Computing Reachable Sets of Differential Inclusions

2014 ◽  
pp. 357-365
Author(s):  
Sanja Živanović Gonzalez ◽  
Pieter Collins
Keyword(s):  
Differential Inclusions ◽  
Reachable Sets

Reachable Sets and Integral Funnels of Differential Inclusions Depending on a Parameter

2021 ◽  
Vol 104 (1) ◽  
pp. 200-204
Author(s):  
V. N. Ushakov ◽  
A. A. Ershov
Keyword(s):  
Differential Inclusions ◽  
Reachable Sets

Uncertainty in public health models treated by differential inclusions

2020 ◽  
Vol 11 (04) ◽  
pp. 2050040
Author(s):  
Stanislaw Raczynski
Keyword(s):  
Public Health ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Epidemic Models ◽  
Reachable Sets ◽  
Model Construction ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Epidemic Spread ◽  
Epidemic Modeling

An application of differential inclusions in the epidemic spread models is presented. Some mostly used epidemic models are discussed here, and a brief survey of epidemic modeling is given. Most of the models are some modifications of the Susceptible–Infected–Recovered model. Simple simulations are carried out. Then, we consider the influence of some uncertain parameters. It is pointed out that the presence of some fluctuating model parameters can be treated by differential inclusions. The solution to such differential inclusion is given in the form of reachable sets for model variables. Here, we focus on the differential inclusion application rather than the model construction.

scholarly journals A market model: uncertainty and reachable sets

2015 ◽  
Vol 6 ◽  
pp. A2 ◽  
Author(s):  
Stanislaw Raczynski
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Reachable Sets ◽  
Market Model ◽  
Uncertain Parameters ◽  
Optimal Investment Strategy ◽  
Future Events ◽  
Marketing Variables

Uncertain parameters are always present in models that include human factor. In marketing the uncertain consumer behavior makes it difficult to predict the future events and elaborate good marketing strategies. Sometimes uncertainty is being modeled using stochastic variables. Our approach is quite different. The dynamic market with uncertain parameters is treated using differential inclusions, which permits to determine the corresponding reachable sets. This is not a statistical analysis. We are looking for solutions to the differential inclusions. The purpose of the research is to find the way to obtain and visualise the reachable sets, in order to know the limits for the important marketing variables. The modeling method consists in defining the differential inclusion and find its solution, using the differential inclusion solver developed by the author. As the result we obtain images of the reachable sets where the main control parameter is the share of investment, being a part of the revenue. As an additional result we also can define the optimal investment strategy. The conclusion is that the differential inclusion solver can be a useful tool in market model analysis.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

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