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For constrained linear parameter varying systems subject to bounded disturbances and noises, this article investigates an off-line output feedback robust model predictive control approach. The sub-observer gains with robust positively invariant sets, and sub-controller gains with robust control invariant sets are simultaneously off-line optimized and stored in a look-up table. According to real-time estimation error bounds and estimated states, the time-varying sub-observer gains and sub-controller gains are on-line searched. The proposed off-line output feedback robust model predictive control approach with the guarantee of nested robust positively invariant sets and robust control invariant sets in theory reduces the on-line computational burden.

Term “Conventional” sliding mode control (SMC) was introduced in the book Sliding Mode Control and Observation [1] by the authors, working in the area of high order sliding mode (HOSM) control. The term is related to all publications on n-dimensional systems with m- dimensional control and with sliding modes and state trajectories in a manifold of order n-m. Most of publications on HOSM control studied a new phenomenon for systems with a scalar control (m = 1), specifically, the existence of sliding modes in manifolds of dimension lower than n-1 with a finite reaching time. Along with implementation issues, it was natural to discuss to what extent the main principles of the conventional theory were to be revised (definitions, existence conditions, motion equations), what new properties of systems with HOSM can be expected. Partially these questions were discussed in [2] along with several international workshops on SMC and CDC in 2018. In this paper we demonstrate that main concepts are similar for both types of SMC, discuss new developments needed for HOSM control, compare the potential to suppress chattering, complexity of the both methods.

International audience; We consider the first closed-loop separation control experiment on an Ahmed body using a robust, model-based strategy called "sliding mode control" (SMC). The goal is to reduce and further maintain the aerodynamic drag of the square-back Ahmed body flow at Re h = 9 × 10 4 (based on the body height). This study also investigates the practical feasibility of this approach which shows a great promise for industrial applications. The flow is manipulated by a slotted jet placed on the top trailing edge, combined with a predefined angle direction, and sensed by a drag balance. Base pressure and lift measurements are also obtained in real-time. The interaction between the air jet actuator and the mean near-wake flow are depicted by means of Particle Image Velocimetry. In order to compare this closed-loop strategy we first present two open-loop ones. Continuous blowing is initially used to directly influence the recirculation area and hence achieve a reduction in the drag. Approximately a drag reduction of 8% is accomplished making this approach the "optimal case" control strategy. However, because steady blowing mechanisms lead to the highest energy consumption scheme, this strategy will only serve as the first open-loop control reference. The second open-loop strategy involves three periodic forcing frequencies, St A = 0.0765, 0.135 & 0.405. The influence of these frequencies on the near-wake, and its further drag modification, will be further examined. The proposed sliding mode control (closed-loop strategy) is applied to the same Ahmed body configuration and compared to the open-loop cases. It will be designed on the basis of a simplified input-output model which was recently defined for another flow control application. Last, a second experiment is conducted so to show the disturbance rejection of the controller, corroborating the robustness and efficiency of this control approach. Its limitations and difficulties on an experimental setup are also discussed. SMC is able to reduce and maintain the drag to a desire set-point regardless external flow perturbations. Our control strategy was recently used in another context (flow reattachement on a wing) with the same robustness. These successes make guess it is applicable to multiple experimental and industrial contexts.

The stabilization problem of the affine control system ẋ = f0(x)+∑i=1muifi(x) with homogeneous functions f0, fi is studied. This class of systems is of interest due to the robust properties of homogeneity and the fact that many affine systems can be approximated by or transformed to the class under consideration. An advantage of the introduced design method is that the tuning rules are presented in the form of linear matrix inequalities. Performance of the approach is illustrated by a numerical example.

Sub-homogeneity property is introduced and is related to a differential inclusion (DI). It is shown that a nonlinear ordinary differential equation (ODE), which may not admit a homogeneous approximation, can be transformed into a sub-homogeneous DI (which is a homogeneous extension of the original ODE). Using this homogeneous extension, one can directly recover finite-time stability property for some particular classes of nonlinear systems. In the last section, such a sub homogeneity property is used to design a nonlinear finite-time observer.

Fixed-time stability of a class of nonlinear time-varying systems is investigated using the introduced notions of sub- and sup-homogeneity. These concepts allow the systems (even if they do not admit homogeneous approximations) to be analyzed using the homogeneity of their extensions. Then, finite-time and fixed-time stability properties can be recovered. The proposed stability conditions are not based on Lyapunov arguments. In the last section, an example illustrates the obtained results.

