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This paper introduces zonoLAB, a MATLAB-based toolbox for set-based control system analysis using the hybrid zonotope set representation. Hybrid zonotopes have proven to be an expressive set representation that can exactly represent the reachable sets of mixed-logical dynamical systems and tightly approximate the reachable sets of nonlinear dynamic systems. Moreover, hybrid zonotopes can exactly represent the continuous piecewise linear control laws associated with model predictive control and the input-output mappings of neural networks with piecewise linear activation functions. The hybrid zonotope set representation is also highly exploitable, where efficient methods developed for mixed-integer linear programming can be directly used for set operation and analysis. The zonoLAB toolbox is designed to make these capabilities accessible to the dynamic systems and controls community, with functionality spanning fundamental operations with hybrid zonotope, constrained zonotope, and zonotope set representations, powerful set analysis tools, and general-purpose algorithms for reachability analysis of open- and closed-loop systems.

Control Co-Design (CCD) considers the coupled effects of both the plant and control parameters to optimize a system's closed-loop transient performance during the design stage. This paper presents a new method for CCD with guarantees on robustness to nondeterministic disturbances for all initial conditions within a specified region of operation. This is accomplished by calculating the reachable sets of a candidate closed-loop system directly within the optimization problem. Using this approach, the plant and control parameters are simultaneously chosen to shape these reachable sets to be robustly positive invariant and thus safe for all time. Compared to conventional approaches that perform the optimization for a single initial condition and an a priori chosen sequence of disturbances, the proposed set-based method avoids sensitivity to variations in the assumed design scenario. As a representative example, the proposed method is applied to an active suspension system., Comment: 8 pages, 4 figures

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition, and special ordered set approximations to enable linear growth in reachable set memory complexity with time and linear scaling in computational complexity with the system dimension. Facilitating this combination are new identities for constructing nonconvex sets that contain nonlinear functions and for efficiently converting a collection of polytopes from vertex representation to hybrid zonotope representation. Benchmark numerical examples from the literature demonstrate the proposed methods and provide comparison to state-of-the-art techniques.

Latent thermal energy storage (TES) devices could enable advances in many thermal management applications, including peak load shifting for reducing energy demand and cost of HVAC or providing supplemental heat rejection in transient thermal management systems. However, real-time feedback control of such devices is currently limited by the absence of suitable state of charge estimation techniques, given the nonlinearities associated with phase change dynamics. In this paper we design and experimentally validate a state-dependent Riccati equation (SDRE) filter for state of charge estimation in a phase change material (PCM)-based TES device integrated into a single-phase thermal-fluid loop. The advantage of the SDRE filter is that it does not require linearization of the nonlinear finite-volume model; instead, it uses a linear parameter-varying system model which can be quickly derived using graph-based methods. We leverage graph-based methods to prove that the system model is uniformly detectable, guaranteeing that the state estimates are bounded. Using measurements from five thermocouples embedded in the PCM of the TES and two thermocouples measuring the fluid temperature at the inlet and outlet of the device, the state estimator uses a reduced-order finite-volume model to determine the temperature distribution inside the PCM and in turn, the state of charge of the device. We demonstrate the state estimator in simulation and on experimental data collected from a thermal management system testbed to show that the state estimation error converges near zero and remains bounded., Comment: Manuscript submitted to the ASME Journal on Dynamic Systems, Measurement and Control (JDSMC)

The ever-increasing adoption of shared transportation modalities across the United States has the potential to fundamentally change the preferences and usage of different mobilities. It also raises several challenges with respect to the design and development of automated mobilities that can enable a large population to take advantage of this emergent technology. One such challenge is the lack of understanding of how trust in one automated mobility may impact trust in another. Without this understanding, it is difficult for researchers to determine whether future mobility solutions will have acceptance within different population groups. This study focuses on identifying the differences in trust across different mobility and how trust evolves across their use for participants who preferred an aggressive driving style. A dual mobility simulator study was designed in which 48 participants experienced two different automated mobilities (car and sidewalk). The results found that participants showed increasing levels of trust when they transitioned from the car to the sidewalk mobility. In comparison, participants showed decreasing levels of trust when they transitioned from the sidewalk to the car mobility. The findings from the study help inform and identify how people can develop trust in future mobility platforms and could inform the design of interventions that may help improve the trust and acceptance of future mobility., Comment: https://trid.trb.org/view/2117834

