fix typo about the bounds of inputs in exercise 4 and 8 problem descriptions

Author: FenglongSong

programming_exercises/exercise4_mpc/ex4_mpc.ipynb

@@ -25,7 +25,7 @@
     "x^+ = \\begin{bmatrix}0.9752 & 1.4544 \\\\ -0.0327 & 0.9315 \\end{bmatrix} x + \\begin{bmatrix}0.0248 \\\\ 0.0327 \\end{bmatrix} u\n",
     "$$\n",
     "with constraints\n",
-    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1 \\} $$\n",
+    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1.75 \\} $$\n",
     "\n",
     "This is a second-order system with a natural frequency of $0.15r/s$, a damping ratio of $\\eta= 0.1$, which has been discretized at $1.5r/s$. The first state is the position, and the second is velocity.\n",
     "\n",

programming_exercises/exercise4_mpc/ex4_sol_mpc.ipynb

@@ -25,7 +25,7 @@
     "x^+ = \\begin{bmatrix}0.9752 & 1.4544 \\\\ -0.0327 & 0.9315 \\end{bmatrix} x + \\begin{bmatrix}0.0248 \\\\ 0.0327 \\end{bmatrix} u\n",
     "$$\n",
     "with constraints\n",
-    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1 \\} $$\n",
+    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1.75 \\} $$\n",
     "\n",
     "This is a second-order system with a natural frequency of $0.15r/s$, a damping ratio of $\\eta= 0.1$, which has been discretized at $1.5r/s$. The first state is the position, and the second is velocity.\n",
     "\n",

programming_exercises/exercise8_explicit_mpc/ex8_explicit_mpc.ipynb

@@ -25,7 +25,7 @@
     "x^+ = \\begin{bmatrix}0.9752 & 1.4544 \\\\ -0.0327 & 0.9315 \\end{bmatrix} x + \\begin{bmatrix}0.0248 \\\\ 0.0327 \\end{bmatrix} u\n",
     "$$\n",
     "with constraints\n",
-    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1 \\} $$\n",
+    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1.75 \\} $$\n",
     "\n",
     "\n",
     "## Problem 1 | Implement Explicit MPC\n",

programming_exercises/exercise8_explicit_mpc/ex8_sol_explicit_mpc.ipynb

@@ -25,7 +25,7 @@
     "x^+ = \\begin{bmatrix}0.9752 & 1.4544 \\\\ -0.0327 & 0.9315 \\end{bmatrix} x + \\begin{bmatrix}0.0248 \\\\ 0.0327 \\end{bmatrix} u\n",
     "$$\n",
     "with constraints\n",
-    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1 \\} $$\n",
+    "$$ \\mathcal{X} = \\{x \\mid |x_1|\\leq 5, |x_2|\\leq 0.2 \\},\\quad \\mathcal{U} = \\{ u \\mid |u| \\leq 1.75 \\} $$\n",
     "\n",
     "\n",
     "## Problem 1 | Implement Explicit MPC\n",