Handbook of Model Predictive Control

DRAFT Current technology provides remarkable opportunities to improve control systems. A variety of computing devices-ranging from large, powerful computers, PCs, small hobbyist process computers such as the Arduino and Raspberry Pi, PLCs, FPGAs, and others-offer fast computation at affordable prices. One consequence is that almost all modern control systems are implemented digitally. Furthermore, there now exist many inexpensive communication options. Finally, the collection of sensors, and that which can be sensed in (or nearly in) real time has greatly increased. A well-known example of these technologies are the modern automobile with over 100 computers, at least two communication networks, and its extensive collection of sensors. A second example is the modern cell phone that includes-basically as throw ins-GPS, an Inertial Measuring Unit, and the ability to provide walking, driving, or public transit routes almost anywhere. There is a point of similarity between the phone and many digitally implemented control systems. Both use only a small portion of the computational capability to achieve their basic objective. There are two implications of this technology for control practice and theory. Even conventional Single-Input Single-Output (SISO) control systems might be able to use the extra computation that is available (essentially at no cost) to provide additional and improved function, just as the cell phone does. Second, improved communication and more sensing mean that large systems that were heretofore controlled by a collection of weakly, if at all, coordinated SISO systems, can now be controlled as Multi-Input Multi-Output (MIMO) systems. The design of MIMO controllers is, although there are results and we will mention one of them shortly, is still very much an open question. We are arguing that control engineers should be thinking about "computationally intensive controls" a phrase we first heard from Joao Hespanha. Model Predictive Control (MPC) is a particularly effective design method for doing computationally intensive control. It provides the possibility to improve relatively classical SISO controls and it has already proven useful in a large number of MIMO control systems. MPC remains an active research area in both theory and practice. Practicing engineers continue to push beyond the limits of our theoretical understanding, thereby increasing the importance of research into extending the theory. Because MPC is so dependent on prediction and prediction always involves uncertainty, a great deal of current and past theoretical research deals with ways to handle uncertainty such as robust MPC, stochastic MPC, and various related topics. Because MPC requires the solution of an optimization problem in a very short time, a great deal of relevant research addresses methods for solving optimization problems, both theoretically and computationally. Lastly, because applications continue to produce interesting theoretical problems as well as showing how MPC can be applied in the real world, we have included a representative selection of applications in the handbook.