This is the simple example from section 4 (equation 8, 9) of Computation of piecewise quadratic Lyapunov functions for hybrid systems by

This is the simple example from section 5 (equation 18~21) of Computation of piecewise quadratic Lyapunov functions for hybrid systems by

Test a simple linear hybrid system x[n+1] = -0.9 * x[n] if 0 <= x[n] <= 1 x[n+1] = -0.5 * x[n] if -1 <= x[n] <= 0

@param sphere: spherical area surronding the vehicle for collision check

Computes the next state and the currently active mode @param x_start A tensor representing the starting state @param u_start

Compute x[n+1] according to q[n+1] = q[n] + (v[n] + v[n+1]) * dt / 2 v[n+1] - v[n] = ϕ(x̅[n], u[n]) − ϕ(x̅*, u*)

Compute the next state according to pos[n+1] = pos[n] + (v[n] + v[n+1]) * dt / 2 [vel[n+1], rpy[n+1]] = [vel[n], rpy[n]] + ϕ(

Compute the next state as pos[n+1] - pos[n] = ϕ(theta[n], vel[n], theta_dot[n], accel[n]) - ϕ(0, 0, 0, 0)

Twin Delayed Deep Deterministic Policy Gradient (TD3) Args: env_fn : A function which creates a copy of the environment.

Train a network such that network(x) - network(x*) + λ*|x-x*|₁ ≈ cost_to_go(x) @param system An AutonomousHybridLinearSystem

@param v: car's velocity @param nf: hidden layer neuron @param delta_dynamics: bool. True: train different between current and next d

Given some state-action pairs, train a controller ϕ(x) − ϕ(x*) + u* to approximate these state-action pairs.

Given many state-cost pairs, train a value approximator ϕ(x) − ϕ(x*)+λ|x − x*|₁

The forward model network maps (theta[n], vel[n], theta_dot[n], accel[n]) to pos[n+1] - pos[n]

The dataset contains the mapping from state_action to state_next

We train both lyapunov_relu and R such that ϕ(x) − ϕ(x*) + λ|R(x−x*)|₁ approximates the lqr cost-to-go.

We train both lyapunov_relu and R such that ϕ(x) − ϕ(x*) + λ|R(x−x*)|₁ approximates the lqr cost-to-go.

We train both lyapunov_relu and R such that ϕ(x) − ϕ(x*) + λ|R(x−x*)|₁ approximates the lqr cost-to-go.

We train both lyapunov_relu and R such that ϕ(x) − ϕ(x*) + λ|R(x−x*)|₁ approximates the lqr cost-to-go.

Take uniform samples in the box lo <= x <= hi. @return samples A num_samples x x_dim tensor.

Validate that x_equilibrium is acceptable. x_equilibrium should be within x_lo and x_up

Value Iteration Algorithm. Args: nx: number of state in the environment. r: numpy array of size (nx, nx). immediate cost from

Given a ReLU network, and a given activation pattern, the ReLU network can be represented as ReLU(x) = gᵀx+h, while P*x ≤ q we return

@param step int step number @return value of the sigmoid at that point

Parent class for decoders. Decoders should be child classes of this class and implement the forward method (which takes a tensor

See Encoder documentation

See Decoder documentation

See Encoder documentation

See Decoder documentation

See Encoder documentation

See Decoder documentation

Generates problems that help bound the difference between a model and the true cost-to-go it approximates @param model The R

provides a sigmoid function that can be used to do weight scheduling for training @dtype torch data type @param lo fl

Store the slack and binary variables in the dynamics constraint. We also compute the bounds of x_next. For discrete-time systems, x_n

@param x_dim The dimension of x. @param u_dim The dimension of u. @param dtype The torch datatype of A, B, c, P, q.

@param x_dim The dimension of x. @param dtype The torch datatype of A, g, P, q.

Args: x_lo, x_up: We will constrain the state to be within the box x_lo <= x <= x_up. u_lo, u_up: The input lim

Args: phi_a: A neural network that maps x to ϕ_a(x). phi_b: A neural network that maps x to a flat vector [ϕ_b(

@param x_dim The dimension of x. @param num_modes The number of hybrid modes. @param lyapunov_positivity_epsilon ε₁ in the do

Trains a neural network to approximate a value function using adversarial training. Also trains a baseline for comparison, that