We study the temporal robustness of temporal logic specifications and show how to design temporally robust control laws for time-critical control systems. This topic is of particular interest in connected systems and interleaving processes such as multi-robot and human-robot systems where uncertainty in the behavior of individual agents and humans can induce timing uncertainty. Despite the importance of time-critical systems, temporal robustness of temporal logic specifications has not been studied, especially from a control design point of view. We define synchronous and asynchronous temporal robustness and show that these notions quantify the robustness with respect to synchronous and asynchronous time shifts in the predicates of the temporal logic specification. It is further shown that the synchronous temporal robustness upper bounds the asynchronous temporal robustness. We then study the control design problem in which we aim to design a control law that maximizes the temporal robustness of a dynamical system. Our solution consists of a Mixed-Integer Linear Programming (MILP) encoding that can be used to obtain a sequence of optimal control inputs. While asynchronous temporal robustness is arguably more nuanced than synchronous temporal robustness, we show that control design using synchronous temporal robustness is computationally more efficient. This tradeoff can be exploited by the designer depending on the particular application at hand. We conclude the article with a variety of case studies.

In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist non-trivial classes of systems for which learning complexity scales dramatically, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.

Complementarity problems, a class of mathematical optimization problems with orthogonality constraints, are widely used in many robotics tasks, such as locomotion and manipulation, due to their ability to model non-smooth phenomena (e.g., contact dynamics). In this paper, we propose a method to analyze the stability of complementarity systems with neural network controllers. First, we introduce a method to represent neural networks with rectified linear unit (ReLU) activations as the solution to a linear complementarity problem. Then, we show that systems with ReLU network controllers have an equivalent linear complementarity system (LCS) description. Using the LCS representation, we turn the stability verification problem into a linear matrix inequality (LMI) feasibility problem. We demonstrate the approach on several examples, including multi-contact problems and friction models with non-unique solutions.

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical dynamical systems in feedback with a ReLU neural network controller, etc. The proposed method comprises an alternation between a learner and a verifier to search for a Lyapunov function from a family of parameterized Lyapunov function candidates. In each iteration, the learner uses a collection of state samples to select a Lyapunov function candidate through a convex program in the parameter space. The verifier then solves a nonconvex mixed-integer quadratic program in the state space to either validate the proposed Lyapunov function candidate or reject it with a counterexample, i.e., a state where the Lyapunov condition fails. This counterexample is then added to the sample set of the learner to refine the set of Lyapunov function candidates in the next iteration. By designing the learner and the verifier according to the analytic center cutting-plane method from convex optimization, we show that when the set of Lyapunov functions is full-dimensional in the parameter space, our method finds a Lyapunov function in a finite number of steps. We demonstrate our stability analysis method on closed-loop MPC dynamical systems and a ReLU neural network controlled PWA system.

We solve active target tracking, one of the essential tasks in autonomous systems, using a deep reinforcement learning (RL) approach. In this problem, an autonomous agent is tasked with acquiring information about targets of interests using its on-board sensors. The classical challenges in this problem are system model dependence and the difficulty of computing information-theoretic cost functions for a long planning horizon. RL provides solutions for these challenges as the length of its effective planning horizon does not affect the computational complexity, and it drops the strong dependency of an algorithm on system models. In particular, we introduce Active Tracking Target Network (ATTN), a unified deep RL policy that is capable of solving major sub-tasks of active target tracking – in-sight tracking, navigation, and exploration. The policy shows robust behavior for tracking agile and anomalous targets with a partially known target model. Additionally, the same policy is able to navigate in obstacle environments to reach distant targets as well as explore the environment when targets are positioned in unexpected locations.

In this paper, we propose a novel Reinforcement Learning approach for solving the Active Information Acquisition problem, which requires an agent to choose a sequence of actions in order to acquire information about a process of interest using on-board sensors. The classic challenges in the information acquisition problem are the dependence of a planning algorithm on known models and the difficulty of computing information-theoretic cost functions over arbitrary distributions. In contrast, the proposed framework of reinforcement learning does not require any knowledge on models and alleviates the problems during an extended training stage. It results in policies that are efficient to execute online and applicable for real-time control of robotic systems. Furthermore, the state-of-the-art planning methods are typically restricted to short horizons, which may become problematic with local minima. Reinforcement learning naturally handles the issue of planning horizon in information problems as it maximizes a discounted sum of rewards over a long finite or infinite time horizon. We discuss the potential benefits of the proposed framework and compare the performance of the novel algorithm to an existing information acquisition method for multi-target tracking scenarios.

