Class Of Hybrid Systems Research Articles

Contract-Based Design for Hybrid Dynamical Systems and Invariance Properties

This work establishes fundamental principles for verifying contract for interconnected hybrid systems. When system’s hybrid arcs conform to the contract for a certain duration but subsequently violate it, the composition of hybrid dynamical systems becomes challenging. The objective of this work is to analyze the temporal satisfaction of the contract, allowing us to reason about the compositions that do not violate the contract up to a certain point in a hybrid time. Notions of weak and strong satisfaction of an assume-guarantee contract are introduced. These semantics permits the compositional reasoning on hybrid systems of varying complexity depending on the interconnection’s type, feedback or cascade. The results show that both semantics are compatible with cascade composition, while strong semantic is required for feedback composition. Moreover, we have shown how one can go from weak to strong contract satisfaction. Finally, we have studied a particular class of hybrid systems and we have shown that the concept of forward (pre-)invariant relative to a contract makes it possible to deal with feedback compositions. These results are demonstrated throughout the paper with simple numerical examples.

THE ASYMPTOTIC STABILITY OF THE SIMPLEST HYBRID SYSTEMS

The linear autonomous discrete-continuous systems (also known as hybrid systems) with uncertain coefficients is considered. We consider the class of hybrid systems, that consist of difference and ordinary differential equations. We obtain a stability domain for hybrid systems from this class. Two illustrative examples are presented

On partial maps derived from flows

The first-return map, or the Poincar\'e map, is a fundamental concept in the theory of flows. However, it can generally be defined only partially, and additional conditions are required to define it globally. Since this partiality reflects the dynamics, the flow can be described by considering the domain and behavior of such maps. In this study, we define the concept of first-exit maps and first-return maps, which are partial maps derived from flows, to enable such analysis. Moreover, we generalize some notions related to the first-return maps. It is shown that the boundary points of an open set can be classified based on the behavior of these maps, and that this classification is invariant under topological equivalence. Further, we show that some dynamical properties of a flow can be described in terms of the types of boundary points. In particular, if the flow is planar and the open set has a Jordan curve as its boundary, a more detailed analysis is possible, and we present results on the conditions which restrict possible forms of the first-exit maps . Finally, as an application of the results obtained, we consider the relationship between flows and a class of hybrid systems.

Discrete Fault Diagnosis of Structurally Reconfigurable Systems

Abstract Fault diagnosis of a certain class of hybrid systems referred to as structurally reconfigurable (SR) systems is complicated. This is because SR systems tend to switch their configuration, which may or may not be faulty. It is important to identify the mode of the SR system along with the corresponding fault if any, in order to facilitate a fault tolerant action. This paper combines discrete fault diagnosis with mode identification for SR systems to achieve two main objectives: Sensor selection for fault detection, isolation and mode identification, and residual selection for mode identification. The framework is built using a structural analysis-based approach to meet these objectives. This framework is demonstrated for a 10-speed Automatic Transmission, which is an illustrative example of SR systems.

Enclosing the Sliding Surfaces of a Controlled Swing

When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. We show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set-membership uncertainties. An application to the verification of the controller of a child swing is considered to illustrate the principle of the approach.

Opto-Mechanical Photonic Crystal Cavities for Sensing Application

A new class of hybrid systems that couple optical and mechanical nanoscale devices is under development. According to their interaction concepts, two groups of opto-mechanical systems are summarized as mechanically tunable and radiation pressure-driven optical resonators. On account of their high-quality factors and small mode volumes as well as good on-chip integrability with waveguides/circuits, photonic crystal (PhC) cavities have attracted great attention in sensing applications. Benefitting from the opto-mechanical interaction, a PhC cavity integrated opto-mechanical system provides an attractive platform for ultrasensitive sensors to detect displacement, mass, force, and acceleration. In this review, we introduce basic physical concepts of opto-mechanical PhC system and describe typical experimental systems for sensing applications. Opto-mechanical interaction-based PhC cavities offer unprecedented opportunities to develop lab-on-a-chip devices and witness a promising prospect to further manipulate light propagation in the nanophotonics.

