Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

PID-based with Odometry for Trajectory Tracking Control on Four-wheel Omnidirectional Covid-19 Aromatherapy Robot

Inhalation therapy is one of the most popular treatments for many pulmonary conditions. The proposed Covid-19 aromatherapy robot is a type of Unmanned Ground Vehicle (UGV) mobile robot that delivers therapeutic vaporized essential oils or drugs needed to prevent or treat Covid-19 infections. It uses four omnidirectional wheels with a controlled speed to possibly move in all directions according to its trajectory. All motors for straight, left, or right directions need to be controlled, or the robot will be off-target. The paper presents omnidirectional four-wheeled robot trajectory tracking control based on PID and odometry. The odometry was used to obtain the robot's position and orientation, creating the global map. PID-based controls are used for three purposes: motor speed control, heading control, and position control. The omnidirectional robot had successfully controlled the movement of its four wheels at low speed on the trajectory tracking with a performance criterion value of 0.1 for the IAEH, 4.0 for MAEH, 0.01 for RMSEH, 0.00 for RMSEXY, and 0.06 for REBS. According to the experiment results, the robot's linear velocity error rate is 2%, with an average test value of 1.3 percent. The robot heading effective error value on all trajectories is 0.6%. The robot's direction can be monitored and be maintained at the planned trajectory. Doi: 10.28991/esj-2021-SPER-13 Full Text: PD

Robust Distributed Stabilization of Interconnected Multiagent Systems

Many large-scale systems can be modeled as groups of individual dynamics, e.g., multi-vehicle systems, as well as interconnected multiagent systems, power systems and biological networks as a few examples. Due to the high-dimension and complexity in configuration of these infrastructures, only a few internal variables of each agent might be measurable and the exact knowledge of the model might be unavailable for the control design purpose. The collective objectives may range from consensus to decoupling, stabilization, reference tracking, and global performance guarantees. Depending on the objectives, the designer may choose agent-level low-dimension or multiagent system-level high-dimension approaches to develop distributed algorithms. With an inappropriately designed algorithm, the effect of modeling uncertainty may propagate over the communication and coupling topologies and degrade the overall performance of the system. We address this problem by proposing single- and multi-layer structures. The former is used for both individual and interconnected multiagent systems. The latter, inspired by cyber-physical systems, is devoted to the interconnected multiagent systems. We focus on developing a single control-theoretic tool to be used for the relative information-based distributed control design purpose for any combinations of the aforementioned configuration, objective, and approach. This systematic framework guarantees robust stability and performance of the closed-loop multiagent systems. We validate these theoretical results through various simulation studies

Distributed optimal and predictive control methods for networks of dynamic systems

Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents. We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case. We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents. Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem

Finite-time sliding mode control strategies and their applications

In many engineering applications, faster convergence is always sought, such as manufacturing plants, defence sectors, mechatronic systems. Nowadays, most of the physical systems are operated in a closed-loop environment in conjunction with a controller. Therefore, the controller plays a critical role in determining the speed of the convergence of the entire closed-loop system. Linear controllers are quite popular for their simple design. However, linear controllers provide asymptotic convergence speed, i.e., the actual convergence is obtained when the time reaches an infinitely large amount. Furthermore, linear controllers are not entirely robust in the presence of non-vanishing types of disturbances. It is always important to design robust controllers because of the presence of model imperfections and unknown disturbances in almost all kinds of systems. Therefore, it is necessary to design controllers that are not only robust, but will also provide faster convergence speed. Out of many robust non-linear control strategies, a further development in sliding mode control (SMC) strategy is considered in this thesis because of its simplicity and robustness. There have been many contributions in the SMC field in the last decade. Many existingmethods are available for the SMC design for second-order systems. However, the SMC design becomes extremely complex if the system order increases. Therefore, the first part of this thesis focuses on developing arbitrary-order SMC strategies with a relatively simpler design while providing finite-time convergence. Novel methods are developed with both continuous and discontinuous control structures. The second part of this thesis focuses on developing algorithms to provide even faster convergence speed than that of finite-time convergent algorithms. Some practical applications need strict constraints on time response due to security reasons or to ameliorate the productiveness. For example, a missile or any aerial launch vehicle can be hugely affected by a strong wind gust deviating it from the desired trajectory, thus yielding a significant degree of initial tracking error. It is worth mentioning that the state convergence achieved in SMC during sliding can be either asymptotic or in finite-time, depending on the selection of the surface. Furthermore, it primarily depends on the initial conditions of the states. This provides a motivation to focus on developing SMC controllers where the convergence time does not depend on initial conditions, and a well-defined theoretical analysis is provided in the thesis regarding arbitrary-order fixed-time convergent SMC design. Subsequently, a predefined-time convergent second-order differentiator and observer are proposed. The main advantage of the proposed differentiator is to calculate the derivative of a given signal in fixed-time while the least upper bound of the fixed stabilisation time is equal to a tunable parameter. Similarly, the proposed predefined-time observer is robust with respect to bounded uncertainties and can also be used to estimate the uncertainties. The final part of the thesis is focused on the applications of the proposed algorithms. First of all, a novel third-order SMC is designed for a piezoelectric-driven motion systems achieving better accuracy and control performance. Later on, an experimental validation of the proposed controller is conducted on an induction motor setup. Later, a fixed-time convergent algorithm is proposed for an automatic generation control (AGC) of a multi-area interconnected power system while considering the non-linearities in the dynamic system. The final part is focused on developing fixed-time convergent algorithms in a co-operative environment. The reason for selecting such a system is the presence of the highest degree of uncertainties. To this end, a novel distributed algorithm is developed for achieving second-order consensus in the multiagent systems by designing a full-order fixed-time convergent sliding surface

