Stability Arguments Research Articles

Cooperative Trajectory Planning for Haptic Shared Control Between Driver and Automation in Highway Driving

This paper addresses the driver–automation shared driving control for lane keeping and obstacle avoidance of automated vehicles in highway traffic. The proposed shared control framework is established from a novel cooperative trajectory planning algorithm and a fuzzy steering controller. Based on polynomial functions, the cooperative trajectory planning is formulated by judiciously exploiting the information on the maneuver decision, the conflict management, and the driver monitoring. As a result, the planned trajectory of the vehicle is continuously adapted according to the driver's actions and intentions. By means of Lyapunov stability arguments, sufficient conditions in terms of linear matrix inequalities are given to design a Takagi–Sugeno fuzzy model-based controller. This robust steering controller provides a necessary assistive torque to track the planned vehicle trajectory. The new shared driving control framework allows reducing effectively the driver–automation conflict issue while offering the driver more freedom to swerve within a predefined lane. The advantages of the proposed approach are evaluated using both objective and subjective results, experimentally obtained from several human drivers and an advanced interactive dynamic driving simulator.

Entropy‐satisfying scheme for a hierarchy of dispersive reduced models of free surface flow

SummaryThis work is devoted to the numerical resolution in the multidimensional framework of a hierarchy of reduced models of the water wave equations, such as the Serre‐Green‐Naghdi model. A particular attention is paid to the dissipation of mechanical energy at the discrete level, which acts as a stability argument of the scheme, even with source terms such space and time variation of the bathymetry. In addition, the analysis leads to a natural way to deal with dry areas without leakage of energy. To illustrate the accuracy and the robustness of the strategy, several numerical experiments are carried out. In particular, the strategy is capable of treating dry areas without special treatment.

Near-resonance in a System of Sub-Neptunes from TESS

Abstract We report the Transiting Exoplanet Survey Satellite detection of a multi-planet system orbiting the V = 10.9 K0 dwarf TOI-125. We find evidence for up to five planets, with varying confidence. Three transit signals with high signal-to-noise ratio correspond to sub-Neptune-sized planets (2.76, 2.79, and 2.94 R ⊕), and we statistically validate the planetary nature of the two inner planets (P b = 4.65 days, P c = 9.15 days). With only two transits observed, we report the outer object (P .03 = 19.98 days) as a planet candidate with high signal-to-noise ratio. We also detect a candidate transiting super-Earth (1.4 R ⊕) with an orbital period of only 12.7 hr and a candidate Neptune-sized planet (4.2 R ⊕) with a period of 13.28 days, both at low signal-to-noise ratio. This system is amenable to mass determination via radial velocities and transit-timing variations, and provides an opportunity to study planets of similar size while controlling for age and environment. The ratio of orbital periods between TOI-125 b and c (P c /P b = 1.97) is slightly lower than an exact 2:1 commensurability and is atypical of multiple planet systems from Kepler, which show a preference for period ratios just wide of first-order period ratios. A dynamical analysis refines the allowed parameter space through stability arguments and suggests that despite the nearly commensurate periods, the system is unlikely to be in resonance.

𝖥𝖨-hyperhomology and ordered configuration spaces

Using a result of Gan–Li on F I \mathsf {FI} -hyperhomology and a semisimplicial resolution of configuration spaces due to Randal-Williams, we establish an improved representation stability stable range for configuration spaces of distinct ordered points in a manifold. Our bounds on generation degree improve the best known stability slope by a factor of 5/2 in the most general case. We adapt this result of Gan–Li to apply beyond stability arguments involving highly connected simplicial complexes, and our methods suggest that their result may be widely applicable to improving most stability ranges for F I \mathsf {FI} -modules in the current representation stability literature.

