Abstract: This paper formally develops robust optimal predictive control solutions that can accommodate disturbances and stabilize periodic legged locomotion. To this end, we build upon existing optimization-based control paradigms, particularly quadratic programming (QP)-based model predictive controllers (MPCs). We present conditions under which the closed-loop reduced-order systems (i.e., template models) with MPC have the continuous differentiability property on an open neighborhood of gaits. We then linearize the resulting discrete-time, closed-loop nonlinear template system around the gait to obtain a linear time-varying (LTV) system. This periodic LTV system is further transformed into a linear system with a constant state-transition matrix using discrete-time Floquet transform. The system is then analyzed to accommodate parametric uncertainties and to synthesize robust optimal H₂ and H_∞ feedback controllers via linear matrix inequalities (LMIs). The paper then extends the theoretical results to the single rigid body (SRB) template dynamics and numerically verifies them. The proposed robust optimal predictive controllers are used in a layered control structure, where the optimal reduced-order trajectories are provided to a full-order nonlinear whole-body controller (WBC) for tracking at the low level. The developed layered controllers are numerically and experimentally validated for the robust locomotion of the A1 quadrupedal robot subject to various disturbances and uneven terrains. Our numerical results suggest that the H₂ - and H_∞ -optimal MPC controllers significantly improve the robust stability of the gaits compared to the normal MPC.

Abstract: Self-excited systems (SES) arise in numerous applications, such as fluid-structure interaction, combustion, and biochemical systems. In support of system identification and digital control of SES, this paper analyzes discrete-time Lur'e systems with affinely constrained, piecewise-C$^{1}$ feedback nonlinearities. In particular, a novel feature of the discrete-time Lur'e system considered in this paper is the structural assumption that the linear dynamics possess a zero at 1. This assumption ensures that the Lur'e system have a unique equilibrium for each constant, exogenous input and prevents the system from having an additional equilibrium with a nontrivial domain of attraction. The main result provides sufficient conditions under which a discrete-time Lur'e system is self-excited in the sense that its response is 1) nonconvergent for almost all initial conditions, and 2) bounded for all initial conditions. Sufficient conditions for 1) include the instability and nonsingularity of the linearized, closed-loop dynamics at the unique equilibrium and their nonsingularity almost everywhere. Sufficient conditions for 2) include asymptotic stability of the linear dynamics of the Lur'e system and their feedback interconnection with linear mappings that correspond to the affine constraints that bound the nonlinearity, as well as the feasibility of a linear matrix inequality.

Abstract: We consider both leaderless and leader-follower, possibly nonlinear, networks affected by time-varying communication delays. For such systems, we give a set of sufficient conditions that guarantee the convergence of the network towards some desired behaviour while simultaneously ensuring the rejection of polynomial disturbances and the non-amplification of other classes of disturbances across the network. To fulfill these desired properties, and prove our main results, we propose the use of a control protocol that implements a multiplex architecture. The use of our results for control protocol design is then illustrated in the context of formation control. The protocols are validated both in-silico and via an experimental set-up with real robots. All experiments confirm the effectiveness of our approach.

Abstract: In this study, a control theoretic description of resilience is provided to quantify the characteristics of a resilient system. The aim is to establish a paradigm for resilient control design based on tangible control objectives that yield desirable attributes for safety-critical systems. In that regard, durability and recoverability properties are identified as key components of the proposed resilience framework and, to offer a methodology to enforce these attributes, the notion of finite-time robust control barrier function (FR-CBF) is introduced. Furthermore, to offer a comprehensive treatment of the problem, resilient control design is investigated for both continuous and sampled-data systems. To that end, FR-CBF-based design conditions for both continuous and piece-wise constant zero-order hold (ZOH) control inputs are included. Moreover, to provide a concrete example of how the proposed framework could be adopted for safety-critical control applications, in this study we also investigate the voltage regulation problem for inverter-interfaced radial power distribution networks subject to adversarial injections. In that regard, sufficient conditions for both the continuous and sampled-data ZOH control are derived to guarantee finite-time recovery and safe operation of the distribution grid in accordance with the proposed resilience framework. Finally, the efficacy of the proposed results is advocated using a simulation study showing resilient grid performance in the presence of the ‘worst-case’ power injection attack, as reported in (Lindström et al. 2021).