International audience; This study is devoted to the design of an adaptive discontinuous control based on differential neural networks (DNNs) for a class of uncertain homogeneous systems. The control is based on the universal approximation properties of artificial neural networks (ANNs) applied on a certain class of homogeneous nonlinear functions. The adaptation laws for the DNNs parameters are obtained with the application of the Lyapunov stability theory and the homogeneity properties of the approximated nonlinear system. The stability analysis of the closed loop system with the proposed controller is presented. The estimation error in the approximation of the uncertain homogeneous functions is considered in the stability analysis. The performance of the controller is illustrated by means of a numerical simulation of a homogeneous model.

The paper is devoted to the problem of state observation (particularly, in finite time) of linear MIMO systems. The presented nonlinear observer does not require system transformation to a canonical form and guarantees finite-time (asymptotic with a fixed-time attraction of any compact set containing the origin) stability of observation error equation if homogeneity degree is negative (positive). The proposed observer is robust in input-to-state sense with respect to disturbances and measurement noises. Performance of the observer is illustrated by a numerical example.

In this paper we propose a discretisation scheme for continuous and asymptotically stable homogeneous systems. This method is based on the dynamics of the system projected on a level surface of a homogeneous Lyapunov function. The discretisation method is explicit and preserves the convergence rate of the continuous-time system.

International audience; This work addresses the problem of robust control of the continuous bioreactor-namely the chemostat-using an observer-based approach. We design a control law aiming to regulate the growth of a certain species and to stabilize the output-a growth-associated product of interest-in a prescribed level. In addition, to avoid the single-species dogma (which takes only one species into account for control design), we add to the microbial community unknown species competing for the limiting substrate. Finally, this control architecture is able to maintain the productivity, despite this competing heterogeneity (or biodiversity) of the community.

In this paper, a non parametric identifier for homogeneous nonlinear systems affine in the input is proposed. The identification algorithm is based on the neural networks using sigmoidal activation functions. The learning algorithm is derived by means of Lyapunov function method and homogeneity theory. A numerical example demonstrates the performance of the proposed identifier.

In this paper we study some stability properties of discrete-time systems whose transition map can be approximated by a discrete-time homogeneous transition map. This allows us to identify qualitative stability properties of discrete-time systems by only knowing the discrete-time homogeneity degree of its approximation. We show how these results can be applied to the stability analysis of discrete-time systems obtained by means of the explicit and implicit Euler discretization methods.

The Mutnovsky geothermal area is part of the Eastern Kamchatka active volcano belt. Mutnovsky, 80 kY old and an aging strato-volcano (a complex of 4 composite volcanic cones), acts as a magma- and water-injector into the 25-km-long North Mutnovsky extension zone. Magmatic injection events (dykes) are associated with plane-oriented MEQ (Micro Earth Quakes) clusters, most of them occurring in the NE sector of the volcano (2 × 10 km2) at elevations from −4 to −2 km, while some magmatic injections occur at elevations from −6.0 to −4.0 km below the Mutnovsky production field. Water recharge of production reservoirs is from the Mutnovsky volcano crater glacier (+1500 to +1800 masl), which was confirmed by water isotopic data (δD, δ18O) of production wells at an earlier stage of development. The Mutnovsky (Dachny) 260–310 °C high-temperature production geothermal reservoir with a volume of 16 km3 is at the junction of NNE- and NE-striking normal faults, which coincides with the current dominant dyke injection orientation. TOUGH2-modeling estimates of the reservoir properties are as follows: the reservoir permeability is 90–600 e-15 m2, the deep upflow recharge is 80 kg/s and the enthalpy is 1420 kJ/kg. Modeling was used to reproduce the history of the Mutnovsky (Dachny) reservoir exploitation since 1983 with an effective power of 48 MWe by 2016. Modeling also showed that the reservoir is capable of yielding 65–83 MWe of sustainable production until 2055, if additional production drilling in the SE part of the field is performed. Moreover, this power value may increase to 87–105 MWe if binary technologies are applied. Modeling also shows that the predicted power is sensitive to local meteoric water influx during development. Conceptual iTOUGH2-EOS1sc thermal hydrodynamic modeling of the Mutnovsky magma-hydrothermal system as a whole reasonably explains its evolution over the last 1500–5000 years in terms of heat recharge (dyke injection from the Mutnovsky-4 funnel) and mass recharge (water injection through the Mutnovsky-2 and Mutnovsky-3 funnels) conditions as previously mentioned.

