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European control Conference (ECC)

作者： Boris Polyak Andrey Tremba Ya. Z. Tsypkin Laboratory of Adaptive and Robust Systems Institute of Control Sciences Moscow Russia

ISBN: (数字)9783907144022

ISBN: (纸本)9781728188133

We focus on finding sparse and least-ℓ 1 -norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for underdetermined equations can be applied successively for such problems. We demonstrate the approach for pendulum control and inverted pendulum stabilization.

关键词： Mathematical model Newton method Linear programming Optimal control Optimization Heuristic algorithms Approximation algorithms

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Quadratic Stabilization of Bilinear control systems Subjected to Exogenous Disturbances*

Quadratic Stabilization of Bilinear Control Systems Subjecte...

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European control Conference (ECC)

作者： Mikhail V. Khlebnikov Laboratory of Adaptive and Robust Systems V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Moscow Russia

ISBN: (数字)9783907144022

ISBN: (纸本)9781728188133

We consider the design problem for bilinear control systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabilizability ellipsoid and domain of stabilizability for bilinear control systems is proposed and its efficiency is proved. The main tools are the linear matrix inequality technique and the apparatus of quadratic Lyapunov functions. This simple yet general approach is of great potential; for instance, it can be generalized to the discrete-time case, and to the various robust statements of the problem.

关键词： Ellipsoids Linear matrix inequalities Nonlinear systems Trajectory Lyapunov methods Uncertainty

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Quadratic Stabilization of Discrete-Time Bilinear control systems Subjected to Exogenous Disturbances ⁎

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IFAC-PapersOnLine 2020年第2期53卷 4899-4903页

作者： Mikhail V. Khlebnikov Laboratory of Adaptive and Robust Systems V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences 65 Profsoyuznaya str. Moscow 117997 Russia

We consider the design problem for discrete-time bilinear control systems subjected to arbitrary bounded exogenous disturbances. A procedure for the construction of the stabiliz-ability ellipsoids and stabilizability domain for discrete-time bilinear control systems is proposed and its efficiency is proved. The main tools are the linear matrix inequality technique and the apparatus of quadratic Lyapunov functions. This simple yet general approach is of great potential; for instance, it can be generalized to the various robust statements of the problem.

关键词： Discrete-time bilinear systems bounded exogenous disturbances quadratic Lyapunov functions linear feedback stabilizability ellipsoid stabilizability domain linear matrix inequalities

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Tracking Problem for Linear control systems: The Invariant Ellipsoid Approach

Tracking Problem for Linear Control Systems: The Invariant E...

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International Conference on control, Automation and systems ( ICCAS)

作者： Mikhail V. Khlebnikov Laboratory of Adaptive and Robust Systems V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences 65 Profsoyuznaya str. Moscow Russia

In this talk, a simple yet universal approach to the tracking problem for linear control systems via linear static combined feedback is proposed. The approach is based on the invariant ellipsoid concept and LMI technique, where the optimal control design reduce to finding the minimal invariant ellipsoid for the closed-loop system. With such an ideology, the control design problem directly reduces to a semidefinite programming and one-dimensional minimization. Another attractive property of the proposed approach is that it is equally applicable to discrete-time control systems. The efficacy of the technique is illustrated via a benchmark problem.

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Upper Estimates of the Deviations in Linear Dynamical systems Subjected to Uncertainty

Upper Estimates of the Deviations in Linear Dynamical System...

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International Conference on control, Automation, Robotics and Vision

作者： Mikhail Khlebnikov Laboratory of Adaptive and Robust Systems V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences Moscow Russia

In this talk, the linear dynamical system subjected to uncertainty in the system matrix is considered. Using the linear matrix inequality technique we obtain the upper bounds for the deviations in linear systems. An LMI-based stabilizing feedback procedure is proposed which guarantees "as small as possible" deviations. The results of numerical simulations demonstrate the low conservatism of the obtained bounds.

关键词： linear dynamical systems deviations uncertainty robust stability LMIs

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Non-monotone behavior of the heavy ball method

arXiv

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arXiv 2018年

作者： Danilova, Marina Kulakova, Anastasiya Polyak, Boris Institute of Control Sciences RAS Laboratory of Adaptive and Robust Systems Profsoyuznaya 65 Moscow117342 Russia Moscow Institute of Physics and Technology Department of Control and Applied Mathematics Institutskiy per. 9 Dolgoprudniy141700 Russia

We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the accelerated unconstrained optimization method | the Heavy Ball method. We explain non-standard behavior of the method discovered in practical applications. In addition, such non-monotonicity complicates the correct choice of the parameters in optimization methods. We propose to overcome this diffiulty by introducing new Lyapunov function which should decrease monotonically. By use of this function convergence of the method is established under less restrictive assumptions (for instance, with the lack of convexity). We also suggest some restart techniques to speed up the method's convergence. Copyright © 2018, The Authors. All rights reserved.