This paper presents identities for calculating over-approximated successor sets of discrete-time nonlinear systems using hybrid zonotopes. The proposed technique extends the state-update set construct, previously developed for linear hybrid systems, to nonlinear systems. Forward reachability of nonlinear systems can then be performed using only projection, intersection, and Cartesian product set operations with the state-update set. It is shown that use of an over-approximation of the state-update set yields over-approximations of successor sets. A technique to over-approximate a nonlinear function using a special ordered set approximation, equivalently represented as a hybrid zonotope, is then presented. A numerical example of a nonlinear system controlled by a piecewise-affine control law demonstrates that the approach provides a computationally-efficient and tight over-approximation of the closed-loop reachable set.

Many dynamical systems, including thermal, fluid, and multi-agent systems, can be represented as weighted graphs. In this paper we consider whether the unstable states of such systems can be observed from limited discrete-time measurement, that is, whether the discrete formulation of system is detectable. We establish that if the associated graph is fully connected, then a linear time invariant system is detectable by measuring any state. Further, we show that a parameter-varying or time-varying system remains uniformly detectable for a reasonable approximation of its state transition matrix, if the underlying graph structure is maintained.

Shared autonomous vehicles (SAVs) will be introduced in greater numbers over the coming decade. Due to rapid advances in shared mobility and the slower development of fully autonomous vehicles (AVs), SAVs will likely be deployed before privately-owned AVs. Moreover, existing shared mobility services are transitioning their vehicle fleets toward those with increasingly higher levels of driving automation. Consequently, people who use shared vehicles on an "as needed" basis will have infrequent interactions with automated driving, thereby experiencing interaction gaps. Using human trust data of 25 participants, we show that interaction gaps can affect human trust in automated driving. Participants engaged in a simulator study consisting of two interactions separated by a one-week interaction gap. A moderate, inverse correlation was found between the change in trust during the initial interaction and the interaction gap, suggesting people "forget" some of their gained trust or distrust in automation during an interaction gap., Comment: 5 pages, 3 figures

Metal hydrides have been studied for use in energy storage, hydrogen storage, and air-conditioning (A/C) systems. A common architecture for A/C and energy storage systems is two metal hydride reactors connected to each other so that hydrogen can flow between them, allowing for cyclic use of the hydrogen. This paper presents a nonlinear dynamic model and multivariate control strategy of such a system. Each reactor is modelled as a shell-and-tube heat exchanger connected to a circulating fluid, and a compressor drives hydrogen flow between the reactors. We further develop a linear state-space version of this model integrated with a model predictive controller to determine the fluid mass flow rates and compressor pressure difference required to achieve desired heat transfer rates between the metal hydride and the fluid. A series of case studies demonstrates that this controller can track desired heat transfer rates in each reactor, even in the presence of time-varying circulating fluid inlet temperatures, thereby enabling the use of a two-reactor system for energy storage or integration with a heat pump., Comment: 42 pages; 14 Figures

