Index

A

A (mpt4py.AffineSet property) (mpt4py.base.HData attribute) (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.solvers.qp.QuadraticProgram attribute) add() (mpt4py.ConvexSetUnion method) (mpt4py.geometry.union.ConvexSetUnion method) (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.geometry.union.union.ConvexSetUnion method) (mpt4py.PolyUnion method) add_function() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) Ae (mpt4py.base.HData attribute) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.solvers.qp.QuadraticProgram attribute)

affine_dimension (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) affine_hull (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property) affine_hull() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) affine_map() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.zonotope.Zonotope method) (mpt4py.Polyhedron method) AffineFunction (class in mpt4py.functions.affine_function) AffineSet (class in mpt4py) Ath (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) (mpt4py.solvers.qp.QuadraticProgram attribute)

B

b (mpt4py.AffineSet property) (mpt4py.base.HData attribute) B (mpt4py.controllers.mpc_controller.MPCController property) b (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.solvers.qp.QuadraticProgram attribute) Basis (class in mpt4py.util) basis (mpt4py.AffineSet property)

be (mpt4py.base.HData attribute) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.solvers.qp.QuadraticProgram attribute) bounding_box() (mpt4py.geometry.polyhedron.Polyhedron static method) (mpt4py.Polyhedron static method) bth (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) (mpt4py.solvers.qp.QuadraticProgram attribute)

C

c (mpt4py.geometry.zonotope.Zonotope property) (mpt4py.solvers.qp.QuadraticProgram attribute) cartesian_product() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) center (mpt4py.geometry.zonotope.Zonotope property) cheby_center() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) codimension (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) coefficients (mpt4py.AffineSet property) combined_points (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) contains() (mpt4py.ConvexSetUnion method) (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.union.ConvexSetUnion method) (mpt4py.geometry.union.union.ConvexSetUnion method) (mpt4py.Polyhedron method)

control_invariant_set() (mpt4py.systems.lti_system.LTISystem method) ControllerBase (class in mpt4py.controllers.base_controller) convex_hull() (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.PolyUnion method) ConvexSet (class in mpt4py) (class in mpt4py.geometry.convexset) ConvexSetUnion (class in mpt4py) (class in mpt4py.geometry.union) (class in mpt4py.geometry.union.union) cost() (mpt4py.systems.system_base.SystemBase method)

D

d (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) (mpt4py.solvers.qp.QuadraticProgram attribute) dehomogenize (mpt4py.base.HData property) (mpt4py.base.VData property) dim (mpt4py.AffineSet property) (mpt4py.base.HData property) (mpt4py.base.VData property) (mpt4py.ConvexSet property) (mpt4py.ConvexSetUnion property) (mpt4py.Ellipsoid property) (mpt4py.geometry.convexset.ConvexSet property) (mpt4py.geometry.convexset.Ellipsoid property) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.geometry.union.ConvexSetUnion property) (mpt4py.geometry.union.union.ConvexSetUnion property) (mpt4py.geometry.zonotope.Zonotope property) (mpt4py.Polyhedron property)

DimMismatchError, [1] discretize() (mpt4py.systems.lti_system.LTISystem method) (mpt4py.systems.system_base.SystemBase method) distance() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) dynamics() (mpt4py.systems.system_base.SystemBase method)

E

Ellipsoid (class in mpt4py) (class in mpt4py.geometry.convexset) empty_set() (mpt4py.geometry.polyhedron.Polyhedron class method) (mpt4py.Polyhedron class method) evaluate() (mpt4py.controllers.base_controller.ControllerBase method) (mpt4py.controllers.mpc_controller.MPCController method) (mpt4py.functions.function_base.FunctionBase method)

extreme() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) extreme_points (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property) extreme_rays (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property)

F

F (mpt4py.functions.affine_function.AffineFunction property) f (mpt4py.solvers.qp.QuadraticProgram attribute) facet_eqns (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) facets (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) fplot() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.Polyhedron method) (mpt4py.PolyUnion method)

from_basis() (mpt4py.AffineSet static method) from_bounds() (mpt4py.geometry.polyhedron.Polyhedron class method) (mpt4py.Polyhedron class method) from_Hrep() (mpt4py.geometry.polyhedron.Polyhedron class method) (mpt4py.Polyhedron class method) from_Vrep() (mpt4py.geometry.polyhedron.Polyhedron class method) (mpt4py.Polyhedron class method) FunctionBase (class in mpt4py.functions.function_base)

