Andrey Polyakov

Fixed-time Consensus Algorithm for Multi-agent Systems with Integrator Dynamics

Abstract The paper addresses the problem of exact average-consensus reaching in a prespecified time. The communication topology is assumed to be defined by a weighted undirected graph and the agents are represented by integrators. A nonlinear control protocol which ensures a finite-time convergence is proposed. With the designed protocol, any a priori specified convergence time can be guaranteed regardless of the initial conditions.

Brief paper: Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control

A new sliding mode control design algorithm for a linear and a class of nonlinear quasi-Lipschitz disturbed system is presented. It is based on the appropriate selection of the sliding surface via invariant ellipsoid method. The designed control guarantees minimization of unmatched disturbances effects to system motions in a sliding mode. The obtained theoretical results are approved by numerical simulations.

Output stabilization of time-varying input delay systems using interval observation technique

The output stabilization problem for a linear system with an unknown bounded time-varying input delay is considered. The interval observation technique is applied in order to obtain guaranteed interval estimate of the system state. The procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special Silvesters equation. The interval predictor is introduced in order to design a linear stabilizing feedback. The control design procedure is based on Linear Matrix Inequalities (LMI). The theoretical results are supported by numerical simulations and compared with a control design scheme based on a Luenberger-like observer.

New radiocarbon dates and a review of the chronology of prehistoric populations from the Minusinsk Basin, Southern Siberia, Russia

The results are presented of a new program of radiocarbon dating undertaken on 88 human skeletons. The individuals derived from Eneolithic to Early Iron Age sites?Afanasievo, Okunevo, Andronovo (Fedorovo), Karasuk, and Tagar cultures--in the Minusinsk Basin of Southern Siberia. All the new dates have been acquired from human bone, which is in contrast to some of the previous dates for this region obtained from wood and thus possibly unreliable due to old-wood effects or re-use of the timber. The new data are compared with the existing 14C chronology for the region, thereby enabling a clearer understanding to be gained concerning the chronology of these cultures and their place within the prehistory of the Eurasian steppes.

Nonlinear fixed-time control protocol for uniform allocation of agents on a segment

The paper addresses the problem of row straightening of agents via local interactions. A nonlinear control protocol that ensures finite-time equidistant allocation on a segment is proposed. With the designed protocol, any settling time can be guaranteed regardless of the initial conditions. A robust modification of the control algorithm based on sliding mode control technique is presented. The case of multidimensional agents is also considered. The theoretical results are illustrated via numerical simulations.

Finite-time Stabilization Using Implicit Lyapunov Function Technique

The Implicit Lyapunov Function (ILF) method for finite-time stability analysis is introduced. The control algorithm for finite-time stabilization of a chain of integrators is developed. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The robustness of the finite-time control algorithm with respect to system uncertainties and disturbances is studied. The new high order sliding mode (HOSM) control is derived as a particular case of the developed finite-time control algorithm. The settling time estimate is obtained using ILF method. The algorithm of practical implementation of the ILF control scheme is discussed. The theoretical results are supported by numerical simulations.

Fixed-time stabilization of linear systems via sliding mode control

The paper presents some new sliding mode control algorithms for uncertain linear plants. The first class of controllers provide global asymptotic stability of the closed-loop system and allow to adjust a guaranteed convergence time of system trajectories into selected neighborhood of the origin independently on domain of initial system states. The design procedure essentially uses block reduction principles and finite-time attractivity properties for polynomial switching surface. The second class of controllers is meant to guarantee global finite-time stability of the closed-loop system with globally bounded settling-time function. The control design algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

Disruption of substrate binding site in E. coli RNA polymerase by lethal alanine substitutions in carboxy terminal domain of the β subunit

Alanine substitution of four amino acids in two evolutionarily conserved motifs, PSRM and RFGEME, near the carboxy terminus of the β subunit of E. coli RNA polymerase results in a dramatic loss of the enzymes affinity to substrates with no apparent effect on the maximal rate of the enzymatic reaction or on binding to promoters. The magnitude and selectivity of the effect suggest that the mutations disrupt the substrate binding site of the active center.

On settling time function and stability of vector relay systems

The paper addresses the problem of discovering the necessary and sufficient stability conditions of vector relay systems and studying the settling time function of this system. It shows that this function is piecewise linear in some cases and the linearity domains of this function are some convex cones. This fact helps to prove that the existence of the piecewise linear Lyapunov function for such vector relay system is a criterion of its stability. Some theoretical results are supported by numerical example.

Fixed-Time Stabilization via Second Order Sliding Mode Control

Abstract The paper addresses the finite-time stabilization problem with possible predefining of the convergence time independently on the initial conditions. The corresponding extension of finite-time stability concept is called by fixed-time stability. The second order sliding mode control algorithm provided fixed-time stabilization of the multi-input linear control system is presented. Theoretical results are supported by numerical simulations.