An interconnected system is composed of multiple well-defined self-contained subsystems that interact among them and that together create collective behaviours. We can find many examples of interconnected systems in real life. Ranging from biological systems, such as the growth and interaction of populations in diverse and spatially distributed environments, to electric grids connecting power-generating sources, buildings and infrastructures in a country. When studying interconnected systems, a fundamental and natural question is how the properties and characteristics of the individual subsystems and the way they are connected relate to the collective behaviour of the complete system. That is the driving question of the present dissertation. Given that interconnected systems can be found in a wide variety of contexts, their representation and specific research interests can be equally varied. Because of this, it is impossible to answer the aforementioned question uniquely for all interconnected systems, and specific cases must be considered. In this dissertation, we consider two types of interconnected systems: a general class of uncertain multiple-input-multipleoutput (MIMO) systems, and agent-based opinion formation models. The investigation of uncertain MIMO interconnected systems is focused on providing topology-independent conditions for robust stability. The primary motivation for this approach is that, in real systems, it is costly or even impossible to have complete and accurate information on the network topology and subsystem parameters and dynamics. However, it is of critical interest to guarantee the system’s stability. Therefore we need stability conditions that require only partial information about the network and the subsystems to ensure the system’s stability. By studying these systems both in the time and frequency domain, we are able to provide conditions thatmeet these requirements. As for agent-based opinion formation models, we assume that each individual (or agent) in a population has an opinion about a statement. By exchanging opinions among themselves, the agents update their own internal opinion, resulting in a collective dynamic of opinion evolution. When studying these systems, the interests shifts from stability conditions, to a characterisation of the relation between the agents’ individual traits and qualitative properties of the opinion distribution in the population. Several techniques and approaches to analyse opinion formation models are proposed and applied to multiple models, one of which is new to this dissertation. The collective study of the previously mentioned interconnected systems requires the use of multiple and diverse analysis techniques and approaches, from analytical methods based on the Nyquist criterion, Bauer-Fike theorem, and Lyapunov functions to qualitative and numerical analysis techniques like histograms and binomial proportion confidence intervals. It is our hope that some of the presented results, methods, or ideas may advance the knowledge frontier in this scientific field, sparkle new research directions, and either directly or indirectly prove some value to society.

Automation is playing an increasingly important role in today’s society and is revolutionising nearly all industries. In this thesis, the helicopter industry is considered. Helicopters are complex systems capable of Vertical Take-Off and Landing (VTOL). Many companies and organisations are now looking to automate VTOL vehicles in order to break through the urban air mobility market. In order to transport individuals, strict safety regulations have to be adhered to. The goal of this thesis is therefore to address the event of engine failure of a helicopter. In the case of engine failure, a helicopter enters a manoeuvre, called autorotation, in order to safely land. To tackle this problem, a port-Hamiltonian (PH) approach is taken. Within the PH framework, energy transfers between system nodes are defined. By controlling the flow of energy between these nodes, control of the vehicle is possible. This is done by shaping the energy of the system through the use of Passivity-Based Control (PBC). Prior work on the topic of helicopter control using PBC has only been carried out on pointmass models. In order to understand why that is the case, this thesis attempts to derive the PH formulation directly from the Newtonian flight mechanics. It was found that doing so is not possible due to the presence of non-passive terms. These originate from the Blade Element Theory (BET), which is necessary to calculate the thrust and torque of the main rotor. A novel analytical tuning method has also been developed in order to minimise the rise-time and oscillations of the time-response for a PBC. This tuning method has been implemented on a 3-Degrees-of-Freedom (DoF) point-mass model. However, the degree of underactuation of the 6-DoF model has proven to be a limitation for this tuning method. Instead, the 6-DoF was tuned manually. The two models were verified against flight data of the Bo105 helicopter in powered flight. Finally, the first step of the autorotation manoeuvre has been performed. Further work is required to complete the manoeuvre.

Recent studies in game-theory provided ways to steer multi-agent games to their Nash equilibrium by means of a decentralized approach. However, these approaches have not considered the internal dynamics of the individual agents. This thesis work provides decentralized control methods to account for these internal dynamics whilst ensuring that the overall system still reaches the Nash equilibrium.

