OPTIMAL FEEDBACK SOLUTION OF A CONSTRAINED STOCHASTIC ONE-STORAGE MODEL

We describe a method for obtaining the optimal feedback solution to a constrained discrete time linear-quadratic optimal control problem. Th e dimensions of the state and control vectors are one and the stochast icity is represented by a finite number of possible outcomes at each s tage. The method is based on dynamic programming and exploits that the optimal value is piecewise quadratic and that the optimal feedback so lution is piecewise linear. Also the special case with linear criterio n function is considered. Approximation methods which allow a trade-of f between computation times and solution accuracy are discussed. The m ethod is applied to two cases, viz., hydropower scheduling and tempera ture control of a greenhouse. Comparative studies on these two cases w ere made with a mathematical programming formulation solved by a stand ard code. On the cases studied the new method was found to be around 1 00 times faster and to display a better solution stability. (C) 1997 J ohn Wiley & Sons, Ltd.