Mathematical theory of partial differential equations (PDEs) is a pretty old classical area with wide range of applications to almost every branch of science and engineering. With the advanced development of functional analysis and operator theory in the last century, it became a topic of analysis. The theory of homogenization of partial differential equations is a relatively new area of research which helps to understand the multi-scale phenomena which has tremendous applications in a variety of physical and engineering models, like in composite materials, porous media, thin structures, rapidly oscillating boundaries and so on. Hence, it has emerged as one of the most interesting and useful subject to study for the last few decades both as a theoretical and applied topic. In this thesis, we study asymptotic analysis (homogenization) of second-order partial differential equations posed on an oscillating domain. We consider a two dimensional oscillating domain (comb shape type) consisting of a fixed bottom region and an oscillatory (rugose) upper region. We introduce optimal control problems for the Laplace equation. There are mainly two types of optimal control problems; namely distributed control and boundary control. For distributed control problems in the oscillating domain, one can apply control on the oscillating part or on the fixed part and similarly for boundary control problem (control on the oscillating boundary or on the fixed part the boundary). We consider all the four cases, namely distributed and boundary controls both on the oscillating part and away from the oscillating part. The present thesis consists of 8 chapters. In Chapter 1, a brief introduction to homogenization and optimal control is given with relevant references. In Chapter 2, we introduce the oscillatory domain and define the basic unfolding operators which will be used throughout the thesis. Summary of the thesis is given in Chapter 3 and future plan in Chapter 8. Our main contribution is contained in Chapters 4-7. In chapters 4 and 5, we study the asymptotic analysis of optimal control problems namely distributed and boundary controls, respectively, where the controls act away from the oscillating part of the domain. We consider both L2 cost functional as well as Dirichlet (gradient type) cost functional. We derive homogenized problem and introduce the limit optimal control problems with appropriate cost functional. Finally, we show convergence of the optimal solution, optimal state and associate adjoint solution. Also convergence of cost-functional. In Chapter 6, we consider the periodic controls on the oscillatory part together with Neumann condition on the oscillating boundary. One of the main contributions is the characterization of the optimal control using unfolding operator. This characterization is new and also will be used to study the limiting analysis of the optimality system. Chapter 7 deals with the boundary optimal control problem, where the control is applied through Neumann boundary condition on the oscillating boundary with a suitable scaling parameter. To characterize the optimal control, we introduce boundary unfolding operators which we consider as a novel approach. This characterization is used in the limiting analysis. In the limit, we obtain two limit problems according to the scaling parameters. In one of the limit optimal control problem, we observe that it contains three controls namely; a distributed control, a boundary control and an interface control.