Driver-Automation Cooperation Oriented Approach for Shared Control of Lane Keeping Assist Systems

This paper presents a novel shared control concept for lane keeping assist (LKA) systems of intelligent vehicles. The core idea is to combine system perception with robust control so that the proposed strategy can successfully share the control authority between human drivers and the LKA system. This shared control strategy is composed of two parts, namely an operational part and a tactical part. Two local optimal-based controllers with two predefined objectives (i.e., lane keeping and conflict management) are designed in the operational part. The control supervisor in the tactical part aims to provide a decision-making signal which allows for a smooth transition between two local controllers. The control design is based on a human-in-the-loop vehicle system to improve the mutual driver-automation understanding, thus reducing or avoiding the conflict. The closed-loop stability of the whole driver-vehicle system can be rigorously guaranteed using the Lyapunov stability argument. In particular, the control design is formulated as an LMI optimization which can be easily solved with numerical solvers. The effectiveness of the proposed shared control method is clearly demonstrated through various hardware experiments with human drivers.

Mobile observation for distributed parameter system with moving boundary over mobile sensor networks

This paper considers the state observation for a class of distributed parameter systems (DPSs) with moving boundaries modelled by parabolic partial differential equations (PDEs). The method of mobile observation is presented to improve the observation performance of the systems and to eliminate the influence of moving boundaries on system observation with the aids of mobile sensor networks (MSNs). The MSNs which can move throughout the time-dependent spatial domain are used to provide the spatially averaged observations of the DPSs. By using the abstract evolution equation theory of parabolic PDEs and the Lyapunov stability arguments, a centralised observer is designed and a mobile control scheme for each of the mobile sensors is presented while taking account of the dynamics of the MSNs. A numerical example is finally presented to illustrate the effectiveness and the advantages of the proposed approach.

Diffusion in CaCO3 Calcite Investigated by Atomic-Scale Simulations

In the context of CO2 storage, we used ab initio-based atomic-scale modelings and simulations to study oxygen and carbon diffusion in CaCO3 calcite. In overall agreement with earlier experimental findings, oxygen diffusion is found to take place possibly by either interstitial or vacancy mechanisms depending on the thermodynamic conditions. Contrary to almost isotropic interstitial diffusion, the vacancy mechanism strongly favors oxygen jumps within (111) planes characteristic of the CaCO3 layered structure, with significant less-than-unity correlation factors. Our simulations show that such mechanisms cannot be applied to carbon, and complex point defects may be required to explain the diffusion of this element. While stability arguments indicate that vacancy complexes formed with CO or CO3 missing groups may be efficient candidates to convey C diffusion, no low-energy migration path could be identified for these complexes. Focusing on the mostly stable CO vacancy complex and using generic values for unknown migration energies, kinetic Monte Carlo simulations show that this complex mechanism may be responsible for C diffusion roughly 2 orders of magnitude above its oxygen counterpart.

Fuzzy Static Output Feedback Control for Path Following of Autonomous Vehicles With Transient Performance Improvements

This paper provides a new solution for path following control of autonomous ground vehicles. $\mathcal {H}_{2}$ control problem is considered to attenuate the effect of the road curvature disturbance. To this end, we formulate a standard model from the road-vehicle dynamics, the a priori knowledge on the road curvature, and the path following specifications. This standard model is then represented in a Takagi–Sugeno fuzzy form to deal with the time-varying nature of the vehicle speed. Based on a static output feedback scheme, the proposed method allows avoiding expensive vehicle sensors while keeping the simplest control structure for real-time implementation. The concept of $\mathcal {D}-$ stability is exploited using Lyapunov stability arguments to improve the transient behaviors of the closed-loop vehicle system. In particular, the physical upper and lower bounds of the vehicle acceleration are explicitly considered in the design procedure via a parameter-dependent Lyapunov function to reduce drastically the design conservatism. The proposed $\mathcal {H}_{2}$ design conditions are expressed in terms of linear matrix inequalities (LMIs) with a single line search parameter. The effectiveness of the new path following control method is clearly demonstrated with both theoretical illustrations and hardware experiments under real-world driving situations.

