We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with constraints that incorporate the system dynamics, we comp...
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This work considers Gaussian linear control systems where the goal is to guarantee system-state mean-square stability (i. e., E (parallel to x(t)parallel to(2)) infinity or R -> infinity, and sheds further insight...
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ISBN:
(纸本)9781538647813
This work considers Gaussian linear control systems where the goal is to guarantee system-state mean-square stability (i. e., E (parallel to x(t)parallel to(2)) <= D) while minimizing the traffic rate R between the sensor(s) and the controller. Most existing results either assume zero delay or focus on the asymptotic setting that overlooks the impact of delay. Nonetheless, in practice the communication delay is randomly distributed due to varying channel/network conditions. When the sensor measurement finally arrives at the controller, the age-of-information is thus random. Heuristically, an "old" measurement provides less valuable information than a "young" measurement but the quantitative impact of random delay on the optimal rate-cost tradeoff R*(D) remains an open problem. This work provides the first lower bound R-LB(D) for the random delay setting and designs a simple scheme that leads to a numerically evaluated upper bound R-UB(D). Jointly R-LB(D) and R-UB(D) bracket the optimal tradeoff R*(D). The new R-LB(D) is asymptotically tight when either D -> infinity or R -> infinity, and sheds further insights on how the (random) age of information could impact the performance of a cyber-physical control system.
The aim of this paper is to study first order Mean field games subject to a linearcontrolled dynamics on Rd. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria) as Borel probabil...
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Methods for solving systems of differential equations based on the use of wavelets have become very popular recently. Debeshy wavelets, coiflets were used among others. The disadvantage of such wavelets is that they d...
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Methods for solving systems of differential equations based on the use of wavelets have become very popular recently. Debeshy wavelets, coiflets were used among others. The disadvantage of such wavelets is that they do not have an analytical expression. Therefore, there are great difficulties in integrating and differentiating expressions containing these wavelets. The article presents an algorithm for the numerical solution of a system of differential equations with variable coefficients based on spline-wavelets on a interval. The algorithm presented generalizes the well-known method based on Haar wavelets which are a special case of spline-wavelets. The results of the article are used to analyze the output processes of multi-dimensional non-stationary linear control systems.
The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of th...
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This paper introduces the σ-entropy of an input signal. The considered approach to the analysis of linear control systems is based on using the σ-entropy norm, which is defined as the maximum of the ratio of L2 norm...
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In this paper we show that a complete characterization of the controllability property for linearcontrol system on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the e...
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Methods from learning theory are used in the state space of linear dynamical and controlsystems in order to estimate relevant matrices and some relevant quantities such as the topological entropy. An application to s...
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Methods from learning theory are used in the state space of linear dynamical and controlsystems in order to estimate relevant matrices and some relevant quantities such as the topological entropy. An application to stabilization via algebraic Riccati equations is included by viewing a control system as an autonomous system in an extended space of states and control inputs. Kernel methods are the main techniques used in this paper and the approach is illustrated via a series of numerical examples. The advantage of using kernel methods is that they allow to perform function approximation from data and, as illustrated in this paper, allow to approximate linear discrete-time autonomous and controlsystems from data.
We obtain sufficient conditions for uniform exponential stabilization (with a given exponent) of the zero unperturbed solution to a control system defined by a quasi-linear n-order differential equation by means of st...
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ISBN:
(纸本)9781467399975
We obtain sufficient conditions for uniform exponential stabilization (with a given exponent) of the zero unperturbed solution to a control system defined by a quasi-linear n-order differential equation by means of static output feedback.
The paper suggests the modification of the generalized recursion algorithm of the exact reachable sets computation for the linear discrete dynamic systems. The examples of the finite convex hull search problem and the...
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