International audience; This work deals with the problem of finite-time and fixed-time observation of linear multiple input multiple output (MIMO) control systems. The proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed (defined a priori) time. Algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out. The theoretical results are illustrated by numerical examples that consider both noisy and noise-free measurements and a comparison with a high-gain observer is included.

International audience; The problem of state estimation for heat non-homogeneous equations under distributed in space measurements is considered. An interval observer is designed, described by Partial Differential Equations (PDEs), for uncertain distributed parameter systems without application of finite-element approximations. Conditions of boundedness of solutions of interval observer with non-zero boundary conditions and measurement noise are proposed. The results are illustrated by numerical experiments with an academic example.

In this paper, a fault-tolerant control scheme for two physically linked two wheel drive (2WD) mobile robots with multiple and simultaneous actuator faults is proposed. The kinematic and dynamic models are first presented. A kinematic control law is designed, based on which, a dynamic control law is investigated. By applying the proposed dynamic control signal, the desired system stability and tracking properties are ensured. Simulation results are finally presented to verify the effectiveness of the developed fault-tolerant control scheme.

International audience; Output global finite-time stability of locally Lipschitz continuous autonomous systems is characterized by means of smooth Lyapunov functions. The so-called output-Lagrange stable systems are studied with details. Influence of a kind of continuity of the settling-time function is considered. Necessary and sufficient conditions of output finite-time stability are presented. The theoretical results are supported by academic examples and numerical simulations.

Time-delay robustness analysis for homogeneous systems with negative degree is presented in the paper. It is established that if a system is homogeneous with negative degree and asymptotically stable at its origin in the absence of delays, then stability property is preserved with respect to a compact set containing the origin for any delay value. It is shown that obtained results can also be used for locally homogeneous systems. A simulation example is included to support theoretical results.

International audience; The problem of interval observer design is addressed for a class of descriptor linear systems with time delays. First, an interval observation for any input in the system is provided. Second, the control input is designed together with the observer gains in order to guarantee interval estimation and stabilization simultaneously. Efficiency of the proposed approach is illustrated by numerical experiments with Leontief delayed model.

International audience; Theorems on Implicit Lyapunov Functions (ILF) for finite-time and fixed-time stability analysis of nonlinear systems are presented. Based on these resutls, new nonlinear control laws are designed for robust stabilization of a chain of integrators. High order sliding mode (HOSM) algorithms are obtained as particular cases. Some aspects of digital implementations of the presented algorithms are studied, it is shown that they possess a chattering reduction ability. Theoretical results are supported by numerical simulations.

International audience; Several conditions are proposed to check different robustness properties (ISS, iISS, IOSS and OSS) for generic nonlinear systems applying the weighted homogeneity concept (global or local). The advantages of this result are that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.

The paper addresses the finite-time stabilization problem with possible predefining of the convergence time independently on the initial conditions. The corresponding extension of finite-time stability concept is called by fixed-time stability. The second order sliding mode control algorithm provided fixed-time stabilization of the multi-input linear control system is presented. Theoretical results are supported by numerical simulations.

A new sliding mode control design algorithm for a linear and a class of nonlinear quasi-Lipschitz disturbed system is presented. It is based on the appropriate selection of the sliding surface via invariant ellipsoid method. The designed control guarantees minimization of unmatched disturbances effects to system motions in a sliding mode. The obtained theoretical results are approved by numerical simulations.

The paper deals with the problem of a finite-time stability analysis of relay and switching systems described by discontinuous functional-differential equations of a special class. One method of the Lyapunov function designing is presented and demonstrated for the “Italian version” of the second order sliding mode controller, which is also known as “sup-optimal controller”. The theoretical results are supported by numerical simulations.

Sufficient conditions for relay delayed nonlocal stabilization of linear systems are suggested connecting the upper bound of uncertainty in a time delay and the maximum of the real part of system spectrum. Algorithm of delayed relay control gain adaptation for nonlocal stabilization is suggested using delayed information about amplitude of oscillations. Proposed algorithm rejects bounded uncertainties in the time delay: once being designed for the upper bound of uncertainty in the time delay for given system this relay delayed control law ensure nonlocal stabilization for any values of the time delay less than the upper bound even in the case when the delay is variable.

