District heating networks (DHNs) are essential in providing efficient heating services to urban areas through networked pipes. The performance of these systems critically depends on the strategic placement of thermal storage buffers (actuators) and temperature sensors throughout the network. Due to the inherent slow dynamics of thermal transport, these systems exhibit significant delays and periodic behaviors that necessitate time-varying analysis approaches. This paper presents a frequency-domain framework for optimal actuator and sensor placement in DHNs, focusing on metrics derived from frequential Gramians. We provide rigorous analysis of two key metrics, namely the trace and log-determinant of the frequential Gramian, establishing submodularity properties and performance guarantees for greedy selection algorithms. Our theoretical framework naturally handles both the periodic nature of DHNs and their slow transients, outperforming standard approaches in estimation accuracy.

In this article we consider the problem of tether entanglement for tethered mobile robots. One of the main risks of using a tethered connection between a mobile robot and an anchor point is that the tether may get entangled with the obstacles present in the environment or with itself. To avoid these situations, a non-entanglement constraint can be considered in the motion planning problem for tethered robots. This constraint is typically expressed as a set of specific tether configurations that must be avoided. However, the literature lacks a generally accepted definition of entanglement, with existing definitions being limited and partial in the sense that they only focus on specific instances of entanglement. In practice, this means that the existing definitions do not effectively cover all instances of tether entanglement. Our goal in this article is to bridge this gap and to provide new definitions of entanglement, which, together with the existing ones, can be effectively used to qualify the entanglement state of a tethered robot in diverse situations. The new definitions find application in motion planning for tethered robots, where they can be used to obtain more safe and robust entanglement-free trajectories.

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with quantifiable probability and can be exploited to formulate robust stochastic optimization problems with out-of-sample guarantees. We assume the random variable evolves in discrete time under uncertain initial conditions and dynamics, and that noisy partial measurements are available. All random elements have unknown probability distributions and we make inferences about the distribution of the state vector using several output samples from multiple realizations of the process. To this end, we leverage an observer to estimate the state of each independent realization and exploit the outcome to construct the ambiguity sets. We illustrate our results in an economic dispatch problem involving distributed energy resources over which the scheduler has no direct control.

We present a novel framework for formal control of uncertain discrete-time switched stochastic systems against probabilistic reach-avoid specifications. In particular, we consider stochastic systems with additive noise, whose distribution lies in an ambiguity set of distributions that are ε−close to a nominal one according to the Wasserstein distance. For this class of systems we derive control synthesis algorithms that are robust against all these distributions and maximize the probability of satisfying a reach-avoid specification, defined as the probability of reaching a goal region while being safe. The framework we present first learns an abstraction of a switched stochastic system as a robust Markov decision process (robust MDP) by accounting for both the stochasticity of the system and the uncertainty in the noise distribution. Then, it synthesizes a strategy on the resulting robust MDP that maximizes the probability of satisfying the property and is robust to all uncertainty in the system. This strategy is then refined into a switching strategy for the original stochastic system. By exploiting tools from optimal transport and stochastic programming, we show that synthesizing such a strategy reduces to solving a set of linear programs, thus guaranteeing efficiency. We experimentally validate the efficacy of our framework on various case studies, including both linear and non-linear switched stochastic systems. Our results represent the first formal approach for control synthesis of stochastic systems with uncertain noise distribution.

This paper provides a data-driven solution to the problem of coverage control by which a team of robots aims to optimally deploy in a spatial region where certain event of interest may occur. This event is random and described by a probability density function, which is unknown and can only be learned by collecting data. In this work, we hedge against this uncertainty by designing a distributionally robust algorithm that optimizes the locations of the robots against the worst-case probability density from an ambiguity set. This ambiguity set is constructed from data initially collected by the agents, and contains the true density function with prescribed confidence. However, the objective function that the robots seek to minimize is non-smooth. To address this issue, we employ the so-called gradient sampling algorithm, which approximates the Clarke generalized gradient by sampling the derivative of the objective function at nearby locations and stabilizes the choice of descent directions around points where the function may fail to be differentiable. This enables us to prove that the algorithm converges to a stationary point from any initial location of the robots, in analogy to the well-known Lloyd algorithm for differentiable costs when the spatial density is known.