Bounds on the reachable sets of nonlinear control systems

Scott, Joseph K.; Barton, Paul I.

doi:10.1016/j.automatica.2012.09.020

Cited by 90 publications

(98 citation statements)

References 23 publications

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“…In particular, the notion of differential hull can be seen as a special case of Theorem 1 in [2]. Similar results have been established in [10] and [11]. As regarding model reduction, Antoulas offers a substantial account of approximate techniques [12].…”

Section: Introductionsupporting

confidence: 50%

Approximate Reduction of Heterogenous Nonlinear Models With Differential Hulls

Tschaikowski

Tribastone

2016

IEEE Trans. Automat. Contr.

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Abstract-We present a model reduction technique for a class of nonlinear ordinary differential equation (ODE) models of heterogeneous systems, where heterogeneity is expressed in terms of classes of state variables having the same dynamics structurally, but which are characterized by distinct parameters. To this end, we first build a system of differential inequalities that provides lower and upper bounds for each original state variable, but such that it is homogeneous in its parameters. Then, we use two methods for exact aggregation of ODEs to exploit this homogeneity, yielding a smaller model of size independent of the number of heterogeneous classes. We apply this technique to two case studies: a multiclass queuing network and a model of epidemics spread.

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Section: Introductionsupporting

confidence: 50%

Approximate Reduction of Heterogenous Nonlinear Models With Differential Hulls

Tschaikowski

Tribastone

2016

IEEE Trans. Automat. Contr.

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“…The corresponding result with weak inequalities follows from a uniqueness argument, such as (local) Lipschitz-continuity of the ODE right-hand side [25,57]. The parameter-dependent case is also addressed in [57,62].…”

Section: Differential Inequalitiesmentioning

confidence: 99%

“…This method was later extended to propagate affine bounds [62] as well as a pair of convex and concave bounds [58,60] for the solutions of parametric nonlinear ODEs based on differential inequalities and (generalized) McCormick relaxations [41,59]. The refinement of reachable set enclosures by accounting for a priori or physical information about a given system was also investigated in [57,61]. Another way of computing pointwise-in-time, convex under-estimators and concave over-estimators using the α-BB approach [1,40] has been described in [13,49,50].…”

Section: Introductionmentioning

confidence: 99%

Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs

2014

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This paper presents a framework for constructing and analyzing enclosures of the reachable set of nonlinear ordinary differential equations (ODEs) using continuous-time setpropagation methods. The focus is on convex enclosures that can be characterized in terms of their support functions. A generalized differential inequality is introduced, whose solutions describe such support functions for a convex enclosure of the reachable set under mild conditions. It is shown that existing continuous-time bounding methods that are based on standard differential inequalities or ellipsoidal set propagation techniques can be recovered as special cases of this generalized differential inequality. A way of extending this approach for the construction of nonconvex enclosures is also described, which relies on Taylor models with convex remainder bounds. This unifying framework provides a means for analyzing the convergence properties of continuous-time enclosure methods. The enclosure techniques and convergence results are illustrated with numerical case studies throughout the paper, including a six-state dynamic model of anaerobic digestion.

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“…To improve the bounds within the branch-and-cut process, we compute differential inequalities as outlined in Scott and Barton (2013). This involves the solution of an auxiliary simulation problem using the expressions for _ x derived in the reading of the problem.…”

Section: Bound Propagation Based On Differential Inequalitiesmentioning

confidence: 99%