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Georgi Smirnov

Publications and source records attributed to Georgi Smirnov.

7 recordsLinked to original sources
arXiv2026

Optimal Control of Hydro-Electric Power Plants with Uncontrolled Spillways

In this paper, we study an optimal control problem for a cascade of hydroelectric power plants with reversible turbines and uncontrolled spillways. The system dynamics are governed by a linear control model subject to path constraints. The aim is to maximize the power production profit while respecting operational restrictions on reservoir water levels. The challenge is the presence of uncontrollable spillways: their discontinuous nature and the fact that they are activated at the state boundary prevent the application of known necessary conditions of optimality. To overcome this, we derive necessary conditions by approximating the original problem through a sequence of standard optimal control problems using exponential penalty functions. The applicability of resulting conditions are illustrated by an example.

math.OC↗
arXiv2024

Towards optimal control of systems with backlash

In this paper we consider time-optimal control problems for systems with backlash. Such systems are described by second order differential equations coupled with restrictions modeling the inelastic shocks. A main feature of such systems is the lack of uniqueness of solution to the Cauchy problem. Here, we introduce approximation systems where the forces during the impact are taken into account. Such approximations are relevant for two reasons. Firstly, we define a set of solutions as limits of the solutions to the approximation systems. This set may be smaller than the set of of the solutions usually considered in the literature. Secondly, such approximations are adequate to derive necessary condition to the time optimal control of interest. To the best of our knowledge, this is the first attempt to derive necessary conditions of optimality for optimal control problems involving systems with backlash.

math.OC↗
arXiv2023

A Maximum Principle for Optimal Control Problems involving Sweeping Processes with a Nonsmooth Set

We generalize a Maximum Principle for optimal control problems involving sweeping systems previously derived in ``Necessary conditions for optimal control problems with sweeping systems and end point constraints'', by de Pinho, Ferreira and Smirnov, Optimization, N. 71, 11, 2022, to cover the case where the moving set may be nonsmooth. Noteworthy, we consider problems with constrained end point. A remarkable feature of our work is that we rely upon an ingenious smooth approximating family of standard differential equations in the vein of that used in ``Optimal Control involving Sweeping Processes'', by de Pinho, Ferreira and Smirnov, Set-Valued Var. Anal 27, 2019.

math.OC↗
arXiv2018

On the Comparison of Context-Free Grammars

In this paper we consider the problem of context-free grammars comparison from the analysis point of view. We show that the problem can be reduced to numerical solution of systems of nonlinear matrix equations. The approach presented here forms a basis for probabilistic comparison algorithms oriented to automatic assessment of of student's answers in computer science.

cs.FL↗
arXiv2017

Explicit bounds for Lipschitz constant of solution to basic problem in calculus of variations

In this paper we present explicit estimate for Lipschitz constant of solution to a problem of calculus of variations. The approach we use is due to Gamkrelidze and is based on the equivalence of the problem of calculus of variations and a time-optimal control problem. The obtained estimate is used to compute complexity bounds for a path-following method applied to a convex problem of calculus of variations with polyhedral end-point constraints.

math.OC↗
arXiv2017

Explicit bounds for solutions to optimal control problems

In this paper we present explicit bounds for optimal control in a Lagrange problem without end-point constraints. The approach we use is due to Gamkrelidze and is based on the equivalence of the Lagrange problem and a time-optimal problem for diferential inclusions.

math.OC↗