Combined chemo-radiation treatments are often used to enhance tumor cell kill, with respect to their separate treatments. Currently, chemo-radiation therapy treatments are prescribed as a separately optimized radiotherapy treatment with the addition of a generic chemotherapy regimen. The dosing of the combined therapies is mostly based on clinical experience. Hence there is a clear need for the optimization of dosing for combined chemo-radiation therapy treatments. The goal of this thesis is to propose novel approaches to optimize cancer treatment efficiency when combining chemotherapy and radiotherapy by using control-theoretical methods as well as radiation therapy models. A positive switched system is a dynamic system consisting of a set of Metzler state-space matrices and a specific switching law, which determines when and how to switch between the subsystems. Positive switched systems seem particularly appropriate to model cancer evolution under different treatments, and therefore to determine optimal treatment scheduling. They are used to model the effect of combined chemo-radiation treatments, thus enabling the systematic design of optimal therapy planning. The proposed model is especially appropriate for heterogeneous tumors, since it describes the impact of therapies on different tumor cell lines, and includes the possibility of mutations. Metastases are also included since the model considers separate tumor compartments, and the possibility of migrations between compartments are modeled as well. Undesired consequences due to toxicities are incorporated, and an upper bound can be set to limit the possible damage. A clinical dataset was obtained from the Erasmus MC, which was used to validate chemotherapy-alone model outcomes. Combined chemo-radiation treatments were also developed for a set of initial tumors. The model shows promising applications for cancer treatment design. The use of positive switched systems for combined chemo-radiation treatments is a new approach to obtain optimal drug usage and radiation fractionation schemes for each body compartment. The achieved findings could have a significant impact on effective treatment planning by choosing optimal drug durations or by using radiotherapy in combination with chemotherapy, for instance, to target certain chemotherapy-resistant areas, to achieve tumor control with minimal side effects.

This work presents a decentralized optimization conflict resolution method based on a novel Alternating Directions Method of Multipliers (ADMM) variant and model predictive control (MPC). The variant, titled Online Adaptive Alternating Direction Method of Multipliers (OA-ADMM) aims to unify the application of ADMM to online systems, i.e. systems where fast and adaptive real-time optimization is crucial, into one framework. OA-ADMM introduces two user-designed functions: the similarity function (a forgetting factor between two time steps of the online system) and the adaptation function (adjusting the penalty parameters between updates). The similarity function is what allows OA-ADMM to be applied to online systems where conventional optimization is too slow; the adaptation function allows the user to adjust the online feasibility of the system. We prove convergence in the static case and give requirements for online convergence. Combining OA-ADMM and MPC allows for robust decentralized motion planning and control that seamlessly integrates decentralized conflict resolution, instead of using separate subsystems or hierarchical optimization. The additional robustness is achieved by using the adaptation function of OA-ADMM as an additional safety measure, allowing the prioritization of certain constraints for (nearly) unsafe states, whilst the similarity function allows optimization at the desired control frequency. This method is compared with convention ADMM in Matlab, resulting in significant improvements in robustness and conflict resolution speed. Finally, we compare our OA-ADMM and MPC based decentralized conflict resolution method against conventional decentralized conflict resolution methods in the CARLA vehicle simulator. The results show that the OA-ADMM based method has improved performance, safety, robustness, and generality compared with traditional methods. The method also has fewer requirements in terms of prior knowledge (e.g., the geometry of the intersection), making it usable in almost any situation.

