A Course in Robust Control Theory: A Convex Approach

By Geir E. Dullerud, Fernando Paganini. 2005

1,040 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ff5ba83274c9ee6b63d96dc90898ae3d7d69a075

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Citations in the corpus

Cyber–Physical Systems: A Perspective at the Centennial (2012, background): “This led to a very strong foundation of systems theory, with a thorough investigation of optimal control [28], stability [29], linear systems [30], nonlinear control [31], stochastic systems [32], adaptive control [33], robust control [34], infinite-dimensional systems [35], decentralized control of”
Deep learning for universal linear embeddings of nonlinear dynamics (2017, background): “Thus representing nonlinear dynamics in a linear framework is particularly appealing because of powerful and comprehensive techniques for the analysis and control of linear systems [12], which do not readily generalize to nonlinear systems.”
Data-driven discovery of Koopman eigenfunctions for control (2017, background): “Currently there is no overarching framework for nonlinear control as exists for linear systems [9], [10].”
Chaos as an intermittently forced linear system (2016, methodology): “The concept of observability in a linear dynamical system provides conditions for when the full-state of a system may be estimated from a time-history of measurements of the system, providing a rigorous foundation for dynamic estimation, such as the Kalman filter [46, 43, 100, 29, 91].”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, methodology): “Model-based control techniques, such as MPC [12] and optimal control [48, 15], are cornerstones of advanced process control, and are well-positioned to take advantage of the data-driven revolution.”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “However, it is well known that for linear control systems [59], [58], the high-dimensional state may be reconstructed with few sensors, if not a single sensor, by leveraging the time history in conjunction with a model of the dynamics, as exempliﬁed by the Kalman ﬁlter [61], [62].”
Learning omnidirectional path following using dimensionality reduction (2007, background): “For a general overview of robust control, see [31] and [9].”
Model reduction of interconnected linear systems (2009, background): “Even if the structure requirement Ĝ(s) ∈ StructG(s) in (6) is dropped, (6) is a nonconvex optimization problem; see [14].”
Optimization for machine learning (2010, methodology): “The Hoeffding race introduced by Maron and Moore (1993) is an algorithm based on discarding options which are likely to have smaller mean than the optimal one until only one option remains.”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, background): “An excellent treatment of robust control may be found in [93].”
Reinforcement learning in feedback control (2011, methodology): “To overcome the loss of controller quality by a poor system model identification, the research field of robust control (Dullerud 2000) exists explicitly to deal with uncertainty in the design.”
Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning (2021, background): “Robust control can be extended to nonlinear systems whose dynamics can be decomposed into a linear nominal model f̄ and a nonlinear function f̂ with known bound f̂ ∈ D (26).”
On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage (2006, unknown): “1 is where q j is the probability of choosing the j -th sensor while (cid:21) (cid:0) (cid:22) A j (cid:1) refers to the eigenvalue with the maximum magnitude of the unobservable part of A when the pair ( A; C j ) is put in the observable canonical form (Dullerud and Paganini 2000) .”
Implicit Deep Learning (2019, background): “rator (in continuous or discrete time) in place of the static nonlinear map ˚. The idea is also connected to the linearfractional representation (or, transformation, LFT) arising in uncertain systems [19], where now the linear operations actually represent a dynamic system (that is, the matrix Mis a”
On the Sample Complexity of Stability Constrained Imitation Learning (2021, methodology): “We note that the existence of solutions to this Lyapunov equation are guaranteed by continuity of the solution of the Lyapunov equation and that the solution to the DARE P? is the maximizing solution among symmetric solutions [37].”
Dynamical decoupling sequence construction as a filter-design problem (2010, background): “ ˚~ does not respond sensitively to . In control theory language, ˚~ is not very controllable by the noise input . In control theory there is a standard description of this sort of problem as follows [58]: consider a physical system with states described by a vector x undergoing linear dynamics and ”