Time delay does not allow to realize an ideal sliding mode, but implies oscillations in the space of state variables. Two types of predictors are proposed for time delay compensation in input and output delayed systems. Relay control algorithms are suggested ensuring the existence of sliding modes on the intersection of some surfaces in the space of predictor variables, and desired dynamics of systems into this mode.

Time delay does not allows to realize an ideal sliding mode, but implies oscillations in the space of state variables. The notations of c stabilization and weak controllability are introduced. The algorithms for local stabilization of oscillation's amplitudes for weak controllable control systems with input and output delay via relay control was suggested.

Subjects with brainstem lesions due to either an infarct or multiple sclerosis (MS) underwent two types of binaural testing (lateralization testing and interaural discrimination) for three types of sounds (clicks and high and low frequency narrow-band noise) with two kinds of interaural differences (level and time). Two major types of abnormalities were revealed in the lateralization performances: perception of all stimuli, regardless of interaural differences (time and/or level) in the center of the head (center-oriented), or lateralization of all stimuli to one side or the other of the head (side-oriented). Similar patterns of abnormal lateralization (center-oriented and side-oriented) occurred for MS and stroke patients. A subject's pattern of abnormal lateralization testing was the same regardless of the type of stimulus or type of interaural disparity. Lateralization testing was a more sensitive test than interaural discrimination testing for both types of subjects. Magnetic resonance image (MRI) scanning in three orthogonal planes of the brainstem was used to detect lesions. A semi-automated algorithm superimposed the auditory pathway onto each MRI section. Whenever a lesion overlapped the auditory pathway, some binaural performance was abnormal and vice versa. Given a lateralization test abnormality, whether the pattern was center-oriented or side-oriented was mainly determined by lesion site. Center-oriented performance was principally associated with caudal pontine lesions and side-oriented performance with lesions rostral to the superior olivary complex. For lesions restricted to the lateral lemniscus and/or inferior colliculus, whether unilateral or bilateral, just noticeable differences (JNDs) were nearly always abnormal, but for caudal pontine lesions JNDs could be normal or abnormal. MS subjects were more sensitive to interaural time delays than interaural level differences particularly for caudal pontine lesions, while stroke patients showed no differential sensitivity to the two kinds of interaural differences. These results suggest that neural processing of binaural stimuli is multilevel and begins with independent interaural time and level analyzers in the caudal pons.

Our goal is to understand the mechanism of transcription and its regulation. Determining structures of RNA polymerase and transcription complexes is an essential step. Because of their large size and complexity, determination of these structures will require a combination of electron microscopy, biophysical methods, and biochemical methods to identify functionally and structurally relevant subassemblies and domains and x-ray crystallography to determine high-resolution structures of RNA polymerase components and accessory factors. We recently solved the 2.5-A crystal structure of theEscherichia coliRNA polymerase α subunit N-terminal domain, which is the first high-resolution structure of a core component required for RNA polymerase assembly and basal transcription. This structure, combined with a new 19-A resolution structure determined by cryo-electron microscopy of helical crystals ofE. colicore RNAP embedded in vitreous ice, leads to a model for the organization of the RNAP subunits.

Sound lateralization can be induced by interaural intensity disparities (IIDs) or by interaural temporal disparities (ITDs). The purpose of this study was to indicate whether IIDs and ITDs are processed by the same central units that detect interaural disparity in timing of afferent activity. If sound lateralization to intensity and time cues was determined by the same afferent latency disparity detectors in the brainstem, lateralization would be the same, regardless of whether latency disparity was induced by IIDs or ITDs. Moreover, the disparity detectors, and thus their dipole equivalents, would be the same for equal lateralizations, whether induced by IIDs or ITDs. Auditory brainstem evoked potentials (ABEPs) were recorded in response to monaural and binaural clicks, with a variety of IIDs and ITDs. Peak II (proximal auditory nerve activity), peak III (input to the superior olivary complex), and binaural interaction components (BICs) BeI and BeII (binaurally activated upper pons) were identified and their latencies measured. The psychophysical lateralization of the clicks (in cm from vertex) was also measured in response to the same binaural stimuli. The correlations between interaural afferent latency disparities (difference in corresponding peak latencies originating in each ear) and psychophysical click lateralization were calculated. Similarly, the correlations with click lateralization of the BICs equivalent dipole latency as well as orientation change (relative to symmetrical clicks) were determined. A strong correlation with lateralization was found for peaks II and III latency disparities, with steeper slopes for IIDs than for ITDs. Moreover, binaural activity across the same lateralizations differed between IIDs and ITDs. These results, therefore, indicate that interaural time and intensity cues are processed by separate systems in the brainstem, both at the afferent convergence level and after interaural disparities are determined.