Decentralized control and estimation are both active research areas in the field of systems and control. A new approach to these topics utilizes graph theory to characterize inter-agent communication as a graph that, in this thesis, can have time-varying topology. This approach has been named "network-decentralized" and the use of network-decentralized control and estimation can enable multi-agent systems to achieve tasks in low information environments. In this thesis a novel network-decentralized control algorithm is proposed to enable collision avoidance and formation producing behavior in a multi-agent system. Additionally, a network-decentralized estimation algorithm is also proposed that is combined with the network-decentralized control approach yielding a first of its kind network-decentralized network-estimated control algorithm. A multitude of simulation environments are developed to test the algorithm in a 2-D holonomic multi-agent environment and a parameter tuning method is presented. Strong performance is shown in 2-D with collision avoidance guarantees, at the cost of difficult to tune parameters. The use of holonomic agents in 2-D is consistent with most research in decentralized control and estimation. Since this type of agent is common, this thesis extends its work to the 3-D non-holonomic agent case in an attempt to help characterize how accurate, scalable, and useful existing decentralized research is for real world applications. To develop the network-decentralized algorithm to this point, it is first expanded to the holonomic 3-D case where it is further tested in newly developed simulation environments, where again, collision avoidance guarantees are provided. A novel free-space metric is introduced which allows for tests to be compared across dimensions (eg: 2-D and 3-D) and also yields addition insight as to when parameter-performance breakdown will occur. For the extension of the algorithm to a non-holonomic vehicle in 3-D a suitable quadcopter platform is designed. In addition, the Delft Center for Systems and Control (DCSC) Distributed Robotics Lab is re-designed and completely virtualized to allow for students to easily access lab resources, such as motion capture (MoCap) information, quadcopter test-code environments, and documentation all in one location. A first-principles based system identification process is presented and used to identify the designed quadcopter platform so that a suitable controller can be found for in-lab use. Two quadcopter simulation environments are developed to allow for the design of hover-envelope controllers based on identified parameters. Since the DCSC department was unable to acquire multiple physical vehicles for swarm testing the system identification process and quadcopter simulation environments are validated against the test results from a single physical quadcopter in the newly designed lab environment. A more comprehensive multi-agent implementation of the collision avoidance portion of the algorithm is tested in a real-time vehicle simulation environment. It is found that while the single physical agent can closely track the behavior of holonomic agents and quadcopter simulation results, the real-time multi-agent case exhibits a degradation in performance that further declines in obstacle dense environments. This explains a loss of performance that can lead to collisions in the real-time setting where in the holonomic case the exact same test yields successful results.

Stringent control demands from the high-tech mechatronics industry have warranted the need to explore potentially advantageous non-linear controllers. Variable Fractional Order (VFO) calculus provides one such avenue to build non-linear PID-like controllers. VFO calculus is the generalization of integer order differentiation and integration, where, in addition to the possibility of orders being real or even complex, the orders can vary as a function of a variable like time, temperature, etc. However, in this nascent field of VFO control, the focus has mainly been on controller tuning by time domain optimization of the performance for certain specific trajectories or cost functions. On the other hand, Frequency domain tools allow for analysis and tuning of controllers for performance over a wide range of exogenous inputs. For smooth adoption into industry, it is important to develop a frequency domain framework for working with VFO control. Describing function (DF) analysis is a method to obtain an approximate Frequency Response Function (FRF)-like function for non-linear systems. In this thesis, DF analysis is used for developing VFO PID controllers in the frequency domain from an industry compatibility point of view and the closed loop performance of these controllers in controlling a precision positioning stage is examined.

Currently used imaging methods in Atomic Force Microscopy (AFM) including the use of a Lock-In Amplifier or a Phase-Locked Loop, are suboptimal. In this report, the image resolution in AFM is improved by detecting the tip-sample interaction using complete measurements of the input of the cantilever and its measured deflection. Two methods are studied while assuming that the tip-sample interaction is sparse, namely a model-based approach and a data-driven approach. Real-life experiments have shown that the model-based approach improves the image resolution with a factor of 7.5 to 0.555 nm compared to the conventional imaging method, according to a metric using Fourier Ring Correlation in which a reference image is unnecessary. The data-driven approach can be used in the model-based approach to further improve the resolution. In addition to improved resolutions, a Linear Time-Invariant model of the mechanically driven AFM-cantilever immersed in liquid – from piezo input to cantilever deflection – has been obtained through subspace identification with a Variance Accounted For of 79.2%. Recommendations for future research include applying the latter model in detecting the tip-sample interaction, improving the data-driven approach, reducing the computational effort of the model-based approach and implementing algorithms for detecting the tip-sample interaction online.

Multi-Agent Systems, often referred to a network of loosely connected autonomous units, are widely used to model the dynamics of crowds, vehicles, robots and swarms in traffic management, biological environment, distributed control and communication technologies. Recently, the study of multi-agent systems is rapidly growing due to the beneficial advantages of using a team of agents in logistics, mapping, search and rescue, etc.

