Comparison of IDP and LJ Optimization Procedure for Establishing the Optimal Control of a Nonisothermal Fedbatch Reactor

Optimal control of a nonisothermal fedbatch reactor with heat removal constraint is used as a test problem for comparing iterative dynamic programming (IDP) and Luus- Jaakola (LJ) optimization procedure. Although there are only two control variables, the feed rate and the temperature, the heat production rate constraint makes the optimal control problem very difficult. Therefore, the problem is reformulated by using rate of heat production instead of temperature as the second control variable. To parametrize the optimal control problem, the time interval is divided into P time stages of constant length, and piecewise constant control is used at each time stage. For small values of P , both optimization procedures are almost equivalent. However, when is increased beyond 20, IDP becomes more efficient.