Non-Lyapunov stability of the fractional-order time-varying delay systems

U ovom radu, kriterijumi stabilnosti na konačnom vremenskom intervalu su prošireni na nelinearne nehomogene perturbovane sisteme necelobrojnog reda koji sadrže višestruka vremenski promenljiva kašnjenja. Dobijeni su dovoljni uslovi stabilnosti za sisteme necelog reda sa višestrukim vremenskim kašnjenjima korišćenjem generalizovanog i klasičnog Gronwallovog pristupa. Numerički primer je dat u cilju ilustracije značaja dobijenog rezultata.In this paper, the finite-time stability criteria are extended to nonlinear nonhomogeneous perturbed fractional-order systems including multiple time-varying delays. The sufficient conditions of a stability for the fractional systems with multiple time delays are obtained by using the generalized and classical Gronwall's approach. A numerical example is presented to illustrate the validity of the obtained result

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters

PID controller design and tuning in networked control systems

Networked control systems (NCS) are distributed real-time computing and control systems with sensors, actuators and controllers that communicate over a shared medium. The distributed nature of NCS and issues related to the shared communication medium pose significant challenges for control design, as the control system no longer follows the rules of classical control theory. The main problems that are not well covered by the traditional control theory are varying time-delays due to communication and computation, and packet losses. During recent years, the control design of NCS and varying time-delay systems has been extensively researched. This investment has provided us with new results on stability. Often the proposed methods and solutions are far too complex for industrial use, especially if wireless automation applications are considered. The algorithms are computationally heavy, possibly requiring complete information from say, a network of hundreds or thousands of nodes. In the wireless case this is not feasible. The above justifies the use and research of simple controller structures and algorithms for NCS. Despite the growing interest towards more advanced control algorithms, the Proportional-Integral-Derivative (PID) controller still has a dominant status in the industry. Nevertheless, using PID for NCS has not been thoroughly investigated, especially with regard to controller tuning. This thesis proposes several PID tuning methods, which provide robustness against the challenges of NCS, namely varying time-delays (jitter) and packet loss. The doctoral thesis consists of a summary and eight publications that focus on the PID controller design, tuning and experimentation in NCS. The thesis includes a literature review of recent stability and control design results in NCS, a summary of publications and the original publications. The control design methods applied in the publications are also reviewed. In the thesis, several new methods for PID tuning in NCS are proposed. To make the methods usable, a PID tuning tool that implements one of the tuning methods is also developed. In order to verify the results of control design with real processes, the thesis suggests using the MoCoNet platform developed at the Helsinki University of Technology, Finland. The platform provides the tools for remote laboratory experiments in NCS settings. The results of the thesis indicate that the PID controller is well suited for NCS provided that the properties of the integrated communication and control system are taken into account in the tuning phase