approaches leads us to a spatial dynamic programming approach to maximize power extraction under the condition of uniform wind. This differs from prior work in which only a dynamic programming approach for a more restrictive near-field model has been analyzed. In our work, we propose an algorithm that leads to solutions for both the near-field and far-field models. Simulation results are discussed, which demonstrate our algorithm provides improved performance compared to prior work using only near-field approaches.

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Decentralized Control of Linear Switched Nested Systems With $\ell_{2}$-Induced Norm Performance

Cited by 8 publications

References 29 publications

Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

Decentralized Control of Switched Systems With Receding Horizon Modal Information and Path-Dependent Performance Specifications: Theory and an Application

Stability analysis and output-feedback synthesis of hybrid systems affected by piecewise constant parameters via dynamic resetting scalings

Modeling and maximizing power in wind turbine arrays

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