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Lyapunov-based neural network control with input saturation constraints
def forward(self, x):
"""
Args:
x: system dataset
Return:
lyapunov_candidate: Lyapunov candidate function V(x) for system x
control_function: Possible control function u(x) for system x
"""
activation_function = torch.nn.Tanh()
# Apply input constraints to the input data
constrained_x = torch.clamp(x, min_value, max_value)
x_i = activation_function(self.first_layer(constrained_x))
lyapunov_candidate = activation_function(self.second_layer(x_i))
# Apply input constraints to the control function
constrained_control = torch.clamp(self.control(constrained_x), control_min, control_max)
control_function = activation_function(constrained_control)
return lyapunov_candidate, control_function
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