Abstract: Learning is a key function in the brain to be able to achieve the activity patterns required to perform various activities. While specific behaviors are determined by activity in localized regions, the interconnections throughout the entire brain play a key role in enabling its ability to exhibit desired activity. To mimic this setup, this paper examines the use of reservoir computing to control a linear-threshold network brain model to a desired trajectory. We first formally design open- and closed-loop controllers that achieve reference tracking under suitable conditions on the synaptic connectivity. Given the impracticality of evaluating closed-form control signals, particularly with growing network complexity, we provide a framework where a reservoir of a larger size than the network is trained to drive the activity to the desired pattern. We illustrate the versatility of this setup in two applications: selective recruitment and inhibition of neuronal populations for goal-driven selective attention, and network intervention for the prevention of epileptic seizures.

Abstract: Behavioral factors play a crucial role in the emergence, spread, and containment of human diseases, significantly influencing the effectiveness of intervention measures. However, the integration of such factors into epidemic models is still limited, hindering the possibility of understanding how to optimally design interventions to mitigate epidemic outbreaks in real life. This paper aims to fill in this gap. In particular, we propose a parsimonious model that couples an epidemic compartmental model with a population game that captures the behavioral response, obtaining a nonlinear system of ordinary differential equations. Grounded on prevalence-elastic behavior—the empirically proven assumption that the disease prevalence affects the adherence to self-protective behavior—we consider a nontrivial negative feedback between contagions and adoption of self-protective behavior. We characterize the asymptotic behavior of the system, establishing conditions under which the disease is quickly eradicated or a global convergence to an endemic equilibrium is attained. In addition, we elucidate how the behavioral response affects the endemic equilibrium. Then, we formulate and solve an optimal control problem to plan cost-effective interventions for the model, accounting for their healthcare and social-economical implications. Numerical simulations on a case study calibrated on sexually transmitted diseases demonstrate and validate our findings.

Abstract: REFoCUS (Retrospective Encoding For Conventional Ultrasound Sequences) offers great flexibility by enabling synthetic aperture beamforming from conventional ultrasound sequences. This flexibility is beneficial for many aspects in medical ultrasound beamforming, including e.g. combination of different transmit waves, distributed sound speed estimation and common-midpoint gathers. REFoCUS beamforming also has image quality comparable to state-of-art methods such as Retrospective Transmit Beamforming (RTB). However, the previously published implementations of REFoCUS do not address clutter from sidelobes and grating lobes present in the data before the recovery. This reduces image quality due to potentially strong sidelobes and grating lobes, particularly when using REFoCUS in combination with micro-beamforming and matrix array probes. Recordings from micro-beamforming probes may thus not be compliant with the existing REFoCUS methods. We propose to solve the sidelobes and grating lobe issues by introducing a reformulation of REFoCUS that performs multistatic data recovery and beamforming in the time domain, allowing spatial weighting to remove clutter and noise. Spatial weighting is based on common beamforming principles and incorporates element directivity, dynamic F-number, beam geometry weighting, and grating lobe suppression. We also discuss how aperture sampling affects beamforming with REFoCUS. Spatially Weighted REFoCUS (SWR) and critical sampling of the transmit aperture show suppression of receive grating lobes in an in vivo setting with two different micro-beamforming matrix-array probes, leading to an increase in gCNR contrast from 0.44 to 0.96 in a fetal image and from 0.39 to 0.89 in a cardiac image.

Abstract: This article presents a proactive approach to resolving the conflict between safety and optimality for continuous-time (CT) safety-critical systems with unknown dynamics. The presented method guarantees safety and performance specifications by combining two controllers: a safe controller and an optimal controller. On the one hand, the safe controller is designed using only input and state data measurements and without requiring the state derivative data, which are typically required in data-driven control of CT systems. State derivative measurement is costly, and its approximation introduces noise to the system. On the other hand, the optimal controller is learned using a low-complexity one-shot optimization problem, which again does not rely on prior knowledge of the system dynamics and state derivative data. Compared to existing optimal control learning methods for CT systems, which are typically iterative, a one-shot optimization is considerably more sample-efficient and computationally efficient. The share of optimal and safe controllers in the overall control policy is obtained by solving a computationally efficient optimization problem involving a scalar variable in a data-driven manner. It is shown that the contribution of the safe controller dominates that of the optimal controller when the system's state is close to the safety boundaries, and this domination drops as the system trajectories move away from the safety boundaries. In this case, the optimal controller contributes more to the overall controller. The feasibility and stability of the proposed controller are shown. Finally, the simulation results show the efficacy of the proposed approach.

