Distributed Adaptive Consensus Disturbance Rejection: a Directed-spanning-tree Perspective

In this paper, we revisit the problem of consensus disturbance rejection for multiagent systems over a digraph, but from a different perspective, i.e., the perspective of a directed spanning tree (DST). When the minimum nonzero real part of the Laplacian eigenvalues is available, we reproduce the sufficient lower bound for a static homogeneous coupling gain in the literature, by exploring a DST structure of the digraph. The major novelty arises when it is shown that by adaptively tuning the coupling gains along a DST, consensus disturbance rejection can be achieved when the above eigenvalue information is not available. Numerical examples on networks of second-order oscillators and UAVs are included to validate the theoretical results. Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Bart De Schutte

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem

Abstract This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov–Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results

A Separation-Based Methodology to Consensus Tracking of Switched High-Order Nonlinear Multiagent Systems

This work investigates a reduced-complexity adaptive methodology to consensus tracking for a team of uncertain high-order nonlinear systems with switched (possibly asynchronous) dynamics. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping methods successfully developed for low-order systems fail to work. Even the adding-one-power-integrator methodology, well explored for the single-agent high-order case, presents some complexity issues and is unsuited for distributed control. At the core of the proposed distributed methodology is a newly proposed definition for separable functions: this definition allows the formulation of a separation-based lemma to handle the high-order terms with reduced complexity in the control design. Complexity is reduced in a twofold sense: the control gain of each virtual control law does not have to be incorporated in the next virtual control law iteratively, thus leading to a simpler expression of the control laws; the power of the virtual and actual control laws increases only proportionally (rather than exponentially) with the order of the systems, dramatically reducing high-gain issues.Accepted Author ManuscriptTeam DeSchutte

A Directed Spanning Tree Adaptive Control Solution to Time-Varying Formations

In this article, the time-varying formation and time-varying formation tracking problems are solved for linear multiagent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated with the digraph. The solution to these problems relies on an approach that generalizes the directed spanning tree (DST) adaptive method, which was originally limited to consensus problems. Necessary and sufficient conditions for the existence of solutions to the formation problems are derived. Asymptotic convergence of the formation errors is proved via graph theory and Lyapunov analysis.</p

Consensus in high-power multiagent systems with mixed unknown control directions via hybrid Nussbaum-based control

This work investigates the consensus tracking problem for high-power nonlinear multiagent systems with partially unknown control directions. The main challenge of considering such dynamics lies in the fact that their linearized dynamics contain uncontrollable modes, making the standard backstepping technique fail; also, the presence of mixed unknown control directions (some being known and some being unknown) requires a piecewise Nussbaum function that exploits the a priori knowledge of the known control directions. The piecewise Nussbaum function technique leaves some open problems, such as Can the technique handle multiagent dynamics beyond the standard backstepping procedure? and Can the technique handle more than one control direction for each agent? In this work, we propose a hybrid Nussbaum technique that can handle uncertain agents with high-power dynamics where the backstepping procedure fails, with nonsmooth behaviors (switching and quantization), and with multiple unknown control directions for each agent.Accepted Author ManuscriptTeam DeSchutte

Adaptive Prescribed Performance Asymptotic Tracking for High-Order Odd-Rational-Power Nonlinear Systems

Practical tracking results have been reported in the literature for high-order odd-rational-power nonlinear dynamics (a chain of integrators whose power is the ratio of odd integers). Asymptotic tracking remains an open problem for such dynamics. This note gives a positive answer to this problem in the framework of prescribed performance control, without approximation structures (neural networks, fuzzy logic, etc.) being involved in the control design. The unknown system uncertainties are first transformed to unknown but bounded terms using barrier Lyapunov functions, and then these terms are compensated by appropriate adaptation laws. A method is also proposed to extract the control terms in a linear-like fashion during the control design, which overcomes the difficulty that virtual or actual control signals appear in a nonaffine manner. A practical poppet valve system is used to validate the effectiveness of the theoretical findings.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Bart De Schutte

A Switching-Based Adaptive Dynamic Programming Method to Optimal Traffic Signaling

The work presented in this paper concerns a switching-based control formulation for multi-intersection and multiphase traffic light systems. A macroscopic traffic flow modeling approach is first presented, which is instrumental to the development of a model-based and switching-based optimization method for traffic signal operation, in the framework of adaptive dynamic programming (ADP). The main advantage of the switching-based formulation is its capability to determine both 'when' to switch and 'which' mode to switch on without the need to use the cycle-based average flow approximation typical of state-of-the-art formulations. In addition, the framework can handle different cycle times across intersections without the need for synchronization constraints and, moreover, minimum dwell-time constraints can be directly enforced to comply with minimum green/red times in each phase. The simulation experiments on a multi-intersection and multiphase traffic light systems are presented to show the effectiveness of the method.Accepted Author ManuscriptTeam DeSchutte