Cosmological determination to the values of the pre-factors in the logarithmic corrected entropy-area relation

In this paper, we continue investigating the possible values of the pre-factors $\alpha$ and $\beta$ in the logarithmic corrected entropy-area relation based on cosmological stability arguments. In a previous study, we have investigated the stability of the entropy-corrected cosmology using an empirical hyperbolic form of the scale factor. We found that the zero values of the two pre-factors are necessary to obtain a stable flat universe with a deceleration-acceleration transition and no causality violation. The necessity of the zero values of the two pre-factors has also been reached in the current work using a hybrid scale factor Ansatz in the entropy-corrected cosmological equations. Investigating the corrected entropy-area relation in different gravitational and cosmological contexts can provide an accurate estimation to the correct values of the pre-factors. The current work opens a discussion on the validity of the correction terms in the logarithmic corrected entropy-area relation on the cosmological scale. The evolution of the cosmic pressure, energy density, equation of state parameter, jerk parameter and the nonlinear energy conditions has been analyzed.

Robust deadbeat continuous-time observer design based on modulation integrals

In this paper, the state estimation problem of linear continuous-time systems is dealt with by a non-asymptotic state observer, which allows the state estimation error to decay within an arbitrarily-small finite time without resorting to high-gain injection. By processing the measured input and output signals through modulation integrals, a number of auxiliary signals not affected by the initial conditions are obtained, from which the system state can be computed by simple algebra. The problem of internal instability of modulation integrals is addressed by resorting to a periodic rescaling mechanism that prevents error accumulation and singularities. We show that the combination of modulation integrals with periodic rescaling can be implemented as a jump-linear system. The robustness of the devised method with respect to additive measurement perturbations on the system’s input/output is characterized by Input-to-State Stability arguments.

Finite-time estimation of multiple exponentially-damped sinusoidal signals: A kernel-based approach

The problem of estimating the parameters of biased and exponentially-damped multi-sinusoidal signals is addressed in this paper by a finite-time identification scheme based on Volterra integral operators. These parameters are the amplitudes, frequencies, initial phase angles, damping factors and the offset. The proposed strategy entails the design of a new kind of kernel function that, compared to existing ones, allows for the identification of the initial conditions of the signal-generator system. The worst-case behavior of the proposed algorithm in the presence of bounded additive disturbances is fully characterized by Input-to-State Stability arguments. Numerical examples including the comparisons with some existing tools are reported to show the effectiveness of the proposed methodology.

Embedding Constrained Model Predictive Control in a Continuous-Time Dynamic Feedback

This paper introduces a continuous-time constrained control strategy, which mimics the behavior of a traditional model predictive control scheme using dynamic feedback. The approach is based on the idea that the solution of the optimal control problem can be embedded in the internal states of a dynamic control law running in parallel to the system. Using input-to-state stability arguments, it is shown that if the controller dynamics are sufficiently fast with respect to the plant dynamics, the interconnection between the two systems is asymptotically stable. Additionally, it is shown that, by augmenting the proposed scheme with an add-on unit known as an explicit reference governor, it is possible to guarantee recursive feasibility and limit the residual of the optimal control problem, regardless of any changes in the desired set point. Numerical examples featuring aerospace applications demonstrate the effectiveness of the proposed scheme.

Resistances and Speed Estimation in Sensorless Induction Motor Drives Using a Model With Known Regressors

This paper addresses the problem of stator and rotor resistances identification in speed sensorless induction motor (IM) drives. The IM model that is transformable into the adaptive observer form is sought, for which the speed and rotor resistance adaptive observer can be established with rigorous stability arguments under the assumption of constant unknown parameters. However, further inclusion of stator resistance estimation leads to the overparameterization problem. As a result, the adaptive observer based on the first-order approximation of the error dynamics is proposed. This is feasible because the regressors of the adopted IM model consist of known signals only. An experiment is carried out to verify the effectiveness of a sensorless drive with the proposed adaptive observer. Compared with the existing methods, estimation of speed and resistances during a regeneration mode as well as successful slow-speed reversal operation is found possible in the experiments.

Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition.

