Iterative Dynamic Programming for Minimum Energy Control Problems With Time Delay

Abstract

SUMMARYThis paper presents the use of iterative dynamic programming employing exact penalty functions for minimum energy control problems. We show that exact continuously non‐differentiable penalty functions are superior to continuously differentiable penalty functions in terms of satisfying final state constraints. We also demonstrate that the choice of an appropriate penalty function factor depends on the relative size of the time delay with respect to the final time and on the expected value of the energy consumption. A quadratic approximation (QA) of the delayed variables is much better than a linear approximation (LA) of the same for relatively large time delays. The QA improves the rate of convergence and avoids the formation of ‘kinks‘.A more general way of selecting appropriate penalty function factors is given and the results obtained using four illustrative examples of varying complexity corroborate the efficacy of the method.

Numerical solution of dynamic optimization problems with flexible inequality constraints by iterative dynamic programming

“…By using of coarse grid points and region-reduction strategy, IDP not only successfully overcomes the curse and promotes the e ciency of computation but greatly increases numerical accuracy. Since then, extensive researches [6,7,2,3,11] have shown that IDP is one reliable method on obtaining global solution for nonlinear dynamic optimization problems. So, we attempt in this study to integrate the IDP and the fuzzy inference to provide an e cient way on ÿnding the solution of a dynamic optimization problem with exible inequality constraints.…”

Enhancement of the Global Convergence of Using Iterative Dynamic Programming To Solve Optimal Control Problems

“…Similarly, in solving optimal control problems by multipass IDP with a pass region contraction factor η, the optimal control sequence obtained in the current pass of IDP optimization will be used as the central control profile of the next pass. Multiple passes of IDP computation have been used (Bojkov and Luus, 1992a;Dadebo and McAuley, 1995a;Luus and Galli, 1991;Luus and Rosen, 1991) to refine the piecewise-constant control policy by doubling the number of time stages so that it is comparable to the optimal continuous control profile. Recently, it has been found (Luus, 1993d;Luus et al, 1995) that several optimal control problems can be effectively solved by multipass IDP computation using only a single state grid for each stage.…”

“…By contracting the control region for each time stage after each cycle of dynamic programming computation, the IDP finally obtains an optimal control profile. Due to the advantages of being easily implemented on a personal computer and having greater possibility to obtain a globally optimal solution than a nonlinear programming method, the original IDP method and some of the improved versions (Lin and Hwang, 1996b;Hwang and Lin, 1998) have been successfully applied to solve various optimal control problems of nonlinear processes Luus, 1994a,b, 1996;Dadebo and McAuley, 1995b;Keil, 1993a, 1994;Hartig et al, 1996;Keil et al, 1996;Luus, 1990cLuus, , 1991Luus, , 1993aLuus and Bojkov, 1994;Luus et al, 1992;Luus and Galli, 1991;Mekarapiruk and Luus, 1997), including time-delay systems (Dadebo and Luus, 1992;Dadebo and McAuley, 1995a;Lin and Hwang, 1996a) and systems with a large number of state and control variables (Bojkov and Luus, 1992a,b, 1993Hartig and Keil, 1993b;Luus, 1990bLuus, , 1993dLuus and Smith, 1991).…”

Optimal Control of Time-Delay Systems by Forward Iterative Dynamic Programming

“…To obtain a reliable global solution to the optimal control problem of a time-delay system, an iterative dynamic programming (IDP) algorithm has been recently used (Dadebo and Luus, 1992;Dadebo and McAuley, 1995;Jime ´nez-Romero and Luus, 1991). Basically, the IDP algorithm also uses the control parametrization technique.…”