Recent development has lead to the emergence of distributed Wireless Sensor and Actor Networks (WSAN), which are capable of observing the physical environment, processing the data, making decisions based on the observations and performing appropriate actions. WSANs represent an important extension of Wireless Sensor Networks (WSNs) and may comprise a large number of sensor nodes and a smaller number of actor nodes. The sensor nodes are low-cost, low energy, battery powered devices with restricted sensing, computational and wireless communication capabilities. Actor nodes are resource richer with superior processing capabilities, higher transmission powers and a longer battery life. A basic operational scenario of a typical WSAN application follows the following sequence of events. The physical environment is periodically sensed and evaluated by the sensor nodes. The sensed data is then routed towards an actor node. Upon receiving sensed data, an actor node performs an action upon the physical environment if necessary, i.e. if the occurrence of a disturbance or critical event has been detected. The specific characteristics of sensor and actor nodes combined with some stringent application constraints impose unique requirements for WSANs. The fundamental challenges for WSANs are to achieve low latency, high energy efficiency and high reliability. The latency and energy efficiency requirements are in a trade-off relationship. The communication and coordination inside WSANs is managed via a Communication Protocol Stack (CPS) situated on every node. The requirements of low latency and energy efficiency have to be addressed at every layer of the CPS to ensure overall feasibility of the WSAN. Therefore, careful design of protocol layers in the CPS is crucial in attempting to meet the unique requirements and handle the abovementioned trade-off relationship in WSANs. The traditional CPS, comprising the application, network, medium access control and physical layer, is a layered protocol stack with every layer, a predefined functional entity. However, it has been found that for similar types of networks with similar stringent network requirements, the strictly layered protocol stack approach performs at a sub-optimal level with regards to network efficiency. A modern cross-layer paradigm, which proposes the employment of interactions between layers in the CPS, has recently attracted a lot of attention. The cross-layer approach promotes network efficiency optimization and promises considerable performance gains. It is found that in literature, the adoption of this cross-layer paradigm has not yet been considered for WSANs. In this dissertation, a complete cross-layer enabled WSAN CPS is developed that features the adoption of the cross-layer paradigm towards promoting optimization of the network efficiency. The newly proposed cross-layer enabled CPS entails protocols that incorporate information from other layers into their local decisions. Every protocol layer provides information identified as beneficial to another layer(s) in the CPS via a newly proposed Simple Cross-Layer Framework (SCLF) for WSANs. The proposed complete cross-layer enabled WSAN CPS comprises a Cross-Layer enabled Network-Centric Actuation Control with Data Prioritization (CL-NCAC-DP) application layer (APPL) protocol, a Cross-Layer enabled Cluster-based Hierarchical Energy/Latency-Aware Geographic Routing (CL-CHELAGR) network layer (NETL) protocol and a Cross-Layer enabled Carrier Sense Multiple Access with Minimum Preamble Sampling and Duty Cycle Doubling (CL-CSMA-MPS-DCD) medium access control layer (MACL) protocol. Each of these protocols builds on an existing simple layered protocol that was chosen as a basis for development of the cross-layer enabled protocols. It was found that existing protocols focus primarily on energy efficiency to ensure maximum network lifetime. However, most WSAN applications require latency minimization to be considered with the same importance. The cross-layer paradigm provides means of facilitating the optimization of both latency and energy efficiency. Specifically, a solution to the latency versus energy trade-off is given in this dissertation. The data generated by sensor nodes is prioritised by the APPL and depending on the delay-sensitivity, handled in a specialised manor by every layer of the CPS. Delay-sensitive data packets are handled in order to achieve minimum latency. On the other hand, delay-insensitive non critical data packets are handled in such a way as to achieve the highest energy efficiency. In effect, either latency minimization or energy efficiency receives an elevated precedence according to the type of data that is to be handled. Specifically, the cross-layer enabled APPL protocol provides information pertaining to the delay-sensitivity of sensed data packets to the other layers. Consequently, when a data packet is detected as highly delay-sensitive, the cross-layer enabled NETL protocol changes its approach from energy efficient routing along the maximum residual energy path to routing along the fastest path towards the cluster-head actor node for latency minimizing of the specific packet. This is done by considering information (contained in the SCLF neighbourhood table) from the MACL that entails wakeup schedules and channel utilization at neighbour nodes. Among the added criteria, the next-hop node is primarily chosen based on the shortest time to wakeup. The cross-layer enabled MACL in turn employs a priority queue and a temporary duty cycle doubling feature to enable rapid relaying of delay-sensitive data. Duty cycle doubling is employed whenever a sensor node’s APPL state indicates that it is part of a critical event reporting route. When the APPL protocol state (found in the SCLF information pool) indicates that the node is not part of the critical event reporting route anymore, the MACL reverts back to promoting energy efficiency by disengaging duty cycle doubling and re-employing a combination of a very low duty cycle and preamble sampling. The APPL protocol conversely considers the current queue size of the MACL and temporarily halts the creation of data packets (only if the sensed value is non critical) to prevent a queue overflow and ease congestion at the MACL By simulation it was shown that the cross-layer enabled WSAN CPS consistently outperforms the layered CPS for various network conditions. The average end-to-end latency of delay-sensitive critical data packets is decreased substantially. Furthermore, the average end-to-end latency of delay-insensitive data packets is also decreased. Finally, the energy efficiency performance is decreased by a tolerable insignificant minor margin as expected. The trivial increase in energy consumption is overshadowed by the high margin of increase in latency performance for delay-sensitive critical data packets. The newly proposed cross-layer CPS achieves an immense latency performance increase for WSANs, while maintaining excellent energy efficiency. It has hence been shown that the adoption of the cross-layer paradigm by the WSAN CPS proves hugely beneficial with regards to the network efficiency performance. This increases the feasibility of WSANs and promotes its application in more areas. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

ABB s r.o. is one of the most important companies that are concerned with setting of trends in electro-energetic field. One of these trends is digitalization of medium voltage substations that leads to simplified of internal connection and easier connection of substation to the control system. This thesis deals possibilities of connection of communication, methods of controlling logical operations by centralized or distributed system and compares potential of these systems.

