Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State

We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic

A turnpike property for optimal control problems with dynamic probabilistic constraints

In this paper we consider systems that are governed by linear time-discrete dynamics with an initial condition, additive random perturbations in each step and a terminal condition for the expected values. We study optimal control problems where the objective function consists of a term of tracking type for the expected values and a control cost. In addition, the feasible states have to satisfy a conservative probabilistic constraint that requires that the probability that the trajectories remain in a given set F is greater than or equal to a given lower bound. An application are optimal control problems related to storage management systems with uncertain in- and output. We give sufficient conditions that imply that the optimal expected trajectories remain close to a certain state that can be characterized as the solution of an optimal control problem without prescribed initial- and terminal condition. In this way we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics and make a step towards the extension of the turnpike theory to problems with probabilistic constraints

Constrained exact boundary controllability of a semilinear model for pipeline gas flow

While the quasilinear isothermal Euler equations are an excellent model for gas pipeline flow, the operation of the pipeline flow with high pressure and small Mach numbers allows us to obtain approximate solutions by a simpler semilinear model. We provide a derivation of the semilinear model that shows that the semilinear model is valid for sufficiently low Mach numbers and sufficiently high pressures. We prove an existence result for continuous solutions of the semilinear model that takes into account lower and upper bounds for the pressure and an upper bound for the magnitude of the Mach number of the gas flow. These state constraints are important both in the operation of gas pipelines and to guarantee that the solution remains in the set where the model is physically valid. We show the constrained exact boundary controllability of the system with the same pressure and Mach number constraints

Технологические решения для строительства разведочной вертикальной скважины глубиной 2650 метров на газовом месторождении (Красноярский край)

Объектом исследования является разведочная вертикальная скважина глубиной 2650 метров на газовом месторождении (Красноярский край). Целью работы является – спроектировать технологические решения для строительства вертикальной разведочной скважины глубиной 2650 м на газовом месторождении (Красноярский край). Для достижения поставленной цели были поставлены следующие задачи: 1.Спроектировать конструкцию скважины. 2.Спроектировать процессы углубления скважины. 3.Спроектировать процессы заканчивания скважин. 4.Рассмотреть методики совершенствования процесса спуска обсадных колонн. 5.Составить нормативную карту строительства и произвести расчёт сметной стоимости бурения и крепления скважины. 6.Произвести анализ производственной и экологической безопасности.The object of the study is a vertical exploration well with a depth of 2650 meters in a gas field (Krasnoyarsk Territory). The aim of the work is to design technological solutions for the construction of a vertical exploration well with a depth of 2650 m at a gas field (Krasnoyarsk Territory). To achieve this goal, the following tasks were set: 1. Design the well structure. 2. Design well deepening processes. 3. Design well completion processes. 4. Consider methods for improving the process of running casing strings. 5. Draw up a normative construction map and calculate the estimated cost of drilling and well casing. 6. Conduct an analysis of industrial and environmental safety, as well as safety in emergency situations