In this thesis, we focus on the problem of decentralized collision avoidance among multiple intelligent moving agents. Imaging each agent to be a human, a moving car, or an aircraft, it is supposed to make its decision independently based on its perception of the local environment through sensors only. Two different collision avoidance protocols are presented to generate updated reference velocity continuously for each agent that leads to no future collision. The first method, the rotation based method, is adopted by a geometric based algorithm introduced for 2-Dimensional space and the second method, the potential fields based method, could be categorized as an example of Harmonic Potential Fields (HPF) discussed by Masoud. Both methods employing position information of obstacles result in collision-free paths for each agent under the assumption that all other agents following similar maneuvers. Through simulations in MATLAB, satisfied performances are achieved for method 2 in all challenging scenarios we set while method 1 faced some difficulties dealing with multi-obstacle simultaneously as well as 3D scenarios.

Successful implementation of fully autonomous vehicles is a much desired objective. Within the area of unmanned marine craft or unmanned surface vehicles (USV), the implementation of truly autonomous navigation is still a challenge. During times in which humans are still actively involved in the processof maritime navigation, regulations are needed to prevent accidents from happening. It is therefore essential for the transition towards more autonomy that USVs are able to obey the regulations as well and clearly exhibit the right behavior to enable other ships to anticipate the behavior of USVs and reactappropriately and timely. In maritime navigation, ships have to obey the International Regulations for preventing collisions at sea, also known as COLREGS (COLlision REGulationS). This thesis is focused on the guidance of USVs, and is specifically aimed at COLREGS compliant path re-planning to avoid potential collisions. A first method has been conceived based upon the SaturatedFast Marching Square method where trailing points are used to correctly guide the USV past dynamic vessels according to COLREGS. A second novel method builds upon the previous one, by combining the Saturated Fast Marching Square method with a path generating Genetic Algorithm. The first methodperforms as supposed in simple environments such as when encountering a single dynamic obstacle. However, the first method starts to under-perform as complexity increases through the presence of both static and dynamic obstacles. The additional second method performs accurately in complex scenariosas well. Both methods have been tested in single case simulations and in extensive random simulations to assess their COLREGS compliant path re-planning accuracy.

Multi-Agent Systems (MAS) can be used in the exploration and mapping of unknown environments. To cooperate autonomously, each agent of the MAS must know its own location precisely within such an environment. Simultaneous Localization and Mapping (SLAM) techniques are commonly used when the Global Positioning System (GPS) is unavailable or does not provide sufficient accuracy in positioning the agents. In multi-robot SLAM additional challenges, related to data sharing, arise as the number of robots increases. These additional challenges prevent the multi-robot SLAM solutions to be scaled easily. Network-decentralized state estimation can be used to overcome this problem. The information sharing within multi-agent systems can be modelled based on the topology of a graph. The agents form the nodes and communication is only along the edges of this network. Network-decentralized state estimation consists of designing local state observers for a network of agents to asymptotically estimate their own state based on information exchanges with neighboring agents only. In this thesis, the concepts of network-decentralized position estimation and SLAM are combined to form a novel network-decentralized SLAM which can be used by a multi-agent system in unknown environments to build a map of the surroundings. The network-decentralized SLAM is simulated in MATLAB and evaluated based on different metrics. A volume error metric as well as different timing metrics are introduced. Based on the evaluation of these metrics, it is shown that the proposed network-decentralized SLAM can be easily scaled to larger formations to cover unknown areas faster and in a more robust and accurate way.

An often preferred method to control a multi-agent system is by a network-decentralised controller. Network-decentralised means that each agent only has knowledge about its own state and the state of its neighbouring agents. In this thesis the multi-agent system consists of holonomic robots moving in a 2-dimensional configuration space. Each agent is equipped with a collision avoidance algorithm which does not need unmeasurable information from other agents, hence it is completely decentralised. The collision avoidance algorithm gen- erates a reference velocity which is always away and (counter-clockwise) around a possible collision. Cooperation of the agents is reached by estimating their position and moving in an assigned formation by only communicating with neighbouring agents, hence the strategy is network-decentralised. The communication network of the agents is modelled as a graph and described by the associated incidence matrix. This thesis combines for the first time the network-decentralised estimation method proposed by Giordano et al. [1] together with the network-decentralized control method proposed by Blanchini et al. [2] and a collision avoidance algorithm. When anonymity in coordination is possible the agents are able to switch target location. Each agent solves a local optimisation problem to minimise the total distance travelled by itself and its neighbouring agents. The agent with the highest cost sav- ings is allowed to reallocate the target locations. The results obtained in the simulations are very promising and suggest that the proposed algorithms can be successfully implemented to efficiently coordinate agents and avoid collisions in real-world applications.