<div>The goal of this research is to develop a method of control for a team of unmanned aerial and ground robots that is resilient, robust, and scalable given both complete and incomplete information of the environment. The method presented in this paper integrates approximate and optimal methods of path planning integrated with a market-based task allocation strategy. Further work presents a solution to unmanned ground vehicle path planning within the developed mission planning system framework under incomplete information. Deep reinforcement learning is proposed to solve movement through unknown terrain environment. The final demonstration for Advantage-Actor Critic deep reinforcement learning elicits successful implementation of the proposed model.</div>

In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

We consider a class of control problems governed by a linear parabolic initial-boundary value problem with linear-quadratic objective and pointwise constraints on the control. The control system contains different types of perturbations. They appear in the linear part of the objective functional, in the right hand side of the equation, in its boundary condition, and in the initial value. Making use of parabolic regularity in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm is improved to the supremum-norm.

An industrial control valve has been designed by Eaton (AxisPro® valve). The servo performance valve has onboard electronics that features external and internal sensor interfaces, advanced control modes and network capability. Advanced control modes are implement in the valves firmware. With the help of the white space it is possilbe to execute custom code directly on the valve that interact with these controls. Small OEM applications, like rubber moulding machines, benefit from the comination of build in controls and custom code, to provide adaptations for their special machines.

