A dynamic programming successive approximations technique with convergence proofs

Larson, Robert E.; Korsak, A

doi:10.1016/0005-1098(70)90095-6

Cited by 78 publications

(16 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To tackle this dimensional problem, the class of discrete DP techniques -DP successive approximation (Larson 1968;Larson and Korsak 1970), increment DP (Hall et al 1969), discrete differential DP (Heidari et al 1971), incremental DP successive approximation (Giles and Wunderlich 1981), and folded DP (Kumar and Baliarsingh 2003) -is available. However, the discrete algorithms are unsuitable because the state variables -upper and lower water levels or storages -of the rule curve searching are continuous.…”

Section: Introductionmentioning

confidence: 99%

Dynamic programming with the principle of progressive optimality for searching rule curves

Chaleeraktrakoon¹,

Kangrang²

2007

Can. J. Civ. Eng.

View full text Add to dashboard Cite

Rule curves are monthly reservoir-operation guidelines for meeting the minimum of water shortage over the long run. This paper proposes a dynamic programming (DP) approach for finding the optimal rule curves of singleand multi-reservoir systems. The proposed DP approach uses a traditional DP technique conditionally and applies the principle of progressive optimality (PPO) to search its optimal solutions. The proposed DP-PPO approach is suitable because of the multi-stage, nonlinear, and continuous-type characteristics of the rule curve search. Its dimensionality is relatively small, as compared with that of the traditional one. Results of an illustrative application to a multi-reservoir system under two different initial feasible solutions (i.e., new or existing reservoirs) have demonstrated that the DP-PPO approach is generally fast and robust. Its convergence varies only slightly, according to the initial conditions.Key words: rule curves, principle of progressive optimality, dynamic programming (DP), monthly reservoir operation. Résumé :Les courbes des niveaux optimaux sont des lignes directrices mensuelles de gestion de réservoir pour rencontrer le minimum de pénurie d'eau à long terme. Cet article propose une approche de programmation dynamique (« DP ») pour trouver les courbes des niveaux optimaux des systèmes à simple et à plusieurs réservoirs. L'approche « DP » proposée utilise la technique « DP » classique de manière conditionnelle et applique le principe d'optimalité progressive (« PPO ») pour rechercher ses solutions optimales. L'approche « DP-PPO » proposée est appropriée aux caractéristiques de plusieurs étages non linéaires et continus de la recherche de la courbe des niveaux optimaux. Sa dimensionnalité est relativement petite, si on la compare à celle de la technique classique. Les résultats d'une application typique à un système à plusieurs réservoirs sous deux solutions initiales faisables différentes (c.-à-d. nouveaux réser-voirs et réservoirs existants) démontrent que l'approche « DP-PPO » est généralement rapide et robuste. Sa convergence ne varie que légèrement selon les conditions initiales.Mots-clés : courbe des niveaux optimaux, principe d'optimalité progressive, programmation dynamique, gestion mensuelle du réservoir.[Traduit par la Rédaction] Chaleeraktrakoon and Kangrang 176

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamic programming with the principle of progressive optimality for searching rule curves

Chaleeraktrakoon¹,

Kangrang²

2007

Can. J. Civ. Eng.

View full text Add to dashboard Cite

show abstract

“…However, starting with an initial trajectory xo(kT) sufficiently close to the optimum one yields this optimum solution. 21 The speed of convergence of the algorithm may be improved significantly by testing at each iteration only those states (i.e. the quantized values) lying in a strip defined around the previous trajectory (see Figure 5).…”

Section: Pi(kt) = G(qi(kt) Hi(kt)j (14)mentioning

confidence: 99%

Application of linear and dynamic programming to the optimization of the production of hydroelectric power

Olcer

Harsa

Roch

1985

Optim Control Appl Methods

View full text Add to dashboard Cite

Application of the methods of control theory to industrial problems demands a match of the necessary computational tools to the actual financial constraints. The development of suboptimal control algorithms allows performance gains that were limited in the past to installations with extensive computer facilities to be reached now by smaller ones. Advances in this domain lead naturally to a rational use of modern control tools based on mini-and microcomputers.Within this framework, we present a general method for the optimal control ofelectric power plants. The optimization problem is described and formulated as the optimal control of a multivariable state-space model in which the state and control vectors are constrained by sets of equality or inequality relations. The solution is obtained in two steps with linear and dynamic programming methods; the results are expressed in the form of parametric algorithms which set up the working point of the turbine-generator units so that the resulting profit represents a maximum. The application of the method to the optimization of the production of a Swiss electricity company illustrates the approach.

show abstract

“…Therefore, a variety of improved DP algorithms have been extensively used (Zhao et al, 2014), such as Discrete Differential Dynamic Programming (DDDP) (Heidari et al, 1971;Chow et al, 1975;Liao and Shoemaker, 1991;Tospornsampan et al, 2005), Incremental Dynamic Programming (IDP) (Mathlouthi and Lebdi, 2009), Dynamic Programming with Successive Approximation (DPSA) (Larson and Korsak, 1970;Opan, 2011), Incremental Dynamic Programming and Successive Approximations (IDPSA) (Trott and Yeh, 1973), Progressive Optimality Algorithm (POA) (Turgeon, 1981;Cheng et al, 2012;Lu et al, 2013), and so on. These improved DP algorithms have effectively avoided the ''curse of dimensionality'' problem.…”

Section: Introductionmentioning

confidence: 99%

Contrastive analysis of three parallel modes in multi-dimensional dynamic programming and its application in cascade reservoirs operation

Zhang

Jiang

et al. 2015

Journal of Hydrology

View full text Add to dashboard Cite

A dynamic programming successive approximations technique with convergence proofs

Cited by 78 publications

References 0 publications

Dynamic programming with the principle of progressive optimality for searching rule curves

Dynamic programming with the principle of progressive optimality for searching rule curves

Application of linear and dynamic programming to the optimization of the production of hydroelectric power

Contrastive analysis of three parallel modes in multi-dimensional dynamic programming and its application in cascade reservoirs operation

Contact Info

Product

Resources

About