On the Performance of Kalman Filter for Markov Jump Linear Systems with Mode Mismatch

Markov jump linear system (MJLS) is a class of hybrid systems where the continuous states evolve linearly and the discrete state transitions are modeled via a Markov chain. It has been shown that the optimal estimator for MJLS is a mode-based Kalman filter when the discrete mode is given. However, in practical applications, there are situations where the mode information is inaccurate and mode mismatches result in a biased estimate from the mode-based Kalman filter. This paper, for the first time, studies the impact of time correlated mode mismatch errors on MJLS state estimation using a mode-based Kalman filter. Unlike prior efforts that (1) assume mode mismatches are independent and identically distributed and (2) are limited to bi-modal systems, this paper is built on a general MJLS setup with a Markovian model for mode mismatch errors. The main contribution of this work lies in deriving the statistics of the bias term from a mode-based Kalman filter estimation with the aforementioned system setup. The sufficient conditions based on the probabilities of mode mismatch errors for the bias to be statistically convergent are derived. Since time correlated mode mismatch errors can effectively capture communication link impairments in a cyber-physical system, this new fundamental result provides guidance on the design of estimation strategies for MJLS and sheds light on their resilience in the presence of mode mismatch errors.

On techniques of expert systems on the example of the Akinator program

On the example of the online game Akinator, the basic principles on which programs of this type are built are considered. Effective technics have been proposed by which artificial intelligence systems can build logical inferences that allow to identify an unknown subject from its description (predicate). To confirm the considered hypotheses, the terminological analysis of definition of the program "Akinator" offered by the author is carried out. Starting from the assumptions given by the author's definition, the article complements their definitions presented by other researchers and analyzes their constituent theses. Finally, some proposals are made for the next steps in improving the program. The Akinator program, at one time, became one of the most famous online games using artificial intelligence. And although this was not directly stated, it was clear to the experts in the field of artificial intelligence that the program uses the techniques of expert systems and is built on inference rules. At the moment, expert systems have lost their positions in comparison with the direction of neural networks in the field of artificial intelligence, however, in the case considered in the article, we are talking about techniques using both directions – hybrid systems. Games for filling semantics interact with the user, expanding their semantic base (knowledge base) and use certain strategies to achieve the best result. The playful form of such semantics filling programs is beneficial for researchers by involving a large number of players. The article examines the techniques used by the Akinator program, and also suggests possible modifications to it in the future. This study, first of all, focuses on how the knowledge base of the Akinator program is built, it consists of incomplete sets, which can be filled and adjusted as a result of further iterations of the program launches. It is important to note our assumption that the order of questions used by the program during the game plays a key role, because it determines its strategy. It was identified that the program is guided by the principles of nonmonotonic logic – the assumptions constructed by the program are not final and can be rejected by it during the game. The three main approaches to acquisite semantics proposed by Jakub Šimko and Mária Bieliková are considered, namely, expert work, crowdsourcing and machine learning. Paying attention to machine learning, the Akinator program using machine learning to build an effective strategy in the game presents a class of hybrid systems that combine the principles of two main areas in artificial intelligence programs – expert systems and neural networks.

Steady-state, harmonic response and moments of linear systems with periodic jumps

By relying on the recently introduced notion of transfer function for linear hybrid systems with periodic jumps, herein we extend, for the first time, frequency-domain analysis tools – well-known and extensively used in the context of purely continuous or discrete time systems – to such a class of hybrid systems. In fact, knowledge of the transfer function allows for the frequency-domain definition of the notion of 0-th momentof the underlying hybrid system, which is instrumental, e.g. for the solution to model reduction or input-output system identification problems. It is shown, in addition, that the notion of moment based on the hybrid transfer function possesses an interesting time-domain counterpart, hence extending the results obtained for purely continuous-time systems. To further substantiate the theoretical claims, the paper is concluded by the frequency-domain robustness analysis of the classical consensus protocol in the presence of sampled measurements.

