State Trajectories Research Articles

Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing.

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)0006-349510.1016/S0006-3495(77)85544-6] on cellular sensing along multiple dimensions.

Emergency welfare states in action: Social policy adaptations to COVID‐19 in the Czechia, Hungary and Slovakia

AbstractThis article analyses the developments of the welfare state's reaction to the pandemic in Czechia, Hungary and Slovakia during 2020–2022, asking whether the changes in social policy represent only temporary responses to the challenges of the pandemic, or if the changes will likely lead to long‐run transformative changes in social policies. All three countries applied emergency adaptive changes to some extent except for job protection, as the short‐time work schemes represent a permanent change in Czechia and Slovakia. Furthermore, the absorption capacity of the welfare state was relatively good, which enabled the countries to avoid the negative social impacts of the crisis in terms of increased unemployment, poverty, and social exclusion. We argue the governments did not introduce permanent third‐order change because they already introduced such changes during the transition to the market economy in which they introduced a low‐expenditure welfare state trajectory. During the pandemic, this trajectory limited their fiscal space for introducing reforms that could radically expand the welfare state. Policy learning and political constellations also had some influence.

Dynamical analysis and reachable set estimation of T-S fuzzy system with permanent magnet synchronous motor

In this study, we will present the dynamical analysis for permanent magnet synchronous motors (PMSM). Our goal is to identify an ellipsoid that contains the state trajectory of the system in as small a form as possible in the presence of control. First, we designed the non-fragile sampled-data fuzzy controller (NFSDFC) for the PMSM model. Second, the Lyapunov-Krasovskii functional (LKF) strategy, novel integral inequality mechanisms, and certain sufficient conditions are determined, which ensure an ellipsoidal bound of reachable sets for the closed-loop of a system with input constraints derived in terms of linear matrix inequalities (LMIs). Meanwhile, under the larger sampling interval, the corresponding sampled-data controller gains are designed. Finally, numerical examples are given to validate the derived theoretical results.

The future of work: AI, automation, and the changing dynamics of developed economies

Artificial intelligence (AI) and automation technologies are rapidly evolving, which will have far-reaching implications for the future of work and the dynamics of developed economies. This research aims to explore the potential impact of AI and automation on the labor market, employment patterns, and the overall socioeconomic landscape. The study uses a literature review and analysis of existing research, policy documents, and expert opinions to understand AI and automation's current state and future trajectory in developed economies. Key areas of investigation include the potential displacement of human labor, the emergence of new job opportunities, changes in skill requirements, and the implications for income inequality. The findings reveal that AI and automation have already disrupted various sectors of the economy, with routine and repetitive tasks being particularly susceptible to automation. The research highlights the potential for new types of jobs to emerge, requiring a combination of technical skills, creativity, and social intelligence. The study emphasizes the importance of lifelong learning and reskilling programs to prepare the workforce for the changing demands of the future job market. It also emphasizes the need for proactive policies and regulatory frameworks to address potential societal challenges arising from AI and automation. Additionally, it highlights the importance of collaboration between government, academia, and industry stakeholders to navigate the evolving work landscape.

Integration of sEMG-Based Learning and Adaptive Fuzzy Sliding Mode Control for an Exoskeleton Assist-as-Needed Support System

This paper presents an adaptive Fuzzy Sliding Mode Control approach for an Assist-as-Needed (AAN) strategy to achieve effective human–exoskeleton synergy. The proposed strategy employs an adaptive instance-based learning algorithm to estimate muscle effort, based on surface Electromyography (sEMG) signals. To determine and control the inverse dynamics of a highly nonlinear 4-degrees-of-freedom exoskeleton designed for upper-limb therapeutic exercises, a modified Recursive Newton-Euler Algorithm (RNEA) with Sliding Mode Control (SMC) was used. The exoskeleton position error and raw sEMG signal from the bicep’s brachii muscle were used as inputs for a fuzzy inference system to produce an output to adjust the sliding mode control law parameters. The proposed robust control law was simulated using MATLAB-Simulink, and the results showed that it could instantly adjust the necessary support, based on the combined motion of the human–exoskeleton system’s muscle engagement, while keeping the state trajectory errors and input torque bounded within ±5×10−2 rads and ±5 N.m, respectively.

