The circadian rhythm functions as a master clock that regulates many physiological processes in humans including sleep, metabolism, hormone secretion, and neurobehavioral processes. Disruption of the circadian rhythm is known to have negative impacts on health. Light is the strongest circadian stimulus that can be used to regulate the circadian phase. In this paper, we consider the mathematical problem of time-optimal circadian (re)entrainment, i.e., computing the lighting schedule to drive a misaligned circadian phase to a reference circadian phase as quickly as possible. We represent the dynamics of the circadian rhythm using the Jewett-Forger-Kronauer (JFK) model, which is a third-order nonlinear differential equation. The time-optimal circadian entrainment problem has been previously solved in settings that involve either a reduced-order JFK model or open-loop optimal solutions. In this paper, we present (1) a general solution for the time-optimal control problem of fastest entrainment that can be applied to the full order JFK model (2) an evaluation of the impacts of model reduction on the solutions of the time-optimal control problem, and (3) optimal feedback control laws for fastest entrainment for the full order Kronauer model and evaluate their robustness under some modeling errors.

The aim is to synthesize control inputs for robotic manipulator arms that ensure a desired task specification is executed while optimizing a desired performance objective. We use Metric Temporal Logic (MTL) to express the task specifications defined in terms of manipulating objects and implemented a hierarchical method combining Mixed Integer- Linear Programming (at high-level) to obtain a candidate MTL task specification defined in terms of the location of the arm end-effector and gradient descent based optimization (at low-level) for automatic synthesis of the motion plans to execute such candidate task specifications. The gradient descent algorithm is performed over the feasible input space to optimize the manipulator arm trajectory from a given arbitrary initial condition to perform the task at hand. We demonstrate the efficacy of our method by simulating a task specification on a Baxter robot.

In this paper, we present a method to learn (infer) and refine a set of advices from the trajectories generated in the successful and failed attempts in a task or game, in the form of advisory signal temporal logic (STL) formulas. Each advice consists of an advisory motion STL formula that characterizes the spatial-temporal pattern of the motion as a feature of success and an advisory selection STL formula as a criterion for the environment to select the advice. For the inference of advisory STL formulas, we provide a theoretical framework of perfect classification with a labeled set of trajectories with different time lengths. We design an advisory controller that can drive the robots to satisfy an advisory motion STL formula based on the advice selected according to the advisory selection STL formula. The advisory controller can advise or guide the human operators or the robots for better performance with the shared autonomy between the human operator and the controller. We provide two case studies to test the effectiveness of the advisory controller, one with a Baxter-On-Wheels simulator and the other with two quadrotors in an experimental testbed in iteratively improving the success rates of completing the tasks with the help of the designed advisory controller.

We present an energy storage controller synthesis method for power systems with respect to metric temporal logic (MTL) specifications. The power systems with both constant impedance loads and constant power loads are modeled as a set of differential–algebraic equations. After a fault is cleared, with uncertainties in the fault clearing time, the generator machine angles and rotor speed deviations will enter a set of postfault initial states. We use the robust neighborhood approach to cover this set using the initial robust neighborhoods of finitely many simulated postfault trajectories. These simulated postfault trajectories meet the frequency regulation requirements specified in MTL as they are driven by the optimal control input signals obtained through a functional gradient descent approach. In this way, all the possible postfault trajectories with the given uncertainties in the fault clearing time are guaranteed to satisfy the MTL specification. Furthermore, we learn a piecewise linear control law from the data of the simulated trajectories to generate a feedback controller.

In this paper, we propose a method to perform swarm behavior analysis with a novel swarm signal temporal logic (SwarmSTL). We define generalized moments to describe swarm features and propose a logical proposition to represent an event, where the Boolean value of the logical proposition at a certain time is known a priori. We develop methods for SwarmSTL monitoring and inference. As the swarm size can be large, we also propose methods to perform the above tasks by sampling. In particular, we apply our methods to three case studies that aim to monitor swarm "maneuver" behavior using an agent sample, infer a SwarmSTL formula to describe the cause of the split, and explore a SwarmSTL formula to describe "mixed-species foraging flock" of birds.

In complex cyber-physical system operations, fault detection needs to be performed using limited state information for practicality and privacy concerns. While a well-designed observation can distinguish a faulty behavior from the normal behavior, it can also represent the action of hiding some of the state information or discrete mode switchings. In this paper, we present a method for constructing the observation maps in the form of metric temporal logic (MTL) formulas that can be formally proven to detect fault in a switched system, while preserving certain privacy conditions. We provide a theoretical framework of robust temporal logic inference for classification of switched system trajectories with spatial and temporal uncertainties. We simulate finitely many nominal trajectories and use the robust neighborhoods around the simulated trajectories to cover the infinite trajectories that constitute the system behavior. Thus, the designed observation maps with the inferred MTL formulas can detect fault and preserve privacy in a provably correct fashion. Our approach is implemented on the simulation model of a smart building testbed to detect thermal leakage in the room, while preserving multiple privacy conditions of the room occupancy.