Reachable Set Research Articles

Reachable set control for nonlinear Markov jump cyber–physical systems with false data injection attacks

This paper presents the problem of reachable set controller design for a class of nonlinear Markov jump cyber–physical systems (MJCPSs). The adverse effects of bounded peak external disturbances, uncertainties and false data injection (FDI) attacks with certain probability on MJCPSs are considered. The aim is to design an appropriate controller to guarantee that the actual state of the closed-loop MJCPSs is defined by a specified set. Firstly, the Lyapunov functional method is introduced because the time-varying delays are carried by FDI attacks. By using the Lyapunov functional method, an ellipsoid description of the reachable set containing all the states of the system originating from the origin is obtained. Then, the controller gain can be obtained via a set of feasible linear matrix inequalities (LMIs). Finally, the effectiveness of the designed reachable set controller is proved by simulation results.

Well-posedness and properties of the flow for semilinear evolution equations

We derive conditions for well-posedness of semilinear evolution equations with unbounded input operators. Based on this, we provide sufficient conditions for such properties of the flow map as Lipschitz continuity, bounded-implies-continuation property, boundedness of reachability sets, etc. These properties represent a basic toolbox for stability and robustness analysis of semilinear boundary control systems. We cover systems governed by general C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0$$\\end{document}-semigroups, and analytic semigroups that may have both boundary and distributed disturbances. We illustrate our findings on an example of a Burgers’ equation with nonlinear local dynamics and both distributed and boundary disturbances.

Quantum Control by the Environment: Turing Uncomputability, Optimization over Stiefel Manifolds, Reachable Sets, and Incoherent GRAPE

Quantum Control by the Environment: Turing Uncomputability, Optimization over Stiefel Manifolds, Reachable Sets, and Incoherent GRAPE

Reachable Set Estimation for Memristive Complex-Valued Neural Networks With Disturbances.

This brief focuses on reachable set estimation for memristive complex-valued neural networks (MCVNNs) with disturbances. Based on algebraic calculation and Gronwall-Bellman inequality, the states of MCVNNs with bounded input disturbances converge within a sphere. From this, the convergence speed is also obtained. In addition, an observer for MCVNNs is designed. Two illustrative simulations are also given to show the effectiveness of the obtained conclusions.

Fully Automated Verification of Linear Systems Using Inner and Outer Approximations of Reachable Sets

Fully Automated Verification of Linear Systems Using Inner and Outer Approximations of Reachable Sets

Global Reachability of Heterogeneous Multiagent Systems Under Collaborative Interaction Topology and Unknown Delays

The multi-agent rendezvous problem for single- and double-integrator agents in the presence of unknown constant input and communication delays is investigated in this paper. Existing works address the rendezvous problem by incorporating negative gain(s) into the distributed consensus protocol and showing that negative gain(s) expands the reachable set beyond the initial configuration of the agents' convex hull. On the contrary, the present control protocol ensures global reachability of a network of agents with a directed communication topology having non-negative edge weights. This is accomplished with the help of a dynamic distributed control protocol, where the information exchange among agents occurs in the internal controller states. For homogeneous delays, the analytical expression of the rendezvous point confesses the non-dependency of the point with delays, which in turn signifies that rendezvous can be achieved with unknown and arbitrarily large but bounded delays. The very structure of the control protocol ensures rendezvous at any desired point, even if the input delays are heterogeneous and unknown. However, heterogeneity in communication delays has an effect on the rendezvous point, and hence, global reachability of agents can be established if these delays are exactly known. For heterogeneous multi-agent systems composed of single- and double-integrator agents, tuning of the design parameters gets simplified due to the single-integrator based internal controller structure for all agents. Numerical simulations are provided to validate the robustness of the protocol against delays.

Reachable Set of the Dubins Car with an Integral Constraint on Control

Reachable Set of the Dubins Car with an Integral Constraint on Control

Continuous-Thrust Reachable Set for Linear Relative Motion Near Elliptical Orbits

Continuous-Thrust Reachable Set for Linear Relative Motion Near Elliptical Orbits

Improved results on reachable set estimation for singularly perturbed systems with time-varying delay

The problem of reachable set estimation for singularly perturbed systems with time-varying delays and bounded perturbation is studied in this paper. Firstly, a Lyapunov–Krasovskii function related to the perturbed parameter η is established. Secondly, introducing a method of integral inequality scaling and eliminated the influence of singularly perturbed parameter on the system within a certain range. The system state is therefore contained in a η-independent ellipsoid in accordance with a criterion imposed by linear matrix inequalities. Subsequently, examples are used to show that the findings are valid.