COVID-19 and welfare state trajectory in South Korea: Stagnation, consolidation, or transformation?

COVID-19 and welfare state trajectory in South Korea: Stagnation, consolidation, or transformation?

Practical exponential stability of switched homogeneous positive nonlinear systems with stable and unstable modes

In this article, we primarily investigate practical exponential stability of switched homogeneous positive nonlinear systems (SHPNSs) that have partial unstable modes and perturbation. First of all, the max-separable Lyapunov function (MSLF) technique and a special pre-setting switching sequence are used to define a number of significant stability conditions that ensure the state trajectories of the system converge to a confined region in continuous-time and discrete-time domains. In addition, the key results include several earlier findings as special situations and can be directly applied to general switched systems, not necessarily positive. Finally, two important instances are provided to further illustrate the validity of the theoretical findings.

A unified science of matter, life and evolution.

We are accustomed to looking at matter, life and evolution from different viewpoints. In this article, we present a simple but unified theoretical framework inspired by classical mechanics and thermodynamics. Our framework generalizes Newton's third law of matter to encompass life and evolution. The generalized action-reaction relationship includes scale and temporal parameters. This generalization helps explain why life is a system out of equilibrium. Life can go beyond the action-reaction symmetry law of matter. We define life as an open system that is self-aware of the time trajectory of energy state and environment. The theoretical framework we propose for studying life in terms of power reduces to the science of matter as a limiting case. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

An approach to the stability of reset switched systems using dynamics without reset

In this paper, we consider switched linear systems that have jumps in the state (determined by a reset rule) at each switching instant. Those systems are called switched systems with state reset. We show that it is possible to analyze the state trajectories of a switched system with state reset by considering suitable switched systems without state resets, that is, with continuous state trajectories. We establish sufficient conditions for the stability of switched systems with state reset using the associated systems without reset. Moreover, introducing some restrictions, we also derive simple algebraic stability conditions. The obtained results are used in numerical examples to show the effectiveness of the proposed approach.

Modelowanie matematyczne i badania symulacyjne bioreaktora z wymuszonym napowietrzaniem

The composting process is commonly used in waste management as a method of converting or stabilizing organic waste. Due to the complex, non-linear nature of biological and physicochemical phenomena involved, this process is relatively difficult to predict and control. The control is usually aimed at obtaining the final product, that is, the compost that meets legal standards. The article presents a simple mathematical model of the composting process with forced aeration, which will potentially facilitate the control task. A second order model was developed, with two inputs signals. Based on the mathematical model in the form of the state equations, the computer model of the bioreactor was built in the MATLAB/Simulink environment, which was then used to conduct different simulation tests. It was shown that it is possible to control the process using forced aeration, directly influencing the temperature changes in the bioreactor, and consequently also the time of obtaining the final product of the reaction. The analysis of the dynamic properties of the process performed using its model linearized about some nominal state trajectory shows the changes in its internal stability—starting from the unstable character in the initial phases of the reaction, through stabilization in its intermediate phase, up to the asymptotic stability, ending in the stable equilibrium state.

Dynamic soaring in wind turbine wakes

Dynamic soaring for UAVs is a flight technique that enables continuous, powerless periodic flight patterns in the presence of a wind gradient. However, sufficiently large wind gradients are uncommon over land, while at offshore locations the largest wind gradients are located close to the ocean surface, thereby limiting the scope of practical application. An intrinsic feature of wind turbines is that they inherently produce very sharp wind gradients in the near wake. Therefore, in this paper, we propose and investigate periodic stationary dynamic soaring trajectories in the near wake of wind turbines. We additionally consider the potential of dynamic soaring for revitalizing the wind turbine wake. To this end, we apply periodic optimal control based on a simplified model for the glider dynamics and the wind profile in the wake. The cost function maximizes the revitalization of the wake. We compute optimal orbits for a range of different wing spans and different mass-scaling assumptions. The largest glider configuration, with a wingspan of 10 m and a mass of 222.6 kg, achieves a wake revitalization of about 0.94% of the total turbine thrust.