Abstract: In this paper, we introduce the Global Multi-Phase Path Planning (GMP ³ ) algorithm in planner problems, which computes fast and feasible trajectories in environments with obstacles, considering physical and kinematic constraints. Our approach utilizes a Markov Decision Process (MDP) framework and high-level reinforcement learning techniques to ensure trajectory smoothness, continuity, and compliance with constraints. Through extensive simulations, we demonstrate the algorithm's effectiveness and efficiency across various scenarios. We highlight existing path planning challenges, particularly in integrating dynamic adaptability and computational efficiency. The results validate our method's convergence guarantees using Lyapunov's stability theorem and underscore its computational advantages.

Abstract: In beamforming, retrospective change in sound speed and recalculation of focusing delays is attractive both for improving image quality and for using it in an iterative image quality optimization process. Modifying the speed of sound retrospectively for focused transmits is challenging because the transmit focus position is a function of sound speed error. The virtual source model is a common way to calculate the transmit focusing delays where using the correct transmit focus position is imperative. In this paper, we provide the methods necessary to perform a retrospective sound-speed correction by compensating the receive grid and by calculating the effective transmit focus needed to perform proper synthetic transmit focusing. To evaluate the efficacy of our method, we simulate wave propagation and measure the resolution of in vitro images using both phased and curvilinear arrays. The results of the suggested virtual source estimation method match the simulated wave propagation for multiple F-numbers and both positive and negative sound speed errors. We compare beamformed images using correct/incorrect sound speeds and correct/incorrect virtual source positions. The results demonstrate that the Corrected Virtual Source (CVS) method generates artifact-free images with superior quality compared to images with incorrect sound speed. Furthermore, the image beamformed with the correct sound speed, but incorrect virtual source position, exhibits image artifacts and inferior focusing quality compared to the CVS image.

Abstract: Recently, a deep-learning algorithm referred to as Deep Galerkin Method (DGM), has gained a lot of attention among those trying to solve numerically Mean Field Games with finite horizon, even if the performance seems to be decreasing significantly with increasing horizon. On the other hand, it has been proven that some specific classes of Mean Field Games enjoy some form of the turnpike property identified over seven decades ago by economists. The gist of this phenomenon is a proof that the solution of an optimal control problem over a long time interval spends most of its time near the stationary solution of the ergodic version of the corresponding infinite horizon optimization problem. After reviewing the implementation of DGM for finite horizon Mean Field Games, we introduce a “turnpike-accelerated” version that incorporates the turnpike estimates in the loss function to be optimized, and we perform a comparative numerical analysis to show the advantages of this accelerated version over the baseline DGM algorithm. We demonstrate on some of the Mean Field Game models with local-couplings known to have the turnpike property, as well as a new class of linear-quadratic models for which we derive explicit turnpike estimates.

Abstract: Reinforcement learning (RL) has revolutionized decision-making across a wide range of domains over the past few decades. Yet, deploying RL policies in real-world scenarios presents the crucial challenge of ensuring safety. Traditional safe RL approaches have predominantly focused on incorporating predefined safety constraints into the policy learning process. However, this reliance on predefined safety constraints poses limitations in dynamic and unpredictable real-world settings where such constraints may not be available or sufficiently adaptable. Bridging this gap, we propose a novel approach that concurrently learns a safe RL control policy and identifies the unknown safety constraint parameters of a given environment. Initializing with a parametric signal temporal logic (pSTL) safety specification and a small initial labeled dataset, we frame the problem as a bilevel optimization task, intricately integrating constrained policy optimization, using a Lagrangian-variant of the twin delayed deep deterministic policy gradient (TD3) algorithm, with Bayesian optimization for optimizing parameters for the given pSTL safety specification. Through experimentation in comprehensive case studies, we validate the efficacy of this approach across varying forms of environmental constraints, consistently yielding safe RL policies with high returns. Furthermore, our findings indicate successful learning of STL safety constraint parameters, exhibiting a high degree of conformity with true environmental safety constraints. The performance of our model closely mirrors that of an ideal scenario that possesses complete prior knowledge of safety constraints, demonstrating its proficiency in accurately identifying environmental safety constraints and learning safe policies that adhere to those constraints. A Python implementation of the algorithm can be found at https://github.com/SAILRIT/Concurrent-Learning-of-Control-Policy-and-Unknown-Constraints-in-Reinforcement-Learning.git.