Reachable set estimation and H∞$H_\infty$ performance for delayed fuzzy multi‐agent systems under false data injection attacks

AbstractAddressed in this paper is the reachable set estimation (RSE) problem for fuzzy‐model‐based leader‐follower multi‐agent systems with time‐varying delays and false data injection attacks. First, the aperiodic sampled‐data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov‐Krasovskii functional is constructed with the knowledge of sampling patterns and time‐varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single‐link robot arm models are employed to validate the derived theoretical results.

Event-based reachable set synthesis for delayed nonlinear semi-Markov systems

In this study, the issue of the reachable set (RS) synthesis for delayed nonlinear semi-Markov jump systems (s-MJSs) is addressed. An asynchronous controller whose controller mode is different from the system mode is designed. Non-fragile issues are considered in the design of the controller to improve the performance of the controller. Meanwhile, in order to economize on communication resources, the introduction of an event-triggered mechanism is considered in this work. A sufficient condition for the linear matrix inequalities (LMIs) form is obtained by utilizing the theory of Lyapunov functionals and the free-weighting matrix method, which ensures that the RS of the system is constrained by a compact ellipsoid. The controller gains of the system are then obtained by matrix decoupling. Ultimately, a numerical simulation and a practical model are provided to highlight the usability and practicality of the method.

Robust synchronization of coupled logical networks subject to stochastic function perturbations

This article analyzes the robust synchronization of coupled logical networks (LNs) subject to stochastic function perturbations (SFPs). Firstly, by defining a synchronization states set, the robustness of synchronization with probability one (SPO) is divided into two cases. According to these two cases, the rough reachable set and refined reachable set are constructed, based on which, several criteria are derived for the robust SPO of coupled LNs with SFPs. Secondly, with the help of rough reachable set and refined reachable set, several necessary and sufficient conditions are proposed to verify the synchronization in distribution of coupled LNs with SFPs. Finally, the obtained theoretical results are applied to an idealized model of protein-nucleic acid interactions.

On Some Properties of Sets of Bounded Controllability for Stationary Linear Discrete Systems with Total Control Constraints

We consider the problem of constructing reachable sets, i.e., sets of terminal states into which a system can be transferred from the origin in a fixed time, and 0-controllability sets, i.e., sets of initial states, from which a system can be transferred to the origin in a fixed time, for stationary linear discrete systems with a total control constraint. The representation of reachable and 0-controllable sets as linear transformations of superellipsoidal sets of finite and infinite dimensions is proved. A constructive method for describing the desired sets based on the apparatus of supporting half-planes is proposed, including for the limit sets of reachability and controllability. In the case of Euclidean spaces, the description is obtained explicitly. Examples are given. For a three-dimensional satellite motion control system in a near-circular orbit, reachability sets are modeled.

Controllability of generalized asynchronous Boolean networks with periodical impulsive control

The objective of this paper is to investigate the controllability of generalized asynchronous Boolean networks under periodical impulsive control. In order to attain the objective, the semi-tensor product is employed to transform generalized asynchronous Boolean networks that have periodic impulsive control into linear representations. The conversion provides the basis for deriving the general formula of the network transition matrix’s dependence on the controller. Then three different control modes are used to define the controllability of generalized asynchronous Boolean networks: free Boolean sequence periodic impulsive control, input networked periodic impulsive control and feedback networked periodic impulsive control. For each mode, reachable sets of time s under a specific set of controls and arbitrary control are provided. The likelihood of transitioning from one state to another is also calculable. Finally, instances are given for a variety of control modes to illustrate the theorems’ effectiveness and robustness.

Reachable set estimation for positive linear discrete-time systems under the constrained disturbance

This paper studies the problem of estimating the reachable set boundary of positive discrete-time systems with specific inputs in hyperspace. When the L1-norm or L∞-norm of the particular disturbance input to a positive linear discrete-time system is bounded by a constant, by using linear copositive Lyapunov functional method based on S-lemma, the reachable set could be constrained in a hyper-pyramid under some matrix inequality conditions. In an innovative way, by the method of directly calculating the dynamic trajectories of the system state, the reachable set can also be constrained in a hyper-rectangle. The approach of shrinking the size of the reachable set region is also developed. Finally, the validity of the results obtained is verified by examples of passenger flow in and out of customs.

