Dynamic programming approach to Multiple Objective Control problem having deterministic or fuzzy goals

Multiple Objective Control problems (MOCP) are dynamic optimization problems of control systems that can be framed as multistage decision processes. Generalized Dynamic Programming or Multiple Objective Dynamic Programming is a useful technique to solve MOCP. Levary has first given the dynamic programming approach to solve a multiple objective optimization problem involving goal objectives. His formulation is valid if there is only a single decision variable in each stage. Generally, in control problems, such as Multiple Goal Control Problem (MGCP), a decision vector is involved in each stage. Therefore, in this paper Levary’s formulation is extended to MGCP and is illustrated with an example. When the MOCP has fuzzy goals, it is formulated as Fuzzy Goal Control Problem (FGCP). A new formulation of dynamic programming approach to FGCP is proposed here as Dynamic Fuzzy Goal Control Problem and the method of finding its solution is illustrated with an example.