Estimation of reachable set for switched singular systems with time-varying delay and state jump

This paper addresses the estimation problem of the reachable set for switched singular systems with state jump under initial condition and bounded peak disturbance. The aim is to determine a bounded set that contains all reachable states. Initially, a state jump lemma is presented for switched singular systems. Then, a new bounding lemma is shown by analyzing the variation of piecewise continuous functional in subintervals and referencing the definition of the average dwell-time. Afterwards, using lemmas and linear matrix inequalities, sufficient conditions are derived for switched singular systems with and without time-varying delay, which ensure that the state trajectory of the system remains within a closed bounded set. Finally, the obtained results are validated through numerical examples.

Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

In this article, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we call the entropic cost equilibrium (ECE). We show that ECE is a natural extension to multiple agents of maximum entropy optimality for a single agent. We solve both the “forward” and “inverse” problems for the multi-agent ECE game. For the forward problem, we provide a Riccati algorithm to compute closed-form ECE feedback policies for the agents, which are exact in the linear-quadratic-gaussian case. We give an iterative variant to find locally ECE feedback policies for the nonlinear case. For the inverse problem, we present an algorithm to infer the cost functions of the multiple interacting agents given noisy, boundedly rational input and state trajectory examples from agents acting in an ECE. The effectiveness of our algorithms is demonstrated in a simulated multi-agent collision avoidance scenario, and with data from the INTERACTION traffic dataset. In both cases, we show that, by taking into account the agents' game theoretic interactions using our algorithm, a more accurate model of agents' costs can be learned, compared with standard inverse optimal control methods.

Smoother Entropy for Active State Trajectory Estimation and Obfuscation in POMDPs

We study the problem of controlling a partially observed Markov decision process (POMDP) to either aid or hinder the estimation of its state trajectory. We encode the estimation objectives via the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">smoother entropy</i> , which is the conditional entropy of the state trajectory given measurements and controls. Consideration of the smoother entropy contrasts with previous approaches that instead resort to marginal (or instantaneous) state entropies due to tractability concerns. By establishing novel expressions for the smoother entropy in terms of the POMDP belief state, we show that both the problems of minimising and maximising the smoother entropy in POMDPs can surprisingly be reformulated as belief-state Markov decision processes with concave cost and value functions. The significance of these reformulations is that they render the smoother entropy a tractable optimisation objective, with structural properties amenable to the use of standard POMDP solution techniques for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> active estimation and obfuscation. Simulations illustrate that optimisation of the smoother entropy leads to superior trajectory estimation and obfuscation compared to alternative approaches.

Optimal Thermal Management, Charging, and Eco-Driving of Battery Electric Vehicles

This paper addresses optimal battery thermal management, charging, and eco-driving of a battery electric vehicle (BEV) with the goal of improving its grid-to-meter energy efficiency. Thus, an optimization problem is formulated, aiming at finding the optimal trade-off between trip time and charging cost. The formulated problem is then transformed into a hybrid dynamical system, where the dynamics in driving and charging modes are modeled with different functions and with different state and control vectors. Moreover, to improve computational efficiency, we propose modeling the driving dynamics in a spatial domain, where decisions are made along the traveled distance. Charging dynamics are modeled in a temporal domain, where decisions are made along a normalized charging time. The actual charging time is modeled as a scalar variable that is optimized simultaneously with the optimal state and control trajectories, for both charging and driving modes. The performance of the proposed algorithm is assessed over a road with a hilly terrain, where two charging possibilities are considered along the driving route and the battery is soaked to the ambient before departure. According to the results, trip time including driving and charging times, is reduced by 44%, compared to a case without active heating/cooling of the battery.