G

g (mpt4py.functions.affine_function.AffineFunction property) G (mpt4py.geometry.zonotope.Zonotope property) generators (mpt4py.geometry.zonotope.Zonotope property) GeometryError, [1] get_facet() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) get_function() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method)

get_lambda (mpt4py.functions.function_base.FunctionBase property) get_plotter() (in module mpt4py.geometry.visualization) get_tolerance() (in module mpt4py) (in module mpt4py.tolerances) gradient() (mpt4py.functions.affine_function.AffineFunction method) (mpt4py.functions.function_base.FunctionBase method) (mpt4py.functions.quadratic_function.QuadraticFunction method)

H

H (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.solvers.qp.QuadraticProgram attribute) has_function() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) hasHrep (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) hasVrep (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) hausdorff_distance() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) HData (class in mpt4py.base)

He (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) Hexagon (class in mpt4py) homogenize (mpt4py.base.HData property) (mpt4py.base.VData property) homogenize() (mpt4py.AffineSet method) (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) Hrep (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) hull (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) Hyperplane (class in mpt4py)

I

incidence_map (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) indices (mpt4py.util.Basis property) InfeasibleError, [1] input_constraints (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property) interior_point() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) intersect() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) inv_affine_map() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) invariant_set() (mpt4py.systems.lti_system.LTISystem method) is_adjacent() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) is_almost_complementary() (mpt4py.util.Basis method) is_bounded (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.geometry.union.PolyUnion property) (mpt4py.geometry.union.polyunion.PolyUnion property) (mpt4py.Polyhedron property) (mpt4py.PolyUnion property) (mpt4py.Simplex property) is_complementary() (mpt4py.util.Basis method) is_cone (mpt4py.base.HData property) (mpt4py.base.VData property) is_connected (mpt4py.geometry.union.PolyUnion property) (mpt4py.geometry.union.polyunion.PolyUnion property) (mpt4py.PolyUnion property)

is_convex (mpt4py.geometry.union.PolyUnion property) (mpt4py.geometry.union.polyunion.PolyUnion property) (mpt4py.PolyUnion property) is_empty (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) is_feasible() (mpt4py.util.Basis method) is_full_dim (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.geometry.union.PolyUnion property) (mpt4py.geometry.union.polyunion.PolyUnion property) (mpt4py.Polyhedron property) (mpt4py.PolyUnion property) is_lexico_positive() (in module mpt4py.util) is_minimal (mpt4py.base.HData attribute) (mpt4py.base.VData attribute) is_neighbor() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) is_overlapping (mpt4py.geometry.union.PolyUnion property) (mpt4py.geometry.union.polyunion.PolyUnion property) (mpt4py.PolyUnion property) is_p_matrix() (in module mpt4py.util) is_parametric (mpt4py.solvers.lcp.LinearComplementarityProblem property) (mpt4py.solvers.qp.QuadraticProgram property) is_positive_definite() (in module mpt4py.util) is_positive_semidefinite() (in module mpt4py.util) is_symmetric() (in module mpt4py.util)

L

lb (mpt4py.solvers.qp.QuadraticProgram attribute) LCP (in module mpt4py.solvers.lcp) lcp_solve() (in module mpt4py.solvers) lexico_argmax() (in module mpt4py.util) lexico_argmin() (in module mpt4py.util) lift() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method)

LinearComplementarityProblem (class in mpt4py.solvers.lcp) list_functions() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) lqr_gain (mpt4py.systems.lti_system.LTISystem property) lqr_set (mpt4py.systems.lti_system.LTISystem property) LTISystem (class in mpt4py.systems.lti_system)