Much of ecological theory presumes that natural selection should foster species coexistence by phenotypically differentiating competitors so that the stability of the community is increased, but whether this will actually occur is a question of the ecological dynamics of natural selection. I develop an evolutionary model of consumer-resource interactions based on MacArthur's and Tilman's classic works, including both resource and apparent competition, to explore what fosters or retards the differentiation of resources and their consumers. Analyses of this model predict that consumers will differentiate only on specific ranges of environmental gradients (e.g., greater productivity, weaker stressors, lower structural complexity), and where it occurs, the magnitude of differentiation also depends on gradient position. In contrast to "limiting similarity" expectations, greater intraspecific phenotypic variance results in less differentiation among the consumers because of how phenotypic variation alters the fitness landscapes driving natural selection. In addition, the final structure of the community that results from the coevolution of these interacting species may be highly contingent on the initial properties of the species as the community is being assembled. These results highlight the fact that evolutionary conclusions about community structure cannot be based on ecological arguments of community stability or coexistence but rather must be explicitly based on the ecological dynamics of natural selection.

LPV Static Output Feedback for Constrained Direct Tilt Control of Narrow Tilting Vehicles

This brief presents a new direct tilt control (DTC) design to improve the lateral stability and the driving comfort of narrow tilting vehicles. To this end, a conceptual model is constructed from the vehicle dynamics, a simplified model of the driving environment, and the vehicle perceived acceleration. This latter is considered as the main performance variable of the related $\mathcal {H}_{2}$ control problem. The conceptual model is then represented in a polytopic linear parameter varying (LPV) form for control purposes. To avoid the use of costly vehicle sensors while favoring the simplest control structure for real-time implementation, a new LPV static output feedback control method is proposed. Thanks to Lyapunov stability arguments, physical constraints on both system states and DTC actuator are explicitly considered in the design procedure to improve the safety and the comfort of passengers. Moreover, a parameter-dependent Lyapunov function is exploited for theoretical developments. In this way, the finite bounds on vehicle speed and acceleration are effectively taken into account in the control design to reduce the conservatism. The $\mathcal {H}_{2}$ control design is recast as a linear matrix inequality-based optimization which can be easily solved with numerical solvers. The resulting robust DTC controller is evaluated with realistic driving scenarios.

Rousseauian Heritage of Rawls’s Moral Psychology

Some authors have noticed Rousseau's influence on Rawls's original position argument for justice as fairness, but few have argued for Rousseau’s influence on his moral psychology, which constitutes the first part of his stability argument. I will argue that Rawls’s account of moral development parallels, and is grounded in, Rousseau’s thoughts on amour-propre. In particular, I argue that (1) Rawls’s thesis that the sense of justice is derived from love and friendship is an illustration of Rousseau’s thesis that moral sentiments are derived from natural sentiments, that (2) Rawls’s explanation for how we acquire the reciprocity of disposition is grounded in Rousseau’s explanation of how amour-propre can be extended into the sense of justice, and that (3) Rawls’s thoughts on the principle of sympathy parallel Rousseau’s thoughts on compassion.

Global dynamics of a cancer stem cell treatment model

We provide global stability arguments for a cancer treatment model with chemotherapy and radiotherapy that accounts for the cancer stem cell hypothesis. Employing the method of localisation of compact invariant sets, we resolve the global dynamics of the no-treatment, constant radiation, and combination chemotherapy and radiotherapy cases. In our analysis of the combination treatment model, we show that the presence of a chemotherapy agent lowers the required radiation strength for a globally stable cure state.

Global dynamics of a cancer stem cell treatment model

We provide global stability arguments for a cancer treatment model with chemotherapy and radiotherapy that accounts for the cancer stem cell hypothesis. Employing the method of localisation of compact invariant sets, we resolve the global dynamics of the no-treatment, constant radiation, and combination chemotherapy and radiotherapy cases. In our analysis of the combination treatment model, we show that the presence of a chemotherapy agent lowers the required radiation strength for a globally stable cure state.

Augmenting Max-Weight With Explicit Learning for Wireless Scheduling With Switching Costs

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to switch off dynamically a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach -- a Max-Weight algorithm along with a Lyapunov-based stability argument -- does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

Universality of jamming of nonspherical particles

Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of "breathing" particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.