<div>Self-organization in a multi-robot system is a spontaneous process where some form of overall order arises from local interactions between robots in an initially disordered system. Cooperative coordination strategies for self-organization promote teamwork to complete a task while increasing the total utility of the system. In this dissertation, we apply prosocial behavioral concepts such as altruism and cooperation in multi-robot systems and investigate their effects on overall system performance on given tasks. We stress the significance of this research in long-term applications involving minimal to no human supervision, where self-sustainability of the multi-robot group is of utmost importance for the success of the mission at hand and system re-usability in the future.</div><div><br></div><div>For part of the research, we take bio-inspiration of cooperation from the huddling behavior of Emperor Penguins in the Antarctic which allows them to share body heat and survive one of the harshest environments on Earth as a group. A cyclic energy sharing concept is proposed for a convoying structured multi-robot group inspired from penguin movement dynamics in a huddle with carefully placed induction coils to facilitate directional energy sharing with neighbors and a position shuffling algorithm, allowing long-term survival of the convoy as a group in the field. Simulation results validate that the cyclic process allows individuals an equal opportunity to be at the center of the group identified as the most energy conserving position, and as a result robot groups were able to travel over 4 times the distance during convoying with the proposed method without any robot failing as opposed to without the shuffling and energy sharing process. </div><div><br></div><div>An artificial potential based Adaptive Inter-agent Spacing (AIS) control law is also proposed for efficient energy distribution in an unstructured multi-robot group aimed at long-term survivability goals in the field. By design, as an altruistic behavior higher energy bearing robots are dispersed throughout the group based on their individual energy levels to counter skewed initial distributions for faster group energy equilibrium attainment. Inspired by multi-huddle merging and splitting behavior of Emperor Penguins, a clustering and sequential merging based systematic energy equilibrium attainment method is also proposed as a supplement to the AIS controller. The proposed system ensures that high energy bearing agents are not over crowded by low energy bearing agents. The AIS controller proposed for the unstructured energy sharing and distribution process yielded 55%, 42%, 23% and 33% performance improvements in equilibrium attainment convergence time for skewed, bi-modal, normal and random initial agent resource level distributions respectively on a 2D plane using the proposed energy distribution method over the control method of no adaptive spacing. Scalability analysis for both energy sharing concepts confirmed their application with consistently improved performances different sized groups of robots. Applicability of the AIS controller as a generalized resource distribution method under certain constraints is also discussed to establish its significance in various multi-robot applications.</div><div><br></div><div>A concept of group based survival from damaging directional external stimuli is also adapted from the Emperor Penguin huddling phenomenon where individuals on the damaging stimuli side continuously relocate to the leeward side of the group following the group boundary using Gaussian Processes Machine Learning based global health-loss rate minima estimations in a distributed manner. The method relies on cooperation from all robots where individuals take turns being sheltered by the group from the damaging external stimuli. The distributed global health loss rate minima estimation allowed the development of two settling conditions. The global health loss rate minima settling method yielded 12.6%, 5.3%, 16.7% and 14.2% improvement in average robot health over the control case of no relocation, while an optimized health loss rate minima settling method further improved on the global health loss rate settling method by 3.9%, 1.9%, 1.7% and 0.6% for robot group sizes 26, 35, 70 and 107 respectively.</div><div><br></div><div>As a direct application case study of collaboration in multi-robot systems, a distributed shape formation strategy is proposed where robots act as beacons to help neighbors settle in a prescribed formation by local signaling. The process is completely distributed in nature and does not require any external control due to the cooperation between robots. Beacon robots looking for a robot to settle as a neighbor and continue the shape formation process, generates a surface gradient throughout the formed shape that allow robots to determine the direction of the structure forming frontier along the dynamically changing structure surface and eventually reach the closest beacon. Simulation experiments validate complex shape formation in 2D and 3D using the proposed method. The importance of group collaboration is emphasized in this case study without which the shape formation process would not be possible, without a centralized control scheme directing individual agents to specific positions in the structure. </div><div> </div><div>As the final application case study, a collaborative multi-agent transportation strategy is proposed for unknown objects with irregular shape and uneven weight distribution. Although, the proposed system is robust to single robot object transportation, the proposed methodology of transport is focused on robots regulating their effort while pushing objects from an identified pushing location hoping other robots support the object moment on the other end of the center of mass to prevent unintended rotation and create an efficient path of the object to the goal. The design of the object transportation strategy takes cooperation cues from human behaviors when coordinating pushing of heavy objects from two ends. Collaboration is achieved when pushing agents can regulate their effort with one another to maintain an efficient path for the object towards the set goal. Numerous experiments of pushing simple shapes such as disks and rectangular boxes and complex arbitrary shapes with increasing number of robots validate the significance and effectiveness of the proposed method. Detailed robustness studies of changing weight of objects during transportation portrayed the importance of cooperation in multi-agent systems in countering unintended drift effects of the object and maintain a steady efficient path to the goal. </div><div><br></div><div>Each case study is presented independent of one another with the Penguin huddling based self-organizations in response to internal and external stimuli focused on fundamental self-organization methods, and the structure formation and object transportation strategies focused on cooperation in specific applications. All case studies are validated by relevant simulation and experiments to establish the effectiveness of altruistic and cooperative behaviors in multi-robot systems.</div>

Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network.

Dynamic and unforeseeable characteristic of the current market and production environment is not feasible to be met through pre-set parameters being dependent on the predictions. Handling this matter requires to keep focus on production system adaptability. Evolvable Production System has achieved fully system reconfigurability through process oriented modularity and multi agent based distributed control system architecture. One of the essential enhancements provided by EPS on the shop floor is achieving minimized/eliminated system setup time in response to changing product requirements. Manufacturing planning and control system, on the other hand, follows hierarchical principles which are quite much reliant on the predicted information so to structure production and planning environment on it. Production system limitations, such as lack of adaptability in response to changing conditions, are in fact influencing the planning system to be structured on the predictions. The enhancements which are ensured by the architecture of EPS enable to relax the constraints on planning system which are imposed by the limitations of production system. These enhancements have an effect at different levels in the planning hierarchy. On the light of these improvements, the planning framework as it is used so far in the industry becomes invalid and this arise a requirement for planning system structure to be designed according to a fully reconfigurable system to be able to benefit such a production system by all means. This thesis targets to enlighten the relation between the production system characteristics and planning system structure by emphasizing the planning problems and proposing a planning reference architecture solution to be able achieve a responsive planning framework. / <p>QC 20140916</p>