Supervisory Controller Design to Enforce Boundedness, Reversibility and Liveness in Systems Modeled by Timed Petri Nets

Supervisory controller design to enforce boundedness, reversibility, and liveness in discrete-event systems modeled by timed Petri nets where both transitions and places are timed is considered. A controller design approach which uses the approach of stretching is proposed. The approach produces a supervisory controller which guarantees boundedness and reversibility simultaneously. The designed controller also guarantees T -liveness for the largest possible subset T of the set of transitions. Therefore, boundedness, reversibility, and liveness are enforced simultaneously whenever possible. Furthermore, the designed controller is maximally permissive in the sense that no transitions are disabled unnecessarily and the reachability set of the controlled system is the largest possible set in which boundedness and reversibility can be enforced simultaneously. Controller design for an automated manufacturing system example is also presented to demonstrate the proposed approach.

Evolution Function Based Reach-Avoid Verification for Time-varying Systems with Disturbances

In this work, we investigate the reach-avoid problem of a class of time-varying analytic systems with disturbances described by uncertain parameters. Firstly, by proposing the concepts of maximal and minimal reachable sets, we connect the avoidability and reachability with maximal and minimal reachable sets respectively. Then, for a given disturbance parameter, we introduce the evolution function for exactly describing the reachable set, and find a series representation of this evolution function with its Lie derivatives, which can also be regarded as a series function with respect to the uncertain parameter. Afterward, based on the partial sums of this series, over- and under-approximations of the evolution function are constructed, which can be realized by interval arithmetics with designated precision. Further, we propose sufficient conditions for avoidability and reachability and design a numerical quantifier elimination based algorithm to verify these conditions; moreover, we improve the algorithm with a time-splitting technique. We implement the algorithms and use some benchmarks with comparisons to show that our methodology is both efficient and promising. Finally, we additionally extend our methodology to deal with systems with complex initial sets and time-dependent switchings. The performance of our extended method for these systems is also shown by four examples with comparisons and discussions.

Tight set-valued state estimation by combining reachability analysis and set-filtering approaches

In this work, a new approach to design set-valued state estimator for linear discrete-time systems subject to additive and bounded process and measurement uncertainties is proposed. First, the system state equation is rewritten to obtain a stable numerical scheme on which an explicit reachability method is developed, based on zonotopic set computation and a re-initialization procedure. Then, to enhance the accuracy of the computed reachable set, a set-filtering technique is designed based on the system output equation and its intrinsic invariant relationships. The implementation of this filtering method is based on interval analysis coupled to contractor algorithms. The convergence property of the proposed set-valued state estimator is shown under the classical detectability assumption of linear systems. Some simulation results are presented to show the merit of the proposed new set-membership state estimation approach.

Decentralized Safe Control for Distributed Cyber-Physical Systems Using Real-Time Reachability Analysis

In this paper, we present a decentralized safe control (DSC) approach for distributed cyber-physical systems based on conducting reachability analysis in real-time. Each agent can periodically compute the local reachable set from its current local time to some time instant in the near future, and then broadcast a message containing the computed reachable set to the other agents via a shared communication channel. By comparing its own reachable set to unsafe regions such as obstacles, and received reachable sets in a peer-to-peer manner, the agent can predict if any collision may exist shortly. In this circumstance, the agent can utilize the unsafe intersection of its computed reachable set, the unsafe regions and the received reachable sets to recalculate a new set of waypoints and update its corresponding control strategies. As a result, our DSC approach can ensure a distributed system achieving a mission goal with a collision-free guarantee. For evaluation, we applied the proposed DSC method to perform a decentralized control, in real-time, a group of quadcopters conducting a distributed patrol mission with safety guarantees.

On Integral Funnel of Control Systems, Changed at Several Small Time Interval

A nonlinear control system in a finite-dimensional Euclidean space and on a finite time interval is considered, the dynamics of which changes significantly over several small sections from a given time interval. We study the degree of change in the reachable sets and integral funnels of the system under consideration when it varies in these sections. The corresponding changes are estimated in the Hausdorff metric.