关键词： Lyapunov functions

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control of Linear systems Subjected to Exogenous Disturbances: Combined Feedback

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IFAC-PapersOnLine 2016年第13期49卷 111-116页

作者： Khlebnikov, Mikhail V. Laboratory of Adaptive and Robust Control Systems Institute of Control Science Russian Academy of Sciences Profsoyuznaya 65 Moscow Russia

A new approach to rejection of exogenous disturbances in linear control systems via static combined feedback is proposed. Namely, in addition to static linear state feedback, we introduce a linear feedback from the components of exogenous disturbances whose instantaneous values are assumed to be known. The control design is based on the technique of linear matrix inequalities, and the proposed simple approach leads to a convex minimization problem. Moreover, a new approach to the design of sparse combined feedback in linear control systems is proposed; it can be interpreted as reduction of the control resource required to handling the system. © 2016

关键词： Linear matrix inequalities Linear control systems Linear systems State feedback Combined feedbacks Convex minimization Exogenous disturbances Instantaneous value Invariant ellipsoid Linear feedback Linear state feedback Simple approach

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Tracking problem for dynamical systems with exogenous and system disturbances

Tracking problem for dynamical systems with exogenous and sy...

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International Conference on System Theory, control, and Computing (ICSTCC)

作者： Kirill O. Zheleznov Mikhail V. Khlebnikov Laboratory of Adaptive and Robust Systems Institute of Control Sciences RAS Moscow Russia

ISBN: (纸本)9781509027217

In this paper, tracking problem for linear control system with exogenous and system disturbances is considered. The source of system and exogenous disturbances is the same vector signal. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called bounding ellipsoid is designed. Effectiveness of proposed approach in comparison with conventional method is shown on an example task from COMPleib.

关键词： Ellipsoids Linear matrix inequalities control systems robustness Optimization Libraries Lyapunov methods

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adaptive Mirror Descent Algorithm for the Minimization of Expected Cumulative Losses Driven by a Renewal Process

Adaptive Mirror Descent Algorithm for the Minimization of Ex...

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European control Conference

作者： Alexander Nazin Svetlana Anulova Andrey Tremba Pavel Shcherbakov Ya.Z. Tsypkin Laboratory of Adaptive and Robust Systems V.A. Trapeznikov Institute of Control Sciences RAS Laboratory of Statistical Analysis and Information Processing in Control Systems V.A. Trapeznikov Institute of Control Sciences RAS

ISBN: (纸本)9781467371605

The problem considered in this paper is the minimization of expected cumulative losses in a stochastic system. The losses over time horizon are formed by the values of an unknown loss function at the consecutive jump times of a renewal process. The loss is assumed to be a convex function of a vector parameter, and the only available information is represented by an oracle which provides stochastic subgradients of the loss function. The control objective is to minimize the expected cumulative loss over a given convex compact set. We propose an adaptive mirror descent algorithm and prove an explicit upper bound for the related regret, which is the difference between the expected cumulative losses and the minimum. Finally, to exemplify the efficiency of the method, we consider the problem of minimization of the expected cumulative losses over the standard simplex by handling a stream of losses arriving by the Erlang process, and we discuss the simulation results.

关键词： Convex function Renewal descent Mirrors

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Quadratic image of a ball: Towards efficient description of the boundary

Quadratic image of a ball: Towards efficient description of ...

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International Conference on System Theory, control, and Computing (ICSTCC)

作者： Boris Polyak Pavel Shcherbakov Mikhail Khlebnikov Laboratory of Adaptive and Robust Control Systems Russian Academy of Sciences Moscow Russia

We propose a simple efficient machinery for computing “nearly exact” boundary of the image of euclidean ball under multidimensional quadratic mapping. It is based on necessary conditions for a point to be mapped to the boundary. Several special cases are considered, the results of numerical simulations are presented, in particular, as applied to multiobjective optimization and Pareto set discovery.

关键词： Generators Symmetric matrices Eigenvalues and eigenfunctions Transmission line matrix methods Equations Approximation methods Vectors

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