This article presents a new set representation named the hybrid zonotope that is equivalent to the union of $2^N$ constrained zonotopes -- convex polytopes -- through the addition of $N$ binary zonotope factors. The major contribution of this manuscript is a closed-form solution for exact forward reachable sets of discrete-time, linear hybrid systems modeled as mixed logical dynamical systems. The proposed approach captures the worst-case exponential growth in the number of convex sets required to represent the nonconvex reachable set while exhibiting only linear growth in the complexity of the hybrid zonotope set representation. Redundancy removal techniques are provided that leverage binary trees to store the combinations of binary factors of the hybrid zonotope that map to nonempty convex subsets. Numerical examples show the hybrid zonotope's ability to compactly represent nonconvex reachable sets with an exponential number of features. Furthermore, the hybrid zonotope is shown to be closed under linear mappings, Minkowski sums, generalized intersections, and halfspace intersections., Comment: 12 pages, 5 figures. Revised manuscript including full proofs of set operations, theoretical results unchanged

Control co-design (CCD) is a technique for improving the closed-loop performance of systems through the coordinated design of both plant parameters and an optimal control policy. While model predictive control (MPC) is an attractive control strategy for many systems, embedding it within a CCD algorithm presents challenges because obtaining a closed-form solution for this receding-horizon optimization strategy is often not feasible. This paper meets that challenge by including a robust MPC formulation within the inner loop of a CCD algorithm. As exemplified by application to an aircraft thermal management system, the proposed algorithm closely matches the plant design of an open-loop benchmark. However, unlike the open-loop approach, the proposed algorithm can leverage MPC control variables designed a priori to achieve robust online operation under disturbance profiles that differ from those used for design.

Properly calibrated human trust is essential for successful interaction between humans and automation. However, while human trust calibration can be improved by increased automation transparency, too much transparency can overwhelm human workload. To address this tradeoff, we present a probabilistic framework using a partially observable Markov decision process (POMDP) for modeling the coupled trust-workload dynamics of human behavior in an action-automation context. We specifically consider hands-off Level 2 driving automation in a city environment involving multiple intersections where the human chooses whether or not to rely on the automation. We consider automation reliability, automation transparency, and scene complexity, along with human reliance and eye-gaze behavior, to model the dynamics of human trust and workload. We demonstrate that our model framework can appropriately vary automation transparency based on real-time human trust and workload belief estimates to achieve trust calibration., Comment: 10 pages, 8 figures

Human trust in automation plays an essential role in interactions between humans and automation. While a lack of trust can lead to a human's disuse of automation, over-trust can result in a human trusting a faulty autonomous system which could have negative consequences for the human. Therefore, human trust should be calibrated to optimize human-machine interactions with respect to context-specific performance objectives. In this article, we present a probabilistic framework to model and calibrate a human's trust and workload dynamics during his/her interaction with an intelligent decision-aid system. This calibration is achieved by varying the automation's transparency---the amount and utility of information provided to the human. The parameterization of the model is conducted using behavioral data collected through human-subject experiments, and three feedback control policies are experimentally validated and compared against a non-adaptive decision-aid system. The results show that human-automation team performance can be optimized when the transparency is dynamically updated based on the proposed control policy. This framework is a first step toward widespread design and implementation of real-time adaptive automation for use in human-machine interactions., Comment: 21 pages

Today, intelligent machines \emph{interact and collaborate} with humans in a way that demands a greater level of trust between human and machine. A first step towards building intelligent machines that are capable of building and maintaining trust with humans is the design of a sensor that will enable machines to estimate human trust level in real-time. In this paper, two approaches for developing classifier-based empirical trust sensor models are presented that specifically use electroencephalography (EEG) and galvanic skin response (GSR) measurements. Human subject data collected from 45 participants is used for feature extraction, feature selection, classifier training, and model validation. The first approach considers a general set of psychophysiological features across all participants as the input variables and trains a classifier-based model for each participant, resulting in a trust sensor model based on the general feature set (i.e., a "general trust sensor model"). The second approach considers a customized feature set for each individual and trains a classifier-based model using that feature set, resulting in improved mean accuracy but at the expense of an increase in training time. This work represents the first use of real-time psychophysiological measurements for the development of a human trust sensor. Implications of the work, in the context of trust management algorithm design for intelligent machines, are also discussed., Comment: 20 pages