M

M (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) m (mpt4py.solvers.qp.QuadraticProgram attribute) MatplotlibPlotter (class in mpt4py.geometry.visualization) (class in mpt4py.geometry.visualization.plot_matplotlib) me (mpt4py.solvers.qp.QuadraticProgram attribute) merge() (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.PolyUnion method) minHrep() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) minimal_representation() (mpt4py.AffineSet method) minkowski_sum() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.zonotope.Zonotope method) (mpt4py.Polyhedron method) minVrep() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) module mpt4py mpt4py.base mpt4py.controllers.base_controller mpt4py.controllers.mpc_controller mpt4py.exceptions mpt4py.functions mpt4py.functions.affine_function mpt4py.functions.function_base mpt4py.functions.quadratic_function mpt4py.geometry.union mpt4py.geometry.union.polyunion mpt4py.geometry.union.union mpt4py.geometry.visualization mpt4py.geometry.visualization.plot mpt4py.geometry.visualization.plot_matplotlib mpt4py.geometry.visualization.plot_pyvista mpt4py.solvers.lcp mpt4py.solvers.qp mpt4py.systems.lti_system mpt4py.systems.system_base mpt4py.tolerances mpt4py.util MPCController (class in mpt4py.controllers.mpc_controller) mpt4py module

mpt4py.base module mpt4py.controllers.base_controller module mpt4py.controllers.mpc_controller module mpt4py.exceptions module mpt4py.functions module mpt4py.functions.affine_function module mpt4py.functions.function_base module mpt4py.functions.quadratic_function module mpt4py.geometry.union module mpt4py.geometry.union.polyunion module mpt4py.geometry.union.union module mpt4py.geometry.visualization module mpt4py.geometry.visualization.plot module mpt4py.geometry.visualization.plot_matplotlib module mpt4py.geometry.visualization.plot_pyvista module mpt4py.solvers.lcp module mpt4py.solvers.qp module mpt4py.systems.lti_system module mpt4py.systems.system_base module mpt4py.tolerances module mpt4py.util module

N

N (mpt4py.controllers.mpc_controller.MPCController property) n (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) (mpt4py.solvers.qp.QuadraticProgram attribute) (mpt4py.util.Basis property) new_figure() (in module mpt4py) (in module mpt4py.geometry.visualization) normal (mpt4py.Hyperplane property) nu (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.system_base.SystemBase property) num_eq (mpt4py.solvers.qp.QuadraticProgram property) num_extreme_rays (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property)

num_facets (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property) num_ineq (mpt4py.solvers.qp.QuadraticProgram property) num_sets (mpt4py.ConvexSetUnion property) (mpt4py.geometry.union.ConvexSetUnion property) (mpt4py.geometry.union.union.ConvexSetUnion property) num_vertices (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property) nx (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.system_base.SystemBase property) ny (mpt4py.systems.system_base.SystemBase property)

O

offset (mpt4py.Hyperplane property)

P

pB (mpt4py.solvers.qp.QuadraticProgram attribute) pC (mpt4py.solvers.qp.QuadraticProgram attribute) pE (mpt4py.solvers.qp.QuadraticProgram attribute) pF (mpt4py.solvers.qp.QuadraticProgram attribute) plot() (mpt4py.Ellipsoid method) (mpt4py.geometry.convexset.Ellipsoid method) (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.geometry.visualization.plot.PlotterProtocol method) (mpt4py.geometry.visualization.PlotterProtocol method) (mpt4py.Polyhedron method) (mpt4py.PolyUnion method) plot_convexhull() (mpt4py.geometry.visualization.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot.PlotterProtocol method) (mpt4py.geometry.visualization.plot_matplotlib.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot_pyvista.PyvistaPlotter method) (mpt4py.geometry.visualization.PlotterProtocol method) (mpt4py.geometry.visualization.PyvistaPlotter method) plot_ellipsoid() (mpt4py.geometry.visualization.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot.PlotterProtocol method) (mpt4py.geometry.visualization.plot_matplotlib.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot_pyvista.PyvistaPlotter method) (mpt4py.geometry.visualization.PlotterProtocol method) (mpt4py.geometry.visualization.PyvistaPlotter method) PlotterProtocol (class in mpt4py.geometry.visualization) (class in mpt4py.geometry.visualization.plot)

