scholarly journals Multivariate Optimal Control with Payoffs Defined by Submanifold Integrals

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 893 ◽  
Author(s):  
Andreea Bejenaru ◽  
Constantin Udriste
Keyword(s):  
Optimal Control ◽  
Formal Analysis ◽  
Linear Connection ◽  
Riemannian Structure ◽  
State Variables ◽  
Riemann Curvature Tensor ◽  
Local Coordinates ◽  
Geometric Elements ◽  
Cost Functionals

This paper adapts the multivariate optimal control theory to a Riemannian setting. In this sense, a coherent correspondence between the key elements of a standard optimal control problem and several basic geometric ingredients is created, with the purpose of generating a geometric version of Pontryagin’s maximum principle. More precisely, the local coordinates on a Riemannian manifold play the role of evolution variables (“multitime”), the Riemannian structure, and the corresponding Levi–Civita linear connection become state variables, while the control variables are represented by some objects with the properties of the Riemann curvature tensor field. Moreover, the constraints are provided by the second order partial differential equations describing the dynamics of the Riemannian structure. The shift from formal analysis to optimal Riemannian control takes deeply into account the symmetries (or anti-symmetries) these geometric elements or equations rely on. In addition, various submanifold integral cost functionals are considered as controlled payoffs.

Mathematical approaches for optimization of dengue fever dynamics

2019 ◽  
Vol 10 (02) ◽  
pp. 1950006
Author(s):  
Didar Murad ◽  
Noor Badshah ◽  
Muhammad Ali Syed
Keyword(s):  
Optimal Control ◽  
Dengue Fever ◽  
Low Cost ◽  
State Variables ◽  
Control Variables ◽  
Vector Population ◽  
Existence Of Optimal Control ◽  
And Control

Background and Objective: For dengue outbreak prevention and vectors reduction, fundamental role of control parameters like vaccination against dengue virus in human population and insecticide in mosquito population have been addressed theoretically and numerically. For this purpose, an existing model was modified to optimize dengue fever. Methodology: Using Pontryagin’s maximum principle, the dynamics of infection for the optimal control problem was addressed, further, defined cost functional, established existence of optimal control, stated Hamiltonian for characterization of optimization. Results: Numerical simulations for optimal state variables and control variables were performed. Conclusion: Our findings demonstrate that with low cost of control variables, state variable such as recovered population increases gradually and decrease other state variables for host and vector population.

scholarly journals Balancing the formal and the informal in user-centred design

2021 ◽  
Author(s):  
Michael D Harrison ◽  
Paolo Masci ◽  
José Creissac Campos
Keyword(s):  
Formal Methods ◽  
Systematic Approach ◽  
Formal Analysis ◽  
Interactive Systems ◽  
User Evaluation ◽  
Analysis Techniques ◽  
User Centred Design ◽  
Early Design Stages ◽  
Cooperative Evaluation

Abstract This paper explores the role of formal methods as part of the user-centred design of interactive systems. An iterative process is described, developing prototypes incrementally, proving user-centred requirements while at the same time evaluating the prototypes that are executable forms of the developed models using ‘traditional’ techniques for user evaluation. A formal analysis complements user evaluations. This approach enriches user-centred design that typically focuses understanding on context and producing sketch designs. These sketches are often non-functional (e.g. paper) prototypes. They provide a means of exploring candidate design possibilities using techniques such as cooperative evaluation. This paper describes a further step in the process using formal analysis techniques. The use of formal methods provides a systematic approach to checking plausibility and consistency during early design stages, while at the same time enabling the generation of executable prototypes. The technique is illustrated through an example based on a pill dispenser.

scholarly journals Specific and Complete Local Integration of Patterns in Bayesian Networks

2017 ◽  
Author(s):  
Martin Biehl ◽  
Takashi Ikegami ◽  
Daniel Polani
Keyword(s):  
Dynamical Systems ◽  
Lower Bound ◽  
Bayesian Networks ◽  
Upper Bound ◽  
Formal Analysis ◽  
Special Role ◽  
Local Integration

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the i-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.

Role of pine wilt disease based on optimal control strategy at multiple scales: A case study of Korea

2021 ◽  
Vol 46 (4) ◽  
Author(s):  
Muhammad Ozair ◽  
Takasar Hussain ◽  
Kashif Ali Abro ◽  
Sajid Jameel ◽  
Aziz Ullah Awan
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Multiple Scales ◽  
Pine Wilt Disease ◽  
Wilt Disease ◽  
Optimal Control Strategy ◽  
Pine Wilt

An Input-Output Optimal Control Model under Uncertain Influence and its Solution

2012 ◽  
Vol 433-440 ◽  
pp. 2974-2979
Author(s):  
Shu Rong Li ◽  
Feng Wang ◽  
Xiao Yu He
Keyword(s):  
Optimal Control ◽  
Coefficient Matrix ◽  
Control Model ◽  
Chance Constrained Programming ◽  
State Variables ◽  
Input Output ◽  
Bound Constraints ◽  
Uncertain Model ◽  
Calculation Results ◽  
Constrained Programming

An input-output optimal control model is established under uncertain influence in environment. The objective function, terminal constraint of state variables and bound constraints of control variables are considered with fuzziness. The direct consumption coefficient matrix and investment coefficient matrix are regarded as stochastic variables. Membership function and chance constrained programming are applied to convert the uncertain model to a definite one. Penalty function and Particle Swarm Optimization are used to solve the model. The calculation results of an example demonstrate that the uncertain model has more practical value to decision makers compared to a definite one.

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