Abstract by Isaac Becker
Stability for Linearized and Discretized Model Predictive Control (MPC)
Model Predictive Control (MPC) is an advanced method in control theory used in dynamic systems such as robots, cars, and chemical plants. Much effort has gone into speeding up the process of MPC, and it continues to be an active field of research. Algorithms developed by the Robotics and Dynamics Laboratory (RAD Lab) at BYU implement linearization and discretization methods modeling the dynamics used by MPC and achieve favorable response times. Unfortunately, not much is rigorously known about the stability of a system that is linearized or discretized continuously. If an algorithm is unstable it may cause the system to lose control and damage itself and anything in its path. We hope to show that the method of discretizing and linearizing the dynamics used by MPC is stable by creating a Lyapunov function through semi-definite programming and sums of squares decomposition. We will apply this stability to the RAD lab’s algorithms to assure safety in their use.