**Fuzzy Control For an Inverted Pendulum**

Build a fuzzy control system to balance an inverted pendulum in a cart/pole system. Given a simulation of an inverted pendulum on top of a cart that can move in 2 dimensions and provides information regarding position and velocity, design and implement a fuzzy control system that can provide commands to the cart to successfully balance the inverted pendulum and stay within a fixed region with the cart.**Optimal Navigation Strategies with Uncertain Actions**

Determine an approximately optimal navigation strategy for a grid-based navigation task with probabilistic actions (left, right, up, down, each with a 80% success probability) and uncertain state observations (The location's x and y coordinate are returned with a probability of 0.8 for the actual location and 0.1 for each of the neighboring coordinates). Use the techniques introduced in the course to track the belief state and to determine an approximately optimal policy (in the presence of obstacles).**Multi-Mean Estimation of Highly Uncertain Motion Data**

Using the same setup as in Project 1, use a particle filter to estimate the location and motion parameters of a cube where observations consist of a noisy version of the distance of the cube from the left upper corner of the box (the size of the box is provided).**Estimation of Multiple Load Patterns**

Two unknown load patterns (each with different expected packet arrival rates) are present on the same network. Try to estimate both load parameters and the occurrence of switching points between the different patterns.**Optimal Switching Under Varying Load Conditions**

Two network connections of different bandwidth are available, each with a different cost. Determine the optimal switching points given the predicted amount of traffic produced by two randomly operating processes. Here traffic conditions have to be predicted using a filter and a switching policy has to be determined based on the predicted load and the costs associated with the line and the delay caused by queued packets.