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The parameters of a process may be unknown or may change slowly over time. This chapter discusses how one can control a process with unknown parameters. Adaptive methods adjust parameters in response to information about external inputs and system outputs. Adaptive error-correcting techniques often provide a good approach to coping with unknown nonlinear system dynamics.

Control design often seeks the best trajectory along which to move a system from its current state to a target state. Most control methods consider only the first step of the full trajectory toward the target state. Model predictive control considers the full sequence of steps required to move the system optimally from its current state to a future target. The control system then applies the first inputs to start the system along that optimal trajectory. However, rather than continuing, the system takes new inputs and recalculates a new optimal trajectory based on its updated information. The system then begins to move along the new trajectory, updates again, and adjusts its trajectory again. By repeated updating, the system can often perform very well with limited information about nonlinear dynamics and other uncertainties.

Delays often occur between an input into a system and the output from that system. Delays complicate dynamics, create system instabilities, and reduce the information that systems can use to respond to the environment. Adjusting for delays often requires systems to predict future states based on past inputs. Error-correcting feedback can enhance a system’s predictions and improve its ability to cope with delays.

This chapter summarizes the three key topics of feedback, robust control, and design tradeoffs.