Set-theoretic methods in control

By Franco Blanchini, S. Miani. 2007

1,548 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/441ab0498724485f289bcbfd35fcd31f6c2413b5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

In Artificial Intelligence

In Control and Systems Engineering

Citations in the corpus

Optimization of linear systems subject to bounded exogenous disturbances: The invariant ellipsoid technique (2011, background): “Blanchini and the recent monograph [27] by F.”
NMPC without terminal constraints (2012, methodology): “, Blanchini [1999], Blanchini and Miani [2008] and the references therein) and more specifically in MPC. Some variants of MPC (like, e.g., the so called tube based MPC method, see Langson et al. [2004]) even rely on the explicit construction of invariant sets.”
Reference and command governors for systems with constraints: A survey on theory and applications (2017, background): “exploits state feedback, prediction, optimization, and set-invariance arguments [22, 26] to ensure that modifications of the command are performed only when necessary to avoid compromising system performance.”
Robustness of Control Barrier Functions for Safety Critical Control (2016, methodology): “As in Dai et al. (2013), Kong et al.”
Review on computational methods for Lyapunov functions (2015, background): “Blanchini and Miani published a book 2008 [38], where they treat polyhedral Lyapunov functions.”
Discrete‐time control for switched positive systems with application to mitigating viral escape (2011, methodology): “This can be done by applying established dynamic programming methods as follows (see [35] for details).”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “…the synthesis and implementation of explicit model predictive control (MPC) for linear time invariant or piecewise affine systems, the construction of maximal invariant sets or Lyapunov functions for piecewise affine systems, etc (see, e.g., Kurzhanski and Valyi, 1997; Blanchini and Miani, 2008).”
Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics (2014, background): “termed the pointwise min-norm control law [12], [9], [33].”
Predictive Control for Linear and Hybrid Systems (2017, methodology): “An extensive treatment of robust invariant sets can be found in [57, 58, 51, 59].”
Finite-time regional verification of stochastic non-linear systems (2011, background): “2011), there is relatively little work on guaranteeing that these systems can achieve their goals in the presence of unbounded uncertainty (there is substantial work in the case of bounded uncertainty, for instance in the literature on robust constrained control (Blanchini and Miani 2008; Rawlings a”
Output feedback model predictive control of uncertain norm‐bounded linear systems (2011, background): “satisfies the following requirements: • Quadratic stability in the absence of disturbances and input/state constraints; • Confinement of the regulated state trajectory inside a Robust Positive Invariant set (see [17]) in the presence of input/state constraints, bounded disturbances and initial state”
Control Barrier Function Based Quadratic Programs for Safety Critical Systems (2016, positive): “For any r ≥ 0 , the set Using the compactness property stated above and the continuity of L f h , α is a well deﬁned, non-decreasing function on By Nagumo’s theorem [44], [45], the invariance of C is equivalent to which implies that α (0) ≤ 0 .”
Constrained zonotopes: A new tool for set-based estimation and fault detection (2016, background): “Set-based estimators based on convex polytopes have also been extensively developed (Blanchini & Miani, 2008; Shamma & Tu, 1999; Walter & Piet-Lahanier, 1989).”