Symbolic Models for a Class of Impulsive Systems

Symbolic models have been used as the basis of a systematic framework to address control design of several classes of hybrid systems with sophisticated control objectives. However, results available in the literature are not concerned with impulsive systems which are an important modeling framework of many applications. In this letter, we provide an approach for constructing symbolic models for a class of impulsive systems possessing some stability properties. We formally relate impulsive systems and their symbolic models using a notion of so-called alternating simulation function. We show that behaviors of the constructed symbolic models are approximately equivalent to those of the impulsive systems. Finally, we illustrate the effectiveness of our results through a case study.

Hybrid State Constraint Adaptive Disturbance Rejection Controller for a Mobile Worm Bio-Inspired Robot

This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state restrictions in the device articulations; this means the maximum and minimum angular ranges, to avoid any possible damage to the structure. The controller uses an active compensation method to estimate the unknown dynamics of the WBRD by means of an extended state observer. The sequence of movements for the gait cycle of a WBRD is represented as a class of hybrid system by alternative reference frameworks placed at the first and the last link. The stability analysis employs a class of Hybrid Barrier Lyapunov Function to ensure the fulfillment of the angular restrictions in the robotic device. The proposed controller is evaluated using a numerical simulation system based on the virtual version of the WBRD. Moreover, experimental results confirmed that the H-ADRC may endorse the realization of the proposed gait cycle despite the presence of perturbations and modeling uncertainties. The H-ADRC is compared against a proportional derivative (PD) controller and a proportional-integral-derivative (PID) controller. The H-ADRC shows a superior performance as a consequence of the estimation provided by the homogeneous extended state observer.

Voltage Regulation of DC-DC Series Resonant Converter Operating in Discontinuous Conduction Mode: The Hybrid Control Approach

Dynamic modeling and control of dc-dc series resonant converter (SRC) especially when operating in discontinuous conduction mode (DCM) is still a challenge in power electronics. Due to semiconductors switching, SRC is naturally represented as a switched linear system, a class of hybrid systems. Nevertheless, the hybrid nature of the SRC is commonly neglected and it is modeled as a purely continuous dynamics based on the sinusoidal approximation and averaging. However, an SRC may be purposely designed to operate in DCM so the sinusoidal approximation is no longer acceptable. Therefore, it is essential to analyze the stability using a more sophisticated model. This paper presents a novel hybrid control strategy for the output voltage regulation of the SRC operating in DCM. Neither sinusoidal nor averaging is used. The stability of the closed-loop system is systematically fulfilled by satisfying some linear matrix inequalities. The proposed hybrid control approach has simple hardware implementation which does not require fast sampling of the resonant tank waveforms and external voltage-controlled oscillator. A prototype of the SRC is constructed and the hybrid controller is realized on a TMS320F2812 DSP core. The effectiveness of the proposed method is verified by simulation and experimental results.

Stabilization of a Class of Hybrid Systems by Switching Controllers with Input Constraints

In this paper, a hybrid control strategy using appropriate switching between a set of linear controllers is presented for stabilization of a class of hybrid systems with input constraints. The input constraints under consideration are novel reverse polytopic constraints avoiding a set of specified input values. The design procedure of the switching controllers is performed by solving a set of linear matrix inequalities for the full state feedback case and by solving a set of bilinear matrix inequalities for the output feedback case. Under the designed controllers, the closed-loop system is shown to be globally uniformly pre-asymptotically stable if a specific set of matrix inequalities ensuring the existence of a common Lyapunov function are satisfied. To avoid the Zeno behavior, a tunable parameter related to the controller gains is introduced and assessed. It is shown that the proposed switching control is superior to continuous state feedback control with input constraints. In addition, besides continuous linear systems, the proposed control strategy is applicable to hybrid or impulsive systems. Numerical examples are included to illustrate the proposed results.

