Abstract
In this chapter, we introduce optimal control theory for discrete-time systems. We begin with unconstrained optimization of a cost function and then generalize to optimization with equality constraints. We then cover the optimization or optimal control of discrete-time systems. We specialize to the linear quadratic regulator and obtain the optimality conditions for a finite and for an infinite planning horizon. We also address the regulator problem where the system is required to track a nonzero constant signal. We examine the Hamiltonian system, its use in solving the Riccati equation, and its relation to the eigenstructure of the system with optimal control. Finally, we provide a brief introduction to a control design strategy known as model predictive control.
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