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  • Infinite-horizon optimal control  (3)
  • existence theory  (3)
  • Thioredoxin  (2)
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  • 1
    ISSN: 1432-072X
    Keywords: Photosynthesis ; Regulation ; Thioredoxin ; Cyanobacterium ; Chromatium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Enzymes that are regulated by the ferredoxin/thioredoxin system in chloroplasts — fructose-1,6-bisphosphatase (FBPase), sedoheptulose-1,7-bisphosphatase purified from two different types of photosynthetic prokaryotes (cyanobacteria, purple sulfur bacteria) and tested for a response to thioredoxins. Each of the enzymes from the cyanobacterium Nostoc muscorum, an oxygenic organism known to contain the ferredoxin/thioredoxin system, was activated by thioredoxins that had been reduced either chemically by dithiothreitol or photochemically by reduced ferredoxin and ferredoxin-thioredoxin reductase. Like their chloroplast counterparts, N. muscorum FBPase and SBPase were activated preferentially by reduced thioredoxin f. SBPase was also partially activated by thioredoxin m. PRK, which was present in two regulatory forms in N. muscorum, was activated similarly by thioredoxins f and m. Despite sharing the capacity for regulation by thioredoxins, the cyanobacterial FBPase and SBPase target enzymes differed antigenically from their chloroplast counterparts. The corresponding enzymes from Chromatium vinosum, an anoxygenic photosynthetic purple bacterium found recently to contain the NADP/thioredoxin sytem, differed from both those of cyanobacteria and chloroplasts in showing no response to reduced thioredoxin. Instead, C. vinosum FBPase, SBPase, and PRK activities were regulated by a metabolite effector, 5′-AMP. The evidence is in accord with the conclusion that thioredoxins function in regulating the reductive pentose phosphate cycle in oxygenic prokaryotes (cyanobacteria) that contain the ferredoxin/thioredoxin system, but not in anoxygenic prokaryotes (photosynthetic purple bacteria) that contain the NADP/thioredoxin system. In organisms of the latter type, enzyme effectors seem to play a dominant role in regulating photosynthetic carbon dioxide assimilation.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-072X
    Keywords: Thioredoxin ; Cyanobacterium ; Ferredoxin ; Nostoc ; Regulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Cell-free preparations of the cyanobacterium (bluegreen alga) Nostoc muscorum were assayed for thioredoxins and enzymes catalyzing the ferredoxin and NADP-linked reduction of thioredoxin. Nostoc was found to have two different thioredoxins: one of approximate molecular weight 16,000 (designated Nostoc thioredoxin f) that selectively activated chloroplast fructose 1,6-bisphosphatase, and another of approximate molecular weight 9,000 (designated Nostoc thioredoxin m) that selcetively activated chloroplast NADP-malate dehydrogenase. The two thioredoxins could be reduced either chemically with dithiothreitol or photochemically with ferredoxin and ferredoxin-thioredoxin reductase which, like the recently found regulatory iron-sulfur protein ferralterin, was present in Nostoc cells. Nostoc ferredoxin-thioredoxin reductase appeared to be similar to its chloroplast counterpart in enzyme specificity, molecular weight, and spectral properties. The Nostoc and spinach chloroplast ferredoxin-thioredoxin reductases as well as their thioredoxins, ferredoxins, and chlorophyll containing membranes were interchangeable in activating chloroplast fructose 1,6-bisphosphatase and NADP-malate dehydrogenase. There was no evidence for an NADP-linked thioredoxin reductase such as that of E. coli. The results are in accord with the conclusion that the cyanobacteria resemble higher plants in having a functional ferredoxin/thioredoxin system rather than an NADP/thioredoxin system typical of other bacteria.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 49 (1986), S. 207-225 
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; catching-up optimal solutions ; infinite-horizon problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do nota priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching-up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 51 (1986), S. 41-62 
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; finite optimality ; infinite horizons ; continuous dependence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the existence of finitely optimal solutions for the Lagrange problem of optimal control defined on [0, ∞) under weaker convexity and seminormality hypotheses than those of previous authors. The notion of finite optimality has been introduced into the literature as the weakest of a hierarchy of types of optimality that have been defined to permit the study of Lagrange problems, arising in mathematical economics, whose cost functions either diverge or are not bounded below. Our method of proof requires us to analyze the continuous dependence of finite-interval Lagrange problems with respect to a prescribed terminal condition. Once this is done, we show that a finitely optimal solution can be obtained as the limit of a sequence of solutions to a sequence of corresponding finite-horizon optimal control problems. Our results utilize the convexity and seminormality hypotheses which are now classical in the existence theory of optimal control.