On a Class of Optimal Control Problems for Functional Differential Systems

A linear functional differential control system of general form with aftereffect is considered. An optimal control problem with linear constraints on the state and control variables is studied. The control is realized by a linear operator of general form. The cases of distributed and lumped delay in the control loop, as well as the case of impulsive control, are covered. The Cauchy matrix is used to reduce the problem under consideration to a problem formulated only in terms of control variables with the use of some auxiliary variables linked with the defining relations for the Cauchy matrix of the system. In the case where the control is chosen from a finite-dimensional subspace of the control space, a problem effectively solvable by standard software tools is written explicitly. An example of an applied optimal control problem that arises in economic dynamics is presented. A class of hybrid systems (systems with continuous and discrete times) reducible to the system under consideration is described.

Disturbance Decoupling with Stability for Impulsive Switching Linear Systems

Abstract This paper deals with the problem of decoupling the output of a hybrid system from a disturbance input by means of a switching state feedback, which, at the same time, stabilizes, in a suitable sense, the compensated system. The class of hybrid systems considered consists of impulsive switching linear systems, that is switching linear systems whose state exhibits impulsive discontinuities, called jumps, at the switching instants. Switching is assumed to be time-driven and the distance between consecutive switching instants is assumed to be lower bounded by some positive number. Structural geometric methods and tools are used to investigate the decoupling problem and to study feedback stabilizability. Necessary and sufficient solvability conditions are given in the case in which the distance between consecutive switching instants can be assumed to be sufficiently large. A sufficient solvability condition is also provided in the case in which the lower bound for such distance is assigned.

A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust H∞ performance γ. By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

Finite Control Set Predictive Control and State Estimation of Partially Observable Switching Linear Systems: Application to a Multicellular Converter

This article is about a feedback control and state observation of a class of hybrid systems with some unobservable subsystems. When the system reaches an unobservable configuration, the state observer performance decreases, impacting the overall control performance of the system. For that reason, the majority of the existing controllers uses only measurements of the system’s continuous states when they are equal to the system outputs. To deal with this issue, control trajectories are constrained with respect to -observability criteria using a finite control set predictive control algorithm. The experimentations performed on a multicellular converter are presented and the results obtained show the efficiency of the proposed method.

Interval estimation for continuous-time switched linear systems

This paper deals with the design of interval observers for switched linear systems (SLS), a class of hybrid systems. Under the assumption that the disturbances and the measurement noise are bounded, upper and lower bounds for the state are calculated. New conditions of cooperativity in discrete-time instants are firstly proposed. Then, some techniques for interval estimation are developed in continuous-time. It is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences. The performances of the developed techniques are illustrated through numerical examples.

Modelling and analysis of hybrid stochastic timed Petri net

In this paper, an interesting Hybrid Stochastic Timed Petri Net (HSTPN) is proposed for a class of hybrid systems. The proposed HSTPN can be adopted to represent hybrid systems with discrete, continuous, conflicting, time-delay and stochastic characteristics simultaneously. The proposed HSTPN outperforms conventional hybrid Petri net models in terms of describing the scalability and immediacy of hybrid systems. Advantages of the HSTPN on describing hybrid system are verified by establishing some equivalent models of HPN and its derived models.

Compositional Analysis of Hybrid Systems Defined Over Finite Alphabets

We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state machines (DFSMs). This class of hybrid systems can be used to model physical systems controlled by software. For such classes of systems, we use a method based on dissipativity theory for compositional analysis that allows us to study stability, passivity and input-output norms. We show that the certificates of the method based on dissipativity theory can be computed by solving a set of semi-definite programs. Nonetheless, the formulation based on semi-definite programs become computationally intractable for relatively large number of discrete and continuous states. We demonstrate that, for systems with large number of states consisting of an interconnection of smaller hybrid systems, accelerated alternating method of multipliers can be used to carry out the computations in a scalable and distributed manner. The proposed methodology is illustrated by an example of a system with 60 continuous states and 18 discrete states.