arXiv subjects

Qing-Guo Wang

Publications and source records attributed to Qing-Guo Wang.

4 recordsLinked to original sources

arXiv2026

Automated Synthesis of Lyapunov Functions for Multi-Agent Systems under Jointly Connected Topology

This article investigates the consensus tracking problem of multi-agent systems under jointly connected topology through automated synthesis of Lyapunov functions. Based on the proposed distributed nonlinear control protocol, several consensus criteria for first-order multi-agent systems are established and certified by the construction and synthesis of more general polynomial Lyapunov functions. By employing sum-of-squares decomposition for multivariate polynomials, we can efficiently synthesize polynomial Lyapunov functions to achieve consensus verification in polynomial time, although the widely used quadratic Lyapunov functions do not exist. Moreover, polynomial coupling functions for our proposed protocol are concomitantly generated. Furthermore, the distributed nonlinear control protocol is extended to deal with second-order multi-agent systems, while ensuring second-order consensus verification. Finally, an example is presented to demonstrate the efficacy of our method.

math.OC↗

arXiv2021

Control Design with Guaranteed Transient Performance: an Approach with Polyhedral Target Tubes

In this paper a novel approach is presented for control design with guaranteed transient performance for multiple-input multiple-output discrete-time linear polytopic difference inclusions. We establish a theorem that gives necessary and sufficient conditions for the state to evolve from one polyhedral subset of the state-space to another. Then we present an algorithm which constructs a time-varying output feedback law which guarantees that the state evolves within a time-varying polyhedral target-tube specifying the system's desired transient performance. We present generalisations involving constraints on the control, and a bounded additive disturbance term. Our formulation is very general and includes reference tracking with any desired transient behaviour in the face of disturbances, as specified, for example, by the most popular step response specifications. The approach is demonstrated by an example involving the control of water levels in two coupled tanks.

math.OC↗

arXiv2013

A Statistical Learning Theory Approach for Uncertain Linear and Bilinear Matrix Inequalities

In this paper, we consider the problem of minimizing a linear functional subject to uncertain linear and bilinear matrix inequalities, which depend in a possibly nonlinear way on a vector of uncertain parameters. Motivated by recent results in statistical learning theory, we show that probabilistic guaranteed solutions can be obtained by means of randomized algorithms. In particular, we show that the Vapnik-Chervonenkis dimension (VC-dimension) of the two problems is finite, and we compute upper bounds on it. In turn, these bounds allow us to derive explicitly the sample complexity of these problems. Using these bounds, in the second part of the paper, we derive a sequential scheme, based on a sequence of optimization and validation steps. The algorithm is on the same lines of recent schemes proposed for similar problems, but improves both in terms of complexity and generality. The effectiveness of this approach is shown using a linear model of a robot manipulator subject to uncertain parameters.

math.OC↗

arXiv2013

Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.

eess.SY↗