The potential offered by the abundance of sensors, actuators, and communications in the Internet of Things (IoT) era is hindered by the limited computational capacity of local nodes. Several key challenges should be addressed to optimally and jointly exploit the network, computing, and storage resources, guaranteeing at the same time feasibility for time-critical and mission-critical tasks. We propose the DRUID-NET framework to take upon these challenges by dynamically distributing resources when the demand is rapidly varying. It includes analytic dynamical modeling of the resources, offered workload, and networking environment, incorporating phenomena typically met in wireless communications and mobile edge computing, together with new estimators of time-varying profiles. Building on this framework, we aim to develop novel resource allocation mechanisms that explicitly include service differentiation and context-awareness, being capable of guaranteeing well-defined Quality of Service (QoS) metrics. DRUID-NET goes beyond the state of the art in the design of control algorithms by incorporating resource allocation mechanisms to the decision strategy itself. To achieve these breakthroughs, we combine tools from Automata and Graph theory, Machine Learning, Modern Control Theory, and Network Theory. DRUID-NET constitutes the first truly holistic, multidisciplinary approach that extends recent, albeit fragmented results from all aforementioned fields, thus bridging the gap between efforts of different communities.

We study discrete time linear constrained switching systems with additive disturbances, in the general setting where the switching acts on the system matrices, the disturbance sets, and the state constraint sets. Our primary goal is to extend the existing invariant set constructions when the switching signal is constrained by a given automation. We achieve it by working with a relaxation of invariance, namely the multi-set invariance. By exploiting recent results on computing the stability metrics for these systems, we establish explicit bounds on the number of iterations required for each construction. Last, as an application, we develop new maximal invariant set constructions for the case of linear systems in far fewer iterations compared to the state-of-the-art.

We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another'”. Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions.

The evolution of the Industrial Internet of Things (IIoT) and edge computing enables resource-constrained mobile robots to offload the computationally intensive localization algorithms. Naturally, utilizing the remote resources of an edge server to offload these tasks encounters the challenge of a joint co-design in communication, control, estimation, and computing infrastructure. We introduce a set-based estimation offloading framework, for the specific case of the navigation of a unicycle robot toward a target position. The robot is subject to modeling and measurement uncertainties, and the estimation set is calculated using overapproximation techniques that alleviate additional computations. A switching set-based control mechanism provides accurate navigation and triggers more precise estimation algorithms when needed. To guarantee the convergence of the system and optimize the utilization of remote resources, a utility-based offloading mechanism is designed, which takes into account both the dynamic network conditions and the available computing resources at the network edge. The performance of the proposed framework is demonstrated through simulations and comparison with alternative offloading schemes.

We develop a new framework for trajectory planning on predefined paths, for general N-link manipulators. Different from previous approaches generating open-loop minimum time controllers or pre-tuned motion profiles by time-scaling, we establish analytic algorithms that recover all initial conditions that can be driven to the desirable target set while adhering to environment constraints. More technologically relevant, we characterise families of corresponding safe state-feedback controllers with several desirable properties. A key enabler in our framework is the introduction of a state feedback template, that induces ordering properties between trajectories of the resulting closed-loop system. The proposed structure allows working on the nonlinear system directly in both the analysis and synthesis problems. Both offline computations and online implementation are scalable with respect to the number of links of the manipulator. The results can potentially be used in a series of challenging problems: Numerical experiments on a commercial robotic manipulator demonstrate that efficient online implementation is possible.