## Abstract

In this chapter we consider quantitative control objectives for rather general systems. The inputs are chosen to minimize a function that expresses the costs associated with the system evolution. This can be solved by dynamic programming. We pay special attention to the so-called LQ-problem, where the system is linear and the cost function is quadratic. In this case the optimal control is given by state feedback, and the feedback matrix can be computed by solving certain matrix equations (so-called Riccati equations).

## Keywords

Cost Function Dynamic Programming Optimal Control Problem State Feedback Riccati Equation
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## Copyright information

© Birkhäuser Verlag 2007