Swarm Robotics

Collectively working robot teams can solve a problem more efficiently than a single robot, while also providing robustness and flexibility to the group. Swarm robotics model is a key component of a cooperative algorithm that controls the behaviors and interactions of all individuals. The robots in the swarm should have some basic functions, such as sensing, communicating, and monitoring, and satisfy the following properties

Event-Triggered Consensus and Formation Control in Multi-Agent Coordination

The focus of this thesis is to study distributed event-triggered control for multi-agent systems (MASs) facing constraints in practical applications. We consider several problems in the field, ranging from event-triggered consensus with information quantization, event-triggered edge agreement under synchronized/unsynchronized clocks, event-triggered leader-follower consensus with Euler-Lagrange agent dynamics and cooperative event-triggered rigid formation control. The first topic is named as event-triggered consensus with quantized relative state measurements. In this topic, we develop two event-triggered controllers with quantized relative state measurements to achieve consensus for an undirected network where each agent is modelled by single integrator dynamics. Both uniform and logarithmic quantizers are considered, which, together with two different controllers, yield four cases of study in this topic. The quantized information is used to update the control input as well as to determine the next trigger event. We show that approximate consensus can be achieved by the proposed algorithms and Zeno behaviour can be completely excluded if constant offsets with some computable lower bounds are added to the trigger conditions. The second topic considers event-triggered edge agreement problems. Two cases, namely the synchronized clock case and the unsynchronized clock case, are studied. In the synchronized clock case, all agents are activated simultaneously to measure the relative state information over edge links under a global clock. Edge events are defined and their occurrences trigger the update of control inputs for the two agents sharing the link. We show that average consensus can be achieved with our proposed algorithm. In the unsynchronized clock case, each agent executes control algorithms under its own clock which is not synchronized with other agents' clocks. An edge event only triggers control input update for an individual agent. It is shown that all agents will reach consensus in a totally asynchronous manner. In the third topic, we propose three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work concerning event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics which include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain agent parameters. The last topic discusses cooperative stabilization control of rigid formations via an event-triggered approach. We first design a centralized event-triggered formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the trigger condition, event function and trigger behaviour are discussed in detail, and the exponential convergence of the formation system is guaranteed

