Optimal Control Problem for Switched System with the Nonsmooth Cost Functional

We examine the relationships between lower exhausters, quasidifferentiability (in the Demyanov and Rubinov sense), and optimal control for switching systems. Firstly, we get necessary optimality condition for the optimal control problem for switching system in terms of lower exhausters. Then, by using relationships between lower exhausters and quasidifferentiability, we obtain necessary optimality condition in the case that the minimization functional satisfies quasidifferentiability condition

Geometry in structured optimisation problems

In this thesis, we start by providing some background knowledge on importance of convex analysis. Then, we will be looking at the Demyanov-Ryabova conjecture. This conjecture claims that if we convert between finite families of upper and lower exhausters with the given convertor function, the process will reach a cycle of length at most two. We will show that the conjecture is true in the afflinely independent special case, and also provide an equivalent algebraic reformulation of the conjecture. After that, we will generalise the outer subdifferential construction for max type functions to pointwise minima of regular Lipschitz functions. We will also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential. Lastly, we will address the question of what kind of dimensional patterns are possible for the faces of general closed convex sets.  We show that for any finite increasing sequence of positive integers, there exist convex compact sets which only have faces with dimensions from  this prescribed  sequence. We will also discuss another approach to dimensionality by considering  the dimension of the union of all faces of the same dimension. We will demonstrate that the problems arising from this approach are highly nontrivial by providing some examples of convex sets where the sets of extreme points have fractal dimensions

Analysis of Control System of Fuel Combustion in Boilers with Oxygen Sensor

The method of fuel quality control is considered, which is based on the using of the oxygen sensor (without sensors of incomplete fuel combustion products). An algorithm for the electric drive of a fan is proposed, which is based on a step changing in the rotation speed. The choice of broadband oxygen sensor as a basis for the development of a fuel combustion control system is determined. In the course of experimental studies, the possibility of reconstructing the boiler by replacing a burner with an installed control system was demonstrated. The commissioning works were carried out with the installed system, the optimum operating conditions of the boiler were determined (with the formation of CO in the flue gases at a minimum level <50 ppm). The technical characteristics of the boiler operation under different loads (from 10 % to 100 %) are considered. Ecological and economic analysis of the developed fuel combustion control system was carried out