Counterexamples in Optimal Control Theory

Serovaiskii, S. Ya.

doi:10.1515/9783110915532

Cited by 6 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In optimal control theory, there is evidence that singular controls may become local optima or even global optimal solutions (e.g., in time optimal control of rockets [12]). For quantum systems, very few related studies seem to exist.…”

Section: Introductionmentioning

confidence: 99%

Singularities of quantum control landscapes

et al. 2012

View full text Add to dashboard Cite

Quantum control landscape theory was formulated to assess the ease of finding optimal control fields in simulations and in the laboratory. The landscape is the observable as a function of the controls, and a primary goal of the theory is the analysis of landscape features. In what is referred to as the kinematic picture of the landscape, prior work showed that the landscapes are generally free of traps that could halt the search for an optimal control at a suboptimal observable value. The present paper considers the dynamical picture of the landscape, seeking the existence of singular controls, especially of a nonkinematic nature along with an assessment of whether they correspond to traps. We analyze the necessary and sufficient conditions for singular controls to be kinematic or nonkinematic critical solutions and the likelihood of their being encountered while maximizing an observable. An algorithm is introduced to seek singular controls on the landscape in simulations along with an associated Hessian landscape analysis. Simulations are performed for a large number of model finite-level quantum systems, showing that all the numerically identified kinematic and nonkinematic singular critical controls are not traps, in support of the prior empirical observations on the ease of finding high-quality optimal control fields.

show abstract

Section: Introductionmentioning

confidence: 99%

Singularities of quantum control landscapes

et al. 2012

View full text Add to dashboard Cite

show abstract

“…The derivation of (21) is formal in the sense that we assume that an OC

k : [0, \infty) \to double-struckR

exists and gives a finite value

J (k, v) < \infty

; that

k

and the associated solution

v : normalΩ \times double-struckR \to double-struckR

are sufficiently smooth such that the integration by parts in

x

and

t

is valid; that the transversality condition holds. These are nontrivial assumptions. There are simple ODE OC problems where naive application of maximum principles yields the wrong results (see, e.g., Lenhart & Workman, , example 2.1, or Serovaiskii, for various further examples and a thorough discussion) . Thus, it would be desirable to prove the existence of an OC

k

for (5), and to prove that (21) yields all candidates.…”

Section: The Cs Formalismmentioning

confidence: 99%

Optimal fishery with coastal catch

Grass

Uecker²,

Upmann

2019

Natural Resource Modeling

View full text Add to dashboard Cite

In many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite time‐horizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forward–backward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal time‐dependent paths, and their dependence on parameters. We start with some one‐species fishing models, and then extend the analysis to a predator–prey model of the Lotka–Volterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls. Recommedations for Resource Managers Just like ordinary differential equation‐constrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs). These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states. The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a low‐stock initial state, and nonmonotonic (in time) harvesting efforts. Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators.

show abstract

“…While the focus of studies mainly on the model parameters estimation, model behaviour through stability analysis, and model simulation, the use of optimisation-based modeling, i.e., the optimal control framework, has emerged in providing advance analysis towards the disease. Even though that many things can go wrong as pointed out by (Serovaiskii 2004), however, the optimal control theory has positive side in term of methods of solving such problems and practicality in applications (Lenhart & Workman 2007, Alipour 2017. Optimal control analysis allows evaluating various scenarios of pandemic management.…”

Section: Introductionmentioning

confidence: 99%

Controlling COVID-19 spread in Jakarta, Indonesia, using quarantine, testing and medical treatment

Fitri

Bakhtiar

2021

KJS publishes peer-review articles in Mathematics, Computer Sci

View full text Add to dashboard Cite

The SARS-CoV-2 outbreak that started in China created COVID-19 pandemic all around the world. This pandemic is declared as a world health crisis by the World Health Organization in 2020. In response to this pandemic, many countries have been conducting various measures to manage the spread of the disease employing lockdown, contacts tracing, and massive testing. As the vaccine and medicine for this virus are under development, the governments all around the world can only apply non-curative measures. With many considerations, especially in the economic sector, governments seem hesitant to apply extensive control measures and this results in a considerable financial loss. In this paper, a generic mathematical model with thirteen compartments is developed, of which it is equipped with five control measures namely quarantine, active carrier identification, recovered individual identification, past infection identification, and medical treatment. We employ the COVID-19 outbreak in Jakarta as a study case to evaluate a series of control scenarios. Optimal control approach is used to find the best control strategy in managing the pandemic. It is suggested that adding the efforts on testing policy and medical treatment 40 days after the first confirmed infection is the most cost-effective strategy with the number of death decreased as much as 60:21 percent of the death cases under initial control strategy.

show abstract

Counterexamples in Optimal Control Theory

Cited by 6 publications

References 0 publications

Singularities of quantum control landscapes

Singularities of quantum control landscapes

Optimal fishery with coastal catch

Controlling COVID-19 spread in Jakarta, Indonesia, using quarantine, testing and medical treatment

Contact Info

Product

Resources

About