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 64 (1990), S. 55-69 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimal solutions ; decision-horizon optimal solutions ; agreeable plans ; sufficient conditions for optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we investigate the relationship between two classes of optimality which have arisen in the study of dynamic optimization problems defined on an infinite-time domain. We utilize an optimal control framework to discuss our results. In particular, we establish relationships between limiting objective functional type optimality concepts, commonly known as overtaking optimality and weakly overtaking optimality, and the finite-horizon solution concepts of decision-horizon optimality and agreeable plans. Our results show that both classes of optimality are implied by corresponding uniform limiting objective functional type optimality concepts, referred to here as uniformly overtaking optimality and uniformly weakly overtaking optimality. This observation permits us to extract sufficient conditions for optimality from known sufficient conditions for overtaking and weakly overtaking optimality by strengthening their hypotheses. These results take the form of a strengthened maximum principle. Examples are given to show that the hypotheses of these results can be realized.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 66 (1990), S. 311-336 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; Volterra integral equations ; recursive objective functionals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work, we concern ourselves with the existence of optimal solutions to optimal control problems defined on an unbounded time interval with states governed by a nonlinear Volterra integral equation. These results extend both the work of Baum and others in infinite-horizon control of ordinary differential equations as well as the work of Angell concerning integral equations. In addition, we incorporate into the objective functional (described by an improper integral) a discount factor which reflects a hereditary dependence on both state and control. In this manner, we are able to generalize the recent results of Becker, Boyd, and Sung in which they establish an existence theorem in the calculus of variations with objective functionals of the so-called recursive type. Our results are obtained through the use of appropriate lower-closure theorems and compactness conditions. Examples are presented in which the applicability of our results is demonstrated.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 53 (1987), S. 219-235 
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theory ; sporadically catching-up optimality ; infinite-horizon optimal control problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we extend the existence theory of Brock and Haurie concerning the existence of sporadically catching-up optimal solutions for autonomous, infinite-horizon optimal control problems. This notion of optimality is one of a hierarchy of types of optimality that have appeared in the literature to deal with optimal control problems whose cost functionals, described by an improper integral, either diverge or are unbounded below. Our results rely on the now classical convexity and seminormality hypotheses due to Cesari and are weaker than those assumed in the work of Brock and Haurie. An example is presented where our results are applicable, but those of the above-mentioned authors do not.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 78 (1993), S. 465-491 
    ISSN: 1573-2878
    Keywords: Infinite-horizon optimal control ; overtaking optimality ; economic growth ; chattering states
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the Lagrange problem of optimal control defined on an unbounded time interval in which the traditional convexity hypotheses are not met. Models of this form have been introduced into the economics literature to investigate the exploitation of a renewable resource and to treat various aspects of continuous-time investment. An additional distinguishing feature in the models considered is that we do not assume a priori that the objective functional (described by an improper integral) is finite, and so we are led to consider the weaker notions of overtaking and weakly overtaking optimality. To treat these models, we introduce a relaxed optimal control problem through the introduction of chattering controls. This leads us naturally to consider the relationship between the original problem and the convexified relaxed problem. In particular, we show that the relaxed problem may be viewed as a limiting case for the original problem. We also present several examples demonstrating the applicability of our results.
    Type of Medium: Electronic Resource
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