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning controllers. Existing methods in the literature for estimating the Lipschitz constant suffer from either lack of accuracy or poor scalability. In this paper, we present a convex optimization framework to compute guaranteed upper bounds on the Lipschitz constant of DNNs both accurately and efficiently. Our main idea is to interpret activation functions as gradients of convex potential functions. Hence, they satisfy certain properties that can be described by quadratic constraints. This particular description allows us to pose the Lipschitz constant estimation problem as a semidefinite program (SDP). The resulting SDP can be adapted to increase either the estimation accuracy (by capturing the interaction between activation functions of different layers) or scalability (by decomposition and parallel implementation). We illustrate the utility of our approach with a variety of experiments on randomly generated networks and on classifiers trained on the MNIST and Iris datasets. In particular, we experimentally demonstrate that our Lipschitz bounds are the most accurate compared to those in the literature. We also study the impact of adversarial training methods on the Lipschitz bounds of the resulting classifiers and show that our bounds can be used to efficiently provide robustness guarantees.

The proposed paper presents a method to optimally select components of a drivetrain for an electrically actuated machine. A simple mathematical model of the machine is established and inequality constraints which determine the choice of drivetrain components are formulated. Elements to be picked (namely, a motor, a gearbox, and a drive) are taken from a discrete set of data provided in the catalogs of industrial motors and drives manufacturers. By solving an optimization problem, a combination of components which both satisfy design requirements and minimize the total drivetrain cost is selected. The operation of the selected drivetrain is verified against the motor loadability curves. In addition, feasibility of other possible drivetrain configurations is checked and benchmarked with the optimal solution. Practical significance of the current work is demonstrated on a winch mechanism which is a popular part of many engineering applications, however, methods presented here could easily be adapted to other machines and industries. The results of the current work allow to reduce conservatism when designing actuation systems, while still satisfying the safety requirements specified by the designer. The system operating conditions are therefore effectively shifted to be closer to the constraints, which results in increasing the overall efficiency of the design and proving its cost-effectiveness.

Some aerial tasks are achieved more efficiently and at a lower cost by a group of independently controlled micro aerial vehicles (MAVs) when compared to a single, more sophisticated robot. Controlling formation flight can be cast as a two-level problem: stabilization of relative distances of agents (formation shape control) and control of the center of gravity of the formation. To date, accurate shape control of a formation of MAVs usually relies on external tracking devices (e.g. fixed cameras) or signals (e.g. GPS) and uses centralized control, which severely limits its deployment. In this paper, we present an environment-independent approach for relative MAV formation flight, using a distributed control algorithm which relies only on embedded sensing and agentto- agent communication. In particular, an on-board monocular camera is used to acquire relative distance measurements in combination with a consensus-based distributed Kalman filter. We evaluate our methods in- and outdoors with a formation of three MAVs while controlling the formation's center of gravity manually.

This paper considers the efficient operation of shared mobility systems via the combination of intelligent routing decisions for staff-based vehicle redistribution and real-time price incentives for customers. The approach is applied to London's Barclays Cycle Hire scheme, which the authors have simulated based on historical data. Using model-based predictive control principles, dynamically varying rewards are computed and offered to customers carrying out journeys, based on the current and predicted state of the system. The aim is to encourage them to park bicycles at nearby underused stations, thereby reducing the expected cost of redistributing them using dedicated staff. In parallel, routing directions for redistribution staff are periodically recomputed using a model-based heuristic. It is shown that it is possible to trade off reward payouts to customers against the cost of hiring staff to redistribute bicycles, in order to minimize operating costs for a given desired service level.

Control of grid inverters aims to meet two challenging objectives: zero steady-state tracking offset in the grid current to achieve a high power factor, and attenuation of the inverter and grid harmonics to respect the limits imposed on the current harmonics injected into the grid. This paper proposes an observer-based model predictive control approach to meet these control objectives for single and three-phase grid inverters with LCL filters. A Kalman-filter based observer design is used to estimate the system states and harmonic disturbances based on the grid current measurement. A model predictive control scheme is employed to achieve offset-free reference tracking for the grid current, and rejection of low frequency harmonics. The scheme features not only rejection of grid voltage harmonics, but also rejection of low frequency inverter distortion caused, for example, by nonlinear filter inductances. The effectiveness of the scheme is demonstrated in simulation.

The paper investigates optimal modulation of isolated two-quadrant and multisource DC-DC converters. Due to their numerous degrees of freedom there are infinitely many possibilities to modulate the voltage patterns in order to achieve the desired power transfer. The objective of this work is to exploit this flexibility to derive a modulation strategy that minimises the system power losses. A systematic modelling and optimisation approach is proposed that allows to minimise the overall losses subject to constraints on particular devices. The obtained optimal modulation angles are stored in look-up tables. The impact of the transformer leakage inductance on the efficiency is investigated, which gives some indications on how to design the transformer. Effectiveness of the approach is demonstrated in simulation.