points (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) PolyhedralPlottingData (class in mpt4py.geometry.visualization) (class in mpt4py.geometry.visualization.plot) Polyhedron (class in mpt4py) (class in mpt4py.geometry.polyhedron) PolyUnion (class in mpt4py) (class in mpt4py.geometry.union) (class in mpt4py.geometry.union.polyunion) pontryagin_difference() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) PqpSolution (class in mpt4py.solvers.qp) preprocess() (mpt4py.base.HData method) (mpt4py.base.VData method) print_tolerances() (in module mpt4py) (in module mpt4py.tolerances) problem_type (mpt4py.solvers.qp.QuadraticProgram attribute) project() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) projection() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.geometry.zonotope.Zonotope method) (mpt4py.Polyhedron method) pY (mpt4py.solvers.qp.QuadraticProgram attribute) PyvistaPlotter (class in mpt4py.geometry.visualization) (class in mpt4py.geometry.visualization.plot_pyvista)

Q

Q (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) q (mpt4py.solvers.lcp.LinearComplementarityProblem attribute) Q (mpt4py.systems.lti_system.LTISystem property) Qf (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property)

QP (in module mpt4py.solvers.qp) qp2lcp() (mpt4py.solvers.qp.QuadraticProgram method) QuadraticFunction (class in mpt4py.functions.quadratic_function) QuadraticProgram (class in mpt4py.solvers.qp)

R

R (mpt4py.base.VData attribute) (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) (mpt4py.systems.lti_system.LTISystem property) range_space() (in module mpt4py.util) ray_length (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute) rays (mpt4py.geometry.visualization.plot.PolyhedralPlottingData attribute) (mpt4py.geometry.visualization.PolyhedralPlottingData attribute)

regions (mpt4py.solvers.qp.PqpSolution attribute) remove() (mpt4py.ConvexSetUnion method) (mpt4py.geometry.union.ConvexSetUnion method) (mpt4py.geometry.union.PolyUnion method) (mpt4py.geometry.union.polyunion.PolyUnion method) (mpt4py.geometry.union.union.ConvexSetUnion method) (mpt4py.PolyUnion method) remove_all_functions() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) remove_function() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method)

S

sample() (mpt4py.geometry.polyhedron.Polyhedron method) (mpt4py.Polyhedron method) seperate() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) set_tolerance() (in module mpt4py) (in module mpt4py.tolerances) shoot() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) show() (mpt4py.geometry.visualization.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot.PlotterProtocol method) (mpt4py.geometry.visualization.plot_matplotlib.MatplotlibPlotter method) (mpt4py.geometry.visualization.plot_pyvista.PyvistaPlotter method) (mpt4py.geometry.visualization.PlotterProtocol method) (mpt4py.geometry.visualization.PyvistaPlotter method)

Simplex (class in mpt4py) singleton() (mpt4py.geometry.polyhedron.Polyhedron class method) (mpt4py.Polyhedron class method) solve() (mpt4py.solvers.lcp.LinearComplementarityProblem method) (mpt4py.solvers.qp.QuadraticProgram method) solve_for_param() (mpt4py.solvers.lcp.LinearComplementarityProblem method) (mpt4py.solvers.qp.QuadraticProgram method) solve_pqp_with_ppopt() (in module mpt4py.solvers.qp) state_constraints (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property) status (mpt4py.solvers.qp.PqpSolution attribute) support() (mpt4py.ConvexSet method) (mpt4py.geometry.convexset.ConvexSet method) SystemBase (class in mpt4py.systems.system_base)

T

terminal_constraints (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property)

to_explicit() (mpt4py.controllers.mpc_controller.MPCController method)

U

u_opt_traj (mpt4py.controllers.mpc_controller.MPCController property) u_ref (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property)

ub (mpt4py.solvers.qp.QuadraticProgram attribute) UnboundedError, [1]

V

V (mpt4py.base.VData attribute) (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) VData (class in mpt4py.base) vertices (mpt4py.geometry.visualization.plot.PolyhedralPlottingData property) (mpt4py.geometry.visualization.PolyhedralPlottingData property)

volume (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property) Vrep (mpt4py.geometry.polyhedron.Polyhedron property) (mpt4py.Polyhedron property)

X

x0 (mpt4py.AffineSet property) x_opt_traj (mpt4py.controllers.mpc_controller.MPCController property)

x_ref (mpt4py.controllers.mpc_controller.MPCController property) (mpt4py.systems.lti_system.LTISystem property)

Z

Zonotope (class in mpt4py.geometry.zonotope)