This paper presents an efficient algorithmic solution to the infinite horizon linear quadratic optimal control problem for a discrete-time SISO plant subject to bound constraints on a scalar variable. The solution to the corresponding quadraticprogramming problem is based on the active set method and on dynamic programming. It is shown that the optimal solution can be updated after inclusion or removal of an active constraint by a simple procedure requiring in the order of kn operations, nbeing the system order and k the time at which the constraint is included or removed.
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