Abstract: Advanced traffic navigation systems, which provide routing recommendations to drivers based on real-time congestion information, are nowadays widely adopted by roadway transportation users. Yet, the emerging effects on the traffic dynamics originating from the widespread adoption of these technologies have remained largely unexplored until now. In this paper, we propose a dynamic model where drivers imitate the path preferences of previous drivers, and we study the properties of its equilibrium points. Our model is a dynamic generalization of the classical traffic assignment framework, and extends it by accounting for dynamics both in the path decision process and in the network's traffic flows. We show that, when travelers learn shortest paths by imitating other travelers, the overall traffic system benefits from this mechanism and transfers the maximum admissible amount of traffic demand. On the other hand, we demonstrate that, when the travel delay functions are not sufficiently steep or the rates at which drivers imitate previous travelers are not adequately chosen, the trajectories of the traffic system may fail to converge to an equilibrium point, thus compromising asymptotic stability. Illustrative numerical simulations combined with empirical data from highway sensors illustrate our findings.

Abstract: This study demonstrated the first air-coupled pMUT using sol-gel PZT thin film that could deliver ultrasonic waves to mid-air. First, the deposition conditions for making PZT thin film with high remanent polarization were determined. Then, air-coupled pMUTs with resonance frequencies close to 40 kHz were designed using the circular plate model. According to the design, pMUTs with radii measuring $600~\mu $ m to $775~\mu $ m were fabricated to evaluate the acoustic output pressure. Among these, the pMUT with the $725~\mu $ m radius achieved a maximum sound pressure output of 4.42 Pa at 3 cm above when driven with 10 Vpp, and the resonance frequency was 40.48 kHz. Finally, the output pressure of a phased array consisting of sol-gel PZT-based pMUTs with a $725~\mu $ m radius was calculated using the k-Wave toolbox. The output pressure of the $11\times 11$ pMUT array reached 365.62 Pa when focused at 3 cm above it. This result revealed that the output pressure of the proposed pMUT array could fulfill the requirement for most mid-air ultrasound applications.

Abstract: This paper examines pairwise collaborations in heterogeneous multi-robot systems. In particular, we focus on how individual robots, with different functionalities and dynamics, can enhance their resilience by forming collaborative arrangements that result in new capabilities. Control barrier functions are utilized as a mechanism to encode the safe operating regions of individual robots, with the idea being that a robot may be able to operate in new regions that it could not traverse alone by working with other robots. We explore answers to three questions: “Why should robots collaborate?”, “When should robots collaborate?”, and “How can robots collaborate?” To that end, we introduce the safely reachable set – capturing the regions that individual robots can reach safely, either with or without help, while considering their initial states and dynamics. We then describe the conditions under which a help-providing robot and a help-receiving robot can engage in collaboration. Next, we describe the pairwise collaboration framework, modeled through hybrid automata, to show how collaborations can be structured within a heterogeneous multi-robot team. Finally, we present case studies that are conducted on a team of mobile robots.

Abstract: This work introduces a 2D PnC-based acoustic spectrometer capable of analyzing small solution volumes (25 μl) in aqueous environments with significative accuracy and reliability, thus addressing key limitations in current acoustic spectroscopic techniques. Optimally introducing rows of defects into the PnC structure enables guided acoustic modes to propagate at desired frequencies within the bandgap. We construct an acoustic interferometer to leverage the properties of acoustic cavities within these waveguides, which can configure and modulate wave propagation. Our approach involves harnessing the interference between acoustic waves in the two arms of a defects-based waveguide within a PnC, one arm containing an analyte cavity-holder. We demonstrate that the presence of an analyte (sucrose solutions at various concentrations) induces alterations in the acoustic properties of the cavity, leading to observable shifts in transmission characteristics of the propagating acoustic modes. We achieve exceptional spectral resolution through experimentation, facilitating highly sensitive acoustic sensing even with small analyte volumes (< 25 μl). We utilize finite element method simulations to validate our findings and predict spectral shifts resulting from modified acoustic interference. Additionally, we provide a phenomenological description using tight-binding models. Notably, our approach surpasses conventional PnC sensors like Mach-Zehnder interferometers by overcoming challenges associated with analyte uniformity.

