Add runge kutta

Author: Shunichi09

PythonLinearNonlinearControl/common/utils.py

@@ -41,4 +41,60 @@ def fit_angle_in_range(angles, min_angle=-np.pi, max_angle=np.pi):
     output += min_angle
 
     output = np.minimum(max_angle, np.maximum(min_angle, output))
-    return output.reshape(output_shape)
+    return output.reshape(output_shape)
+
+def update_state_with_Runge_Kutta(state, u, functions, dt=0.01):
+    """ update state in Runge Kutta methods
+    Args:
+        state (array-like): state of system
+        u (array-like): input of system
+        functions (list): update function of each state,
+            each function will be called like func(*state, *u)
+            We expect that this function returns differential of each state 
+        dt (float): float in seconds
+    
+    Returns:
+        next_state (np.array): next state of system
+    
+    Notes:
+        sample of function is as follows:
+
+        def func_x(self, x_1, x_2, u):
+            x_dot = (1. - x_1**2 - x_2**2) * x_2 - x_1 + u
+            return x_dot
+        
+        Note that the function return x_dot.
+    """
+    state_size = len(state)
+    assert state_size == len(functions), \
+        "Invalid functions length, You need to give the state size functions"
+    
+    k0 = np.zeros(state_size)
+    k1 = np.zeros(state_size)
+    k2 = np.zeros(state_size)
+    k3 = np.zeros(state_size)
+
+    inputs = np.concatenate([state, u])
+
+    for i, func in enumerate(functions):
+        k0[i] = dt * func(*inputs)
+
+    add_state = state + k0 / 2.
+    inputs = np.concatenate([add_state, u])
+
+    for i, func in enumerate(functions):
+        k1[i] = dt * func(*inputs)
+    
+    add_state = state + k1 / 2.
+    inputs = np.concatenate([add_state, u])
+    
+    for i, func in enumerate(functions):
+        k2[i] = dt * func(*inputs)
+
+    add_state = state + k2
+    inputs = np.concatenate([add_state, u])
+
+    for i, func in enumerate(functions):
+        k3[i] =  dt * func(*inputs)
+
+    return (k0 + 2. * k1 + 2. * k2 + k3) / 6.

PythonLinearNonlinearControl/configs/nonlinear_system_sample.py

@@ -0,0 +1,98 @@
+import numpy as np
+import scipy
+from scipy import integrate
+from .env import Env
+from ..common.utils import update_state_with_Runge_Kutta
+
+class NonlinearSampleEnv(Env):
+    """ Nonlinear Sample Env
+    """
+    def __init__(self):
+        """
+        """
+        self.config = {"state_size" : 2,\
+                       "input_size" : 1,\
+                       "dt" : 0.01,\
+                       "max_step" : 250,\
+                       "input_lower_bound": [-0.5],\
+                       "input_upper_bound": [0.5],
+                       }
+
+        super(NonlinearSampleEnv, self).__init__(self.config)
+    
+    def reset(self, init_x=np.array([2., 0.])):
+        """ reset state
+        Returns:
+            init_x (numpy.ndarray): initial state, shape(state_size, )  
+            info (dict): information
+        """
+        self.step_count = 0
+        
+        self.curr_x = np.zeros(self.config["state_size"])
+
+        if init_x is not None:
+            self.curr_x = init_x
+
+        # goal
+        self.g_x = np.array([0., 0.])
+        
+        # clear memory
+        self.history_x = []
+        self.history_g_x = []
+
+        return self.curr_x, {"goal_state": self.g_x}
+
+    def step(self, u):
+        """
+        Args:
+            u (numpy.ndarray) : input, shape(input_size, )
+        Returns:
+            next_x (numpy.ndarray): next state, shape(state_size, ) 
+            cost (float): costs
+            done (bool): end the simulation or not
+            info (dict): information 
+        """
+        # clip action
+        u = np.clip(u,
+                    self.config["input_lower_bound"],
+                    self.config["input_upper_bound"])
+
+        funtions = [self._func_x_1, self._func_x_2]
+
+        next_x = update_state_with_Runge_Kutta(self._curr_x, u,
+        functions, self.config["dt"])
+
+        # cost
+        cost = 0
+        cost = np.sum(u**2)
+        cost += np.sum((self.curr_x - self.g_x)**2)
+
+        # save history
+        self.history_x.append(next_x.flatten())
+        self.history_g_x.append(self.g_x.flatten())
+        
+        # update
+        self.curr_x = next_x.flatten()
+        # update costs
+        self.step_count += 1
+
+        return next_x.flatten(), cost, \
+               self.step_count > self.config["max_step"], \
+               {"goal_state" : self.g_x}
+    
+    def _func_x_1(self, x_1, x_2, u):
+        """
+        """
+        x_dot = x_2
+        return x_dot
+    
+    def _func_x_2(self, x_1, x_2, u):
+        """
+        """
+        x_dot = (1. - x_1**2 - x_2**2) * x_2 - x_1 + u
+        return x_dot
+    
+    def plot_func(self, to_plot, i=None, history_x=None, history_g_x=None):
+        """
+        """
+        raise ValueError("NonlinearSampleEnv does not have animation")