The structure of E. coli core RNA polymerase (RNAP) has been determined to approximately 23 A resolution by three-dimensional reconstruction from electron micrographs of flattened helical crystals. The structure reveals extensive conformational changes when compared with the previously determined E. coli RNAP holoenzyme structure, but resembles the yeast RNAPII structure. While each of these structures contains a thumb-like projection surrounding a channel 25 A in diameter, the E. coli RNAP holoenzyme thumb defines a deep but open groove on the molecule, whereas the thumb of E. coli core and yeast RNAPII form part of a ring that surrounds the channel. This may define promoter-binding and elongation conformations of RNAP, as E. coli holoenzyme recognizes promoter sites on double-stranded DNA, while both E. coli core and yeast RNAPII are elongating forms of the polymerase and are incapable of promoter recognition.

Three-channel Lissajous' trajectories (3-CLTs) of the binaural interaction component (BI) of auditory middle latency evoked potentials (AMLEPs) were derived from 14 normally hearing adults by subtracting the response to binaural clicks from the algebraic sum of monaural responses. AMLEPs were recorded in response to 65 dB nHL, rarefraction clicks, presented at a rate of 3.3/s. A normative set of BI 3-CLT measures was calculated and compared with the corresponding measures of simultaneously recorded, single-channel vertex-left mastoid and vertex-neck derivations of BI and of AMLEP to binaural stimulation (B). 3-CLT measures included: apex latency, amplitude and orientation, as well as planar segment duration, orientation, size and shape. The results showed seven main apices and associated planar segments (‘Be’, ‘Bf’, ‘Bg’, ‘Bh’, ‘Bi1’, ‘Bi2’ and ‘Bj’) in the 3-CLT of BI. Apex latencies of the BI 3-CLT were comparable to peak latencies of the vertex-left mastoid and vertex-neck AMLEP and BI records, both in their absolute values and in intersubject variability. Durations of BI planar segments were approximately 5.0 ms. Apex amplitudes of BI 3-CLT were larger than the respective peak amplitudes of the vertex-mastoid and vertex-neck BI records, while their intersubject variabilities were comparable. The lateralization of BI components may indicate asymmetric processing of binaural auditory input, or may be connected with anatomical asymmetry such as skull thickness. Preliminary analyses did not reveal a clear correlation between the lateralization of the BI component ‘Bi2’ and the handedness of the subject. We suggest that BI components of AMLEP may be associated with the primary auditory cortex and subcortical ascending structures.

The 3-channel Lissajous' trajectory (3-CLT) of the binaural interaction components (BI) in auditory brain-stem evoked potentials (ABEPs) was derived from 17 normally hearing adults by subtracting the response to binaural clicks (B) from the algebraic sum of monaural responses (L + R). ABEPs were recorded in response to 65 dB nHL, alternating polarity clicks, presented at a rate of 11/sec. A normative set of BI 3-CLT measures was calculated and compared with the corresponding measures of simultaneously recorded, single-channel vertex-left mastoid and vertex-neck derivations of BI and of ABEP L + R and B. 3-CLT measures included: apex latency, amplitude and orientation, as well as planar segment duration and orientation. The results showed 3 apices and associated planar segments ("BdII," "Be" and "Bf") in the 3-CLT of BI which corresponded in latency to the vertex-mastoid and vertex-neck peaks IIIn, V and VI of ABEP L + R and B. These apices corresponded in latency and orientation to apices of the 3-CLT of ABEP L + R and ABEP B. This correspondence suggests generators of the BI components between the trapezoid body and the inferior colliculus output. Durations of BI planar segments were approximately 1.0 msec. Apex amplitudes of BI 3-CLT were larger than the respective peak amplitudes of the vertex-mastoid and vertex-neck recorded BI, while their intersubject variabilities were comparable.

The active center of DNA-dependent RNA polymerase performs the principal biochemical reaction of gene expression. Using cross-linkable substrate analogs and site-directed mutations, two evolutionarily invariant amino acids in the beta subunit of the Escherichia coli enzyme (Lys1065 and His1237) were mapped close to the binding site of the priming substrate of the reaction. Surprisingly, the mutational substitution of these residues (Lys1065----Arg and His1237----Ala) did not inactivate the catalytic function, but inhibited transition from the initiation to the elongation stage of transcription.