Efficient polyhedral enclosures for the reachable set of nonlinear control systems

DOI10.1007/s00498-015-0153-2zbMath1338.93064OpenAlexW2303451770MaRDI QIDQ276023

Paul I. Barton, Stuart M. Harwood

Publication date: 26 April 2016

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1721.1/103782

zbMATH Keywords

linear programmingreachabilitycontrol systemsaffine relaxations

Mathematics Subject Classification ID

Linear programming (90C05) Nonlinear systems in control theory (93C10) Attainable sets, reachability (93B03) Control/observation systems governed by ordinary differential equations (93C15)

Related Items

Tight reachability bounds for constrained nonlinear systems using mean value differential inequalities ⋮ Global dynamic optimization using edge-concave underestimator ⋮ A higher order method for input-affine uncertain systems ⋮ Sensitivity Analysis of Uncertain Dynamic Systems Using Set-Valued Integration ⋮ Convergence-order analysis for differential-inequalities-based bounds and relaxations of the solutions of ODEs ⋮ Exploiting nonlinear invariants and path constraints to achieve tighter reachable set enclosures using differential inequalities ⋮ Semidefinite Approximations of Reachable Sets for Discrete-time Polynomial Systems ⋮ Optimization-based convex relaxations for nonconvex parametric systems of ordinary differential equations

Uses Software

• SUNDIALS
• CPLEX
• libMC
• DFBAlab

Cites Work

• SUNDIALS
• Efficient solution of ordinary differential equations with a parametric lexicographic linear program embedded
• Improved relaxations for the parametric solutions of ODEs using differential inequalities
• Computing reachable sets for uncertain nonlinear hybrid systems using interval constraint-propagation techniques
• A Lohner-type algorithm for control systems and ordinary differential inclusions
• Generalized inverses. Theory and applications.
• Bounds on the reachable sets of nonlinear control systems
• Guaranteed nonlinear state estimator for cooperative systems
• Global optimization with nonlinear ordinary differential equations
• Validated solutions of initial value problems for parametric ODEs
• Nonlinear convex and concave relaxations for the solutions of parametric ODEs
• McCormick-Based Relaxations of Algorithms
• Reachability Analysis of Hybrid Systems Using Support Functions
• On the continuity of the value of a linear program and of related polyhedral-valued multifunctions
• Interval Methods for Systems of Equations
• Difference Methods for Differential Inclusions: A Survey
• Reachability Analysis Using Polygonal Projections
• Bounds on reachable sets using ordinary differential equations with linear programs embedded
• Lipschitz Continuity of Solutions of Linear Inequalities, Programs and Complementarity Problems
• Ordinary Differential Equations in Theory and Practice
• A Hybrid Bounding Method for Computing an Over-Approximation for the Reachable Set of Uncertain Nonlinear Systems
• Computational techniques for hybrid system verification
• A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
• Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations
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