Simultaneous moving horizon estimation and control for nonlinear systems subject to bounded disturbances

SummaryIn this work, we address the output–feedback control problem for nonlinear systems under bounded disturbances using a moving horizon approach. The controller is posed as an optimisation‐based problem that simultaneously estimates the state trajectory and computes future control inputs. It minimizes a criterion that involves finite backward and forward horizons with respect to the unknown initial state, measurement noises and control input variables. The main novelty of this work relies on linking the lengths of the forward and backward windows with the closed‐loop stability, assuming detectability and decoding sufficient conditions to assure system stabilizability. It leads to a formulation that does not require to be a Control Lyapunov Function for the terminal cost of the controller. Simulation examples are carried out to compare the performance of solving simultaneously and independently the estimation and control problems. Furthermore, the examples show how the controller influences the length of the estimation window through its gain.

Robust model predictive control for constrained linear system based on a sliding mode disturbance observer

For perturbed continuous-time systems, this paper proposes a robust model predictive control (RMPC) strategy for the regulation problem, exploiting a sliding mode disturbance observer. The main advantage is that it effectively enables the RMPC to be designed based on a model with reduced uncertainties. The proposed sliding mode observer (SMO) is finite-time convergent allowing the estimation error of the additive disturbance to be explicitly bounded by a predictable and decreasing limit. Due to the compensation of the estimated disturbance, the uncertainty that the RMPC has to handle is reduced from the original disturbance to the estimation error of the disturbance. This ensures all the admissible state trajectories are limited within a shrinking neighborhood of the origin and the steady-state error is therefore reduced. Simulation results show the effectiveness of the proposed method.

A Discrete Integral Sliding Manifold for a Nonlinear System with Time Delay: An Event-Triggered Scheme

This paper presents a new approach to integral sliding mode control for discrete nonlinear systems with time delay. The approach is based on an event-triggered scheme and is applied to Takagi–Sugeno fuzzy models. In the first step, a new integral sliding function is constructed, which avoids the limited assumptions of most existing fuzzy sliding mode control schemes. The design parameter matrices defining the sliding surface are obtained by solving linear matrix inequalities. In the second step, an event trigger-based integral sliding mode control protocol is developed to ensure the state trajectories of the Takagi–Sugeno fuzzy systems with time delays. Finally, the proposed strategies are evaluated through a simulation example to demonstrate their effectiveness.

Dynamic behavior and sliding mode control on a stochastic epidemic model with alertness and distributed delay

In this paper, a stochastic SEIR epidemic model with alertness and distributed delay is studied. The dynamic behavior of the model is analyzed and an integral sliding mode controller is designed. By using Lyapunov function method, sufficient conditions for the existence of unique global positive solution and stationary distribution are obtained. To analyze stochastic stability and stochastic bifurcation through singular boundary theory, we apply stochastic center manifold and stochastic averaging method to transform the model into a one-dimensional Markov diffusion process. The integral sliding mode controller is designed to confine the state trajectories of system to a sufficiently small band around the sliding mode surface, and prevent large outbreak of disease. Numerical simulations verify the correctness of the theoretical analysis and the effectiveness of the controller.

Tracking periodic parametric references using model predictive control

AbstractThis paper presents a model predictive controller for tracking periodic parametric reference curves. The controller is formulated in a single layer so that the time‐parameterization of the reference curve, the trajectory planning, and the trajectory tracking tasks are solved in a single optimization problem which is computed at each sampling time. The auxiliary state and input trajectories are introduced into the optimization problem as decision variables, which become the planned trajectory to be effectively followed. By design, the closed‐loop system guarantees of recursive feasibility of the optimization problem while being able to handle arbitrary changes of reference during execution time. Such properties are discussed in detail, and new results on the asymptotic average performance are presented. Simulation results show the benefits of the proposed strategy.