Abstract: This paper presents a fully risk-aware model predictive control (MPC) framework for chance-constrained discrete-time linear control systems with process noise. Conditional value-at-risk (CVaR) as a popular coherent risk measure is incorporated in both the constraints and the cost function of the MPC framework. This allows the system to navigate the entire spectrum of risk assessments, from worst-case to risk-neutral scenarios, ensuring both constraint satisfaction and performance optimization in stochastic environments. The recursive feasibility and risk-aware exponential stability of the resulting risk-aware MPC are demonstrated through rigorous theoretical analysis by considering the disturbance feedback policy parameterization. In the end, two numerical examples are given to elucidate the efficacy of the proposed method.

Abstract: This paper considers the change point detection problem under dependent samples. In particular, we provide performance guarantees for the MMD-CUSUM test under exponentially $\alpha$ , $\beta$ , and fast $\phi$ -mixing processes, which significantly expands its utility beyond the i.i.d. and Markovian cases used in previous studies. We obtain lower bounds for average-run-length (ARL) and upper bounds for average-detection-delay (ADD) in terms of the threshold parameter. We show that the MMD-CUSUM test enjoys the same level of performance as the i.i.d. case under fast $\phi$ -mixing processes. The MMD-CUSUM test also achieves strong performance under exponentially $\alpha$ / $\beta$ -mixing processes, which are significantly more relaxed than existing results. The MMD-CUSUM test statistic adapts to different settings without modifications, rendering it a completely data-driven, dependence-agnostic change point detection scheme. Numerical simulations are provided at the end to evaluate our findings.

Abstract: This paper tackles the challenge of maintaining resilience in multi-agent systems under Denial of Service (DoS) attacks by proposing a robust architecture that includes an instantaneous detection algorithm for connectivity losses and a dynamic system to activate backup network layers when disruptions occur. We also introduce a simplified approach that reduces the number of required layers through an adaptive repair algorithm. The simulation section, divided into two parts, demonstrates the effectiveness of the algorithm: one part showcases its scalability in a large-scale system, and the other applies it to a real-world power system using the IEEE 123-node system. Both simulations confirm that the proposed approach significantly enhances system stability and performance under attack conditions.

Abstract: The objective of this work was to investigate changes in the acoustic characteristics of micromachined transducers caused by acoustic cross-coupling between cells. We used hexagonal, polymer-based capacitive micromachined ultrasonic transducers (polyCMUTs) consisting of 127 cells connected in parallel. The distances between the cells were varied, while the cell dimensions and number of cells remained constant. The resulting changes in characteristics were evaluated in terms of peak frequency $f_{pk}$ , fractional bandwidth $FBW$ , peak transmit sensitivity $S_{pk}$ and opening angle $\Phi _{t}$ . The study relies on results from an analytic multicell model (MCM) which considers cross-coupling effects between cells through a mutual acoustic impedance matrix. The results are compared with finite element (FE) analyses and measurements on fabricated prototypes. The manufacturing processes used to produce the polyCMUT prototypes are explained in detail. We found significant changes in all acoustic characteristics: as cell spacing increases, $f_{pk}$ and $\Phi _{t}$ decrease, while $S_{pk}$ gradually rises to about twice the initial value. The $FBW$ varies due to the change in $f_{pk}$ , peaking at small to intermediate cell-to-cell distances. While both modeling approaches cover the general effects, discrepancies in comparison to the measurements were identified. The FE model provided better fits than the analytic MCM, albeit at significantly higher computational costs. The effects on the acoustic characteristics were found strongest at lower frequencies and if many cells are in close proximity to each other. Hence, rotational symmetric or square transducers operating at lower frequencies are affected most. The results demonstrate that design approaches based on modeling single cells may lead to significant deviations from design goals. Both, analytic and FE models are suitable tools to estimate the effects of acoustic interactions and to predict the performance. This aids in meeting design requirements of micromachined ultrasound transducers consisting of multiple radiators.