Given the initial state x0 and a list of inputs, simulates the PWA dynamics. If the couple (x(t), u(t)) goes out of the domains D_i r

Simulates the system starting from the state x0 for N steps in closed loop with the feedback law u = K x. Arguments --------

Solves the mpqp (condensed optimal control problem) explicitly. Returns ---------- instance of ExplicitSolution

Numeric value of the optimal value function at the point x. Arguments ---------- x : numpy.ndarray Point

Initilizes the controller. Arguments ---------- S : instance of LinerSystem Linear system to be controll

Initilizes the controller. Arguments ---------- S : instance of PieceWiseAffineSystem PWA system to be co

Instantiates the polyhedron. Arguments ---------- A : numpy.ndarray Left-hand side of the inequalities.

Instantiates the parametric mpQP. Arguments ---------- H : dict of numpy.ndarray Blocks of the quaratic

Instatiates the critical region. Arguments ---------- active_set : list of int List of the indices of th

Stores the set of critical regions. Arguments ---------- critical_regions : list of intances of CriticalRegion

Initializes the mpMIQP. Arguments ----------- H : dict of numpy.ndarry Dictionary with the blocks of the

Initializes the discrete-time linear system. Arguments ---------- A : numpy.ndarray State transition mat

Initializes the discrete-time affine system. Arguments ---------- A : numpy.ndarray State transition mat

Initializes the discrete-time piecewise-affine system. Arguments ---------- affine_systems : list of instances of Af

Arguments ---------- S : PieceWiseAffineSystem PWA system to be controlled. N : int Horizon o

Right hand side of the inequalities describing the critical region. Returns ---------- numpy.ndarray Rig

Checks if the polyhedron is bounded (returns True or False). Math ---------- Consider the non-empty polyhedron P :=

Returns the Chebyshev center of the polyhedron (see self._chebyshev()). Returns ---------- center : numpy.ndarray

Checks if the polyhedron P is empty solving a QP for the x with minimum norm contained in P. Returns ---------- empt

Instantiates a discrete-time affine system starting from its continuous time representation. Arguments ---------- A

Instatiates a LinearSystem starting from the symbolic value of the next state. Arguments ---------- x : sympy matrix

Instatiates a AffineSystem starting from the symbolic value of the next state. Arguments ---------- x : sympy matrix

Instatiates a LinearSystem starting from the symbolic value of the next state. Arguments ---------- x : sympy matrix

Solves the linear program min_x f^T x s.t. A x <= b, C x = d. Finds a partially nonnegative least squares solution to the KKT conditions of t

Solves the linear program min_x f^T x s.t. A x <= b, C x = d. Arguments ---------- f : numpy.ndarray Gradient of the cost fu

Solves the linear program min_x f^T x s.t. A x <= b, C x = d. Arguments ---------- f : numpy.ndarray Gradient of the cost fu

Solves the strictly convex (H > 0) mixed-integer quadratic program min .5 x' H x + f' x s.t. A x <= b, C x = d. The first nc variables in x

Solves the strictly convex (H > 0) mixed-integer quadratic program min .5 x' H x + f' x s.t. A x <= b, C x = d. The first nc variables in x

Numeric value of the dual optimizer at the point x. Arguments ---------- x : numpy.ndarray Point where w

Plots the input sequence and its bounds as functions of time. Arguments ---------- u : list of numpy.ndarray Sequence of the

Plots the level sets of the optimal value function V*(x). Arguments ---------- resolution : float Size o

Plots the output trajectory and its bounds as functions of time. Arguments ---------- C : numpy.ndarray Tranformation matrix

Finds the critical region where the state x is, and returns the PWA feedforward. Arguments ---------- print_active_s

Plots one component of the state x as a function of another (2d plot). Arguments ---------- x : list of numpy.ndarray Trajec

Plots the state trajectory and its bounds as functions of time. Arguments ---------- x : list of numpy.ndarray Sequence of t

Arguments ---------- plant : RigidBodyPlant RigidBodyPlant of the robot. linearization_points : list of numpy.ndarray

Solves the strictly convex (H > 0) quadratic program min .5 x' H x + f' x s.t. A x <= b, C x = d using nonnegative least squres. (See "Bempo

Solves the strictly convex (H > 0) quadratic program min .5 x' H x + f' x s.t. A x <= b, C x = d. Arguments ---------- H : numpy.nd

Solves the strictly convex (H > 0) quadratic program min .5 x' H x + f' x s.t. A x <= b, C x = d. Arguments ---------- H : numpy.nd

Returns the Chebyshev radius of the polyhedron (see self._chebyshev()). Returns ---------- radius : float

Solves the mpMIQP for the given value of the parameter x. Arguments ---------- x : numpy.ndarry Numeric

Tests only if the function macais() il called correctly. For the tests of mcais() see the class TestMCAIS.

Numeric value of the primal optimizer at the point x. Arguments ---------- x : numpy.ndarray Point where

Returns the set of vertices of the polyhdron. It assumes the polyhedron to be bounded (i.e. to be a polytope) and full dimensional (e