Add optimal control example by chatgpt

apps/optimal_control/__init__.py

@@ -0,0 +1 @@
+from .app import main

apps/optimal_control/app.py

@@ -0,0 +1,134 @@
+import streamlit as st
+from amplpy import AMPL
+import matplotlib.pyplot as plt
+from ..common import solver_selector, MP_SOLVERS_LINKS
+
+MODEL = r"""
+# Sets
+param steps;
+set T ordered := 1..steps; # Discrete time steps
+
+# Parameters
+param g default 9.81; # Gravitational constant (m/s^2)
+param Tmax;           # Maximum thrust (N)
+param m0;             # Initial mass of the rocket (kg)
+param mdot;           # Mass flow rate (kg/s)
+param ve;             # Exhaust velocity (m/s)
+
+param x0 default 0;   # Initial x-position (m)
+param y0 default 0;   # Initial y-position (m)
+param vx0 default 0;  # Initial x-velocity (m/s)
+param vy0 default 0;  # Initial y-velocity (m/s)
+
+param xf;             # Final x-position target (m)
+param yf;             # Final y-position target (m)
+param dt;             # Time step duration (s)
+
+# Decision Variables
+var x{T};             # x-position of the rocket at time t
+var y{T};             # y-position of the rocket at time t
+var vx{T};            # x-velocity of the rocket at time t
+var vy{T};            # y-velocity of the rocket at time t
+var m{T} >= 0;        # Mass of the rocket at time t
+var Tmag{T} >= 0, <= Tmax; # Thrust magnitude at time t
+var Tx{T};            # Thrust in x-direction at time t
+var Ty{T};            # Thrust in y-direction at time t
+
+# Objective Function: Minimize fuel consumption
+minimize Fuel_Consumption:
+    sum {t in T} Tmag[t] * dt / ve;
+
+# Dynamics and Constraints
+subject to Dynamics_x {t in T: t != last(T)}:
+    x[t+1] = x[t] + vx[t] * dt;
+
+subject to Dynamics_y {t in T: t != last(T)}:
+    y[t+1] = y[t] + vy[t] * dt;
+
+subject to Dynamics_vx {t in T: t != last(T)}:
+    vx[t+1] = vx[t] + (Tx[t] / m[t]) * dt;
+
+subject to Dynamics_vy {t in T: t != last(T)}:
+    vy[t+1] = vy[t] + (Ty[t] / m[t] - g) * dt;
+
+subject to Dynamics_mass {t in T: t != last(T)}:
+    m[t+1] = m[t] - (Tmag[t] / ve) * dt;
+
+# Thrust vector constraints
+subject to Thrust_Vector {t in T}:
+    Tmag[t] = sqrt(1e-6+Tx[t]^2 + Ty[t]^2);
+
+# Initial conditions
+subject to Initial_Conditions_1:
+    x[first(T)] = x0;
+subject to Initial_Conditions_2:
+    y[first(T)] = y0;
+subject to Initial_Conditions_3:
+    vx[first(T)] = vx0;
+subject to Initial_Conditions_4:
+    vy[first(T)] = vy0;
+subject to Initial_Conditions_5:
+    m[first(T)] = m0;
+
+# Terminal conditions
+subject to Terminal_Conditions_1:
+    x[last(T)] = xf;
+subject to Terminal_Conditions_2:
+    y[last(T)] = yf;
+"""
+
+
+def main():
+    st.title("🎯 Optimal Control by ChatGPT")
+
+    st.code(MODEL)
+
+    ampl = AMPL()
+    ampl.eval(MODEL)
+
+    c1, c2, c3 = st.columns(3)
+    with c1:
+        ampl.param["steps"] = st.slider("How many steps?", 10, 20, 10)
+    with c2:
+        ampl.param["dt"] = st.slider("Time step duration in seconds?", 1, 60, 1)
+    with c3:
+        ampl.param["m0"] = st.slider("Initial rocket mass in kg?", 100, 1000, 500)
+
+    with c1:
+        ampl.param["Tmax"] = st.slider(
+            "Maximum thrust in Newtons?", 10000, 30000, 20000
+        )
+    with c2:
+        ampl.param["mdot"] = st.slider("Mass flow rate in kg/s?", 5, 20, 10)
+    with c3:
+        ampl.param["ve"] = st.slider("Exhaust velocity in m/s?", 2000, 4000, 3000)
+
+    c1, c2 = st.columns(2)
+    with c1:
+        ampl.param["x0"] = st.slider("Initial x-position?", 0, 1000, 0)
+    with c2:
+        ampl.param["y0"] = st.slider("Initial y-position?", 0, 1000, 0)
+    with c1:
+        ampl.param["xf"] = st.slider("Final x-position?", 0, 10000, 10000)
+    with c2:
+        ampl.param["yf"] = st.slider("Final y-position?", 0, 10000, 5000)
+    output = ampl.solve(solver="snopt", return_output=True)
+    st.markdown(f"```\n{output}\n```")
+
+    df = ampl.get_data("x", "y", "vx", "vy", "m", "Tmag").to_pandas()
+    st.dataframe(df)
+
+    # fig, ax = plt.subplots()
+    # ax.plot(
+    #     df["x"], df["y"], marker="o"
+    # )  # Connect points with a line and add markers for clarity
+    # ax.set_title("Line Graph")
+    # ax.set_xlabel("x")
+    # ax.set_ylabel("y")
+    # st.pyplot(fig)
+
+    st.markdown(
+        """
+    #### [[App Source Code on GitHub](https://github.com/fdabrandao/amplopt.streamlit.app/tree/master/apps/optimal_control)] [[ChatGPT Session](https://chatgpt.com/share/673f7f67-a2ec-8011-9633-01a3570ef26f)]
+    """
+    )

apps/tips/app.py

@@ -31,5 +31,5 @@ def update_params():
 
 
 def main_tip7():
-    st.title(f"🎯 {tip7.title[tip7.title.find(':')+1:].strip()}")
+    st.title(f"🏷️ {tip7.title[tip7.title.find(':')+1:].strip()}")
     tip7.run()

streamlit_app.py

@@ -13,6 +13,7 @@
     supply_chain,
     aircrew_training_scheduling,
     risk_return,
+    optimal_control,
     nqueens,
     sudoku,
     tips,
@@ -116,7 +117,8 @@ def page():
         app_page(facility_location.main, "🏭", "Stochastic Facility Location"),
         app_page(supply_chain.main, "📦", "Supply Chain Optimization"),
         app_page(risk_return.main, "📈", "Portfolio Optimization", "Risk_Return"),
-        app_page(tips.main_tip7, "🎯", "Logistic Regression"),
+        app_page(tips.main_tip7, "🏷️", "Logistic Regression"),
+        app_page(optimal_control.main, "🎯", "Optimal Control"),
     ],
     "Puzzles & Games": [
         app_page(nqueens.main, "👑", "N-Queens"),