In recent years, gait robots have become increasingly common for gait rehabilitation in non-ambulatory stroke patients. Cardiovascular treadmill training, which has been shown to provide great benefit to stroke survivors, cannot be performed with non-ambulatory patients. We therefore integrated cardiovascular training in robot-assisted gait therapy to combine the benefits of both training modi. We developed a model of human heart rate as a function of exercise parameters during robot-assisted gait training and applied it for automatic control purposes. This structural model of the physiological processes describes the change in heart rate caused by treadmill speed and the power exchanged between robot and subject. We performed physiological parameter estimation for each tested individual and designed a model-based feedback controller to guide heart rate to a desired time profile. Five healthy subjects and eight stroke patients were recorded for model parameter identification, which was successfully used for heart rate control of three healthy subjects. We showed that a model-based control approach can take into account patient-specific limitations of treadmill speed as well as individual power expenditure.

Irrigation canals transport water from water sources (such as large rivers and lakes) to water users (such as farmers). Irrigation canals are typically very large in nature, covering vast geographical areas, and involving a significant number of control actuators, such as pumps, gates, and locks. The control of such canals is aimed at guaranteeing the adequate delivery of water with minimal water spillage and with minimal control structure usage. To take into account forecasts on, e.g., water consumption and weather, model predictive control (MPC) can be used to determine which actions to take. For large-scale systems, in which different parts of the canal are owned by different parties, distributed MPC control could then be employed. Although iterative distributed MPC approaches proposed earlier in the literature may yield overall optimal performance, the amount of iterations required before achieving this performance may be large, and thus require a significant amount of time. In this paper, the structure of systems consisting of serially interconnected subsystems is exploited to obtain an efficient non-iterative, cascaded MPC scheme. Simulation studies on a 7-reach irrigation canal illustrate the performance of this non-iterative scheme in comparison with an iterative scheme.

Monitored anesthesia care (MAC) is increasingly used to provide patient comfort for diagnostic and minor surgical procedures. The drugs used in this setting can cause profound respiratory depression even in the therapeutic concentration range. Titration to effect suffers from the difficulty to predict adequate analgesia prior to application of a stimulus, making titration to a continuously measurable side effect an attractive alternative. Exploiting the fact that respiratory depression and analgesia occur at similar drug concentrations, we suggest to administer opioids and propofol during MAC using a feedback control system with transcutaneously measured partial pressures of CO2(PtcCO2) as the controlled variable. To investigate this dosing paradigm, we developed a comprehensive model of human metabolism and cardiorespiratory regulation, including a compartmental pharmacokinetic and a pharmacodynamic model for the fast acting opioid remifentanil. Model simulations are in good agreement with ventilatory experimental data, both in presence and absence of drug. Closed-loop simulations show that the controller maintains a predefined CO2target in the face of surgical stimulation and variable patient sensitivity. It prevents dangerous hypoventilation and delivers concentrations associated with analgosedation. The proposed control system for MAC could improve clinical practice titrating drug administration to a surrogate endpoint and actively limiting the occurrence of hypercapnia/hypoxia.

This paper presents newly developed algorithms for automatic adaptation of motion for a robotic rehabilitation device. The algorithms adapt the gait pattern of patients that walk on a treadmill. Three different algorithms were developed. The first one is based on inverse dynamics and online minimization of the human-machine interaction torque. The second one is based on direct dynamics and estimation of the desired variation in the gait-pattern acceleration. The third algorithm is based on impedance control and direct adaptation of the gait pattern angular trajectories. The algorithms were tested and compared in computer simulations and actual experiments on healthy subjects and patients. In simulations, all algorithms have adapted the gait pattern toward the desired one, which led to a greater than 40% reduction of interaction torques. The impedance-control-based algorithm performed best in the experiments.

Online condition monitoring and diagnosis are being utilized more and more for increasing the reliability and availability of technical systems and to reduce their maintenance costs. Today's model-based diagnosis (MBD) tools are able to detect and identify incipient and sudden faults very reliably. For application to cost-sensitive equipment, such as high-voltage circuit breakers (HVCBs), however, the presently available MBD systems are not feasible for economic reasons. In this paper, a novel combination of the model-based with the case-based approach to condition diagnosis is presented, which can be implemented on a low-cost computer and which offers satisfactory performance. The technique is divided into two parts: (1) preparation and (2) diagnosis. The diagnosis part can be executed on an inexpensive low-performance computer. Successful tests on real HVCBs confirm the usefulness of this new approach to condition diagnosis.