Developing an Optimal Controller for Energy Minimization of an Electric Car

Dynamic Programing Approach
The DP approach involves discretizing the state (i.e., speed, v), input (i.e., driving force Fdrive), and position spaces to generate a look-up table that correlates the measured values at a given position to the optimal input. Although it can work with nonlinear costs and constraints, there is potential computational intractability in systems with multiple inputs and states. Furthermore these approaches tend to computationally heavy and therefore time consuming. The approach does guarantee the user to calculate the entire solution space, which is helpful for offline calculation needs.

Model Predictive Controllers
The MPC approach first solves an optimal control problem over a chosen prediction horizon given a measured position, The first input in this sequence is then applied to the system and the new state of the system becomes the initial state for the next optimal control problem. This pattern is then repeated over the entire length of the chosen roadway. One significant issue is dealing with nonlinearity in constraints or cost. For our study dealing with the nonlinearity of efficiency become quite the challenge. MPC are however, very capable of modeling multiple input/state systems.