Router-based network traffic observation by terminal sliding mode control theory

Since the early days of the Internet, network traffic monitoring (NTM) has always played a strategic role in understanding and characterizing users’ activities. Nowadays, with the increased complexity of the Internet infrastructure, applications, and services, this role has become more crucial than ever. The aims of NTM are mainly focused on the three improvements, which include the quality of service (QoS) of the network, optimization of resource usage, and enhancement of security in computer networks. Specifically speaking, firstly, network conditions can be recognized by the network manager with NTM scheme. It provides the complete details about the QoS of networks, such as bandwidth, throughput, propagation delay, link availability, jitter, server memory, database space and etc. Secondly, with NTM being implemented at network nodes, i.e., network gateways, such as routers, or network links, the network traffic that is traversing the network is under online observation. Thereby, the network utilization can be improved by optimizing the resource usage to avoid the network congestions. Thirdly, unauthenticated service or approaches to the server will be identified by regularly monitoring the traffic. The network convention and statistics about the traffic will be known easily which helps to troubleshoot the network. Security events will also be investigated and the entry of the user will be maintained for responsibility. The work in this thesis focuses on the development of an intelligent real-time dynamic router-based network traffic observation (RNTO) by using the terminal sliding-mode theory. The RNTO technique is applied at network gateways, i.e., routers, to estimate the status of the traffic flows at the router level. The aims of the proposed RNTO technique is to estimate the traffic states, such as queue length (QL)in router buffer, average congestion window size (ACwnd), and the queuing dynamics of the additional traffic flows (ATF). The main contributions of the work can be broadly categorized into four parts. First, the problem of router-based network traffic monitoring is formulated as an observer design by using TSM theory for RNTO applications. The proposed TSM observer in the research is a network-based monitoring, which is implemented into the network gateways, i.e., network routers. Different from the static network traffic monitoring methods, the TSM observer is designed by using control methods based on the fluid-flow mathematical model, which represents the traffic dynamics of the interactions in a set of TCP traffic flows through network routers. By considering the time delay and stochastic properties in the data transmission network, the sliding-mode observation strategy is proposed with its high robustness with system parameter uncertainties as well as the external disturbance rejection. Given the natural weakness of chattering in sliding mode control signal, which can affect the system state, the chattering avoiding technique of the proposed TSM observation was utilized by using a smooth control signal for estimating the abnormal dynamics. It does not need any low-pass filler, which will lead to a phase leg. In addition, for the stochastic dynamics of the network traffics, fast transient convergence at a distance from and within a close range of the equilibrium of the traffic dynamics is essential to quickly capture traffic dynamics in network systems. Thus, a fractional term has been considered in the TSM for faster convergence in system states to efficiently estimate the traffic behaviors. Second, the issue of internal dynamics in network observation system is studied by proposing a novel full-order TSM strategy to speed up the convergence rate of the estimation error. In the RNTO scheme, the precise estimation for ACwnd is needed to estimate the queuing dynamics of ATF. However, the estimation error for ACwnd is not available and it converges to origin asymptotically, which results in a long response time in estimation. The proposed novel TSM observer has been designed to drive the estimation error for ACwnd to a defined known area in the finite-time, which can be calculated. Thereby, the estimation error of ACwnd can converge to origin asymptotically within the defined area. This strategy has shortened the response time and improves the estimation accuracy. This further improves the estimation accuracy for ATF. The comparative studies are conducted to evaluate the performance. Third, the issue of algorithm-efficient RNTO is investigated by considering an event triggered sliding-mode observer to reduce the computational load and the communication burden. Instead of the time-driven observation scheme, the control of the sliding mode observer is formulated under the event triggered scheme. The control of the observer is designed to be smooth and is directly applied to estimate the dynamics of the additional traffic flows. The event triggered observation algorithms is developed to reduce the computational load of the network router and the communication resource of output link in the network. Fourth, the problem of global RNTO is addressed by developing a fuzzy TSM observer by using fuzzy theory to achieve global operation under network uncertainties. The existing RNTO schemes are based on the linearization of a certain network conditions, i.e., a fixed number of TCP connections, which is a constant value N. Given the network suffers from time-varying fading, shadowing and interference and the data rate changes over time, the current methods proposed so far might not effectively and accurately monitor and estimate the traffic dynamics under network uncertainties. The T-S fuzzy models are used to model the traffic dynamics of the time-varying data changes in network link resources, i.e. the time-varying number of TCP sections, N(t) in a mathematical model. Based on the T-S fuzzy models, the fuzzy terminal sliding mode observer is established by using the fuzzy logic theory to estimate the states of the network traffic to achieve the global observation performance under the network uncertainties. In the fuzzy terminal sliding mode observer, the control signal is designed to be continuous for application of estimating the additional traffic flows without the low-pass filter. To evaluate the proposed RNTO technique, the networking simulator tool Network Simulator II (NS-II) has been used. The proposed RNTO algorithms are coded and implemented into network routers in NS-II. Numerous simulation scenarios are considered and performed. The comparative studies are also conducted by analyzing the NS-2 results. The results have demonstrated the effectiveness and efficiency of the proposed RNTO algorithms