Impulsive Constraints Research Articles

Stability of impulsive and switched stochastic delay systems via the event-triggered impulsive mechanism

Under the event-triggered impulsive mechanism, this work introduces the pth moment (integral) input-to-state stability (p-(i)ISS) for a general group of impulsive and switched stochastic delay systems. Using the means of mode-dependent average dwell time and mode-dependent average impulsive interval, some sufficient conditions of p-ISS and p-iISS are supplied. By incorporating the input of subsystems and impulses into the triggering functions, two distinct types of event-triggered impulsive constraint is proposed, which is defined as mode-dependent event-triggered impulsive mechanism with input (MDETIMI). Different from the traditional event-triggered impulsive control, two MDETIMI strategy are individually discussed, which one is the supremum of K∞ function of subsystem input and the superposition of impulsive input, and the other is the integral of K∞ function of subsystem input and the superposition of impulsive input. Moreover, it is unveiled that even with the indeterminate derivatives of the Lyapunov functions, the Zeno phenomenon can effectively be avoided by using MDETIMI strategy. Finally, an example shows the effectiveness and practicability of the results.

Semi-Analytical Midcourse Guidance for Coordinated Interception of Multiple Exo-Atmospheric Targets

The simultaneous interception of multiple exo-atmospheric threat targets can leave no buffer time for the targets and greatly reduces targets’ penetration probability. This paper proposes centralized and decentralized two midcourse guidance methods to solve the coordinated interception of multiple exo-atmospheric targets. First, the free-time cooperative interception problem minimizing the total impulses is established, where the nonlinear dynamics of the interceptors and targets, the initial impulse constraints, and the terminal interception constraints are considered. Second, the necessary conditions for the optimal cooperative interception problem are derived and then approximated using higher-order Taylor expansions, which result in a series of analytical nonlinear equations. Then, the semi-analytical centralized guidance mode is designed to achieve simultaneous interception of targets by directly solving the analytical nonlinear equations. To improve computational efficiency, the decentralized cooperative guidance mode is further proposed by using the developed iterative freezing trajectory method, where each interceptor uses information from other interceptors in the previous iteration for prediction and distributed computation. Numerical examples verify the effectiveness and robustness of the proposed two guidance methods. Results show that the computational efficiency of the decentralized guidance mode is more efficient compared with the centralized midcourse guidance mode.

Thrust Integrated Trajectory Optimization for Multipulse Rocket Missiles Using Convex Programming

In this paper, a thrust integrated trajectory optimization algorithm for multipulse rocket missiles is proposed. Maximizing terminal velocity is selected as a performance index for achieving high maneuverability in the homing stage. To incorporate the optimization of thrust profile, thrust parameters are also considered as optimization variables with several thrust constraints such as impulse conservation and maximum/minimum thrust level. The original trajectory optimization problem is reformulated using new independent variables and timescale variables. This method simplifies the dynamics and makes the impulse conservation constraint disappear. Then, a control-affine system is established by defining the angle of attack and its square as new control inputs. The admissible input set is relaxed to a convex set, and mathematical proof is provided to show that the relaxation preserves the solution. The problem is discretized by applying a pseudospectral method for each subinterval. The solution is then obtained using sequential convex programming (SCP). A quadratic variable trust-region constraint is used for robust convergence of SCP. The proposed method robustly optimizes the thrust parameters and trajectory of the multipulse rocket missile within 1 s. Numerical simulation shows the feasibility and effectiveness of the proposed method.

Contact Lagrangian systems subject to impulsive constraints

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily plane and a rolling sphere on a non-uniform plane, both with dissipation.

EMOTIONAL REGULATION FACTORS OF IMPULSE BUYING AND CONFORMITY PSYCHOLOGY

Abstract Background The existing research on impulse buying behavior mainly discusses the influence of external stimuli on impulse buying intention, while there is less research on the internal psychological factors of impulse buying behavior. This paper aims to explore the psychological process of consumers' compliance with impulsive purchase after reading online word-of-mouth, as well as the regulatory effect of impulsive purchase intention and purchase constraint. Research Objects and Methods Taking belief, desire and willingness behavior as the research object, this paper discusses the influence of conformity psychological process on impulsive purchase behavior, as well as the regulatory effect on product demand cognition and purchase constraints. We design a structural equation model from four dimensions: compliance, product desire, impulse purchase intention and product demand cognition. Through this model, we verify the causal relationship between dimensions, the impact of impulsive purchase intention on impulsive purchase behavior and the adjustment of purchase constraints. Through an online survey, 616 valid questionnaires were collected from consumers who had at least online word-of-mouth experience in the past six months. Results Consumers' compliance after reading online word-of-mouth had a positive impact on product desire. Consumers' product desire has a positive impact on impulse purchase intention. Impulse purchase intention has a positive impact on impulse purchase behavior. Purchase constraints have a negative regulatory effect on the impact of impulsive purchase intention on impulsive purchase behavior. Product demand cognition has no moderating effect between conformity and product desire. The results showed that impulse purchase was significantly negatively correlated with economic support ability, self-control and emotion perception, emotion evaluation, emotion control and emotion regulation reflex, emotion regulation self-efficacy (P < 0.01), and emotion regulation self-efficacy (P < 0.05); It was positively correlated with self-care ability, emotion regulation ability and all dimensions (P < 0.01); Incentive autonomy and emotion regulation ability were significantly positively correlated with each dimension (P < 0.01); The ability of self-control and emotion regulation were significantly negatively correlated with each dimension (P < 0.01). Conclusion The same online word of mouth has different effects on different consumers. This influence depends on the conformity degree of consumers, which affects consumers' product desire and indirectly increases the possibility of consumers' impulse purchase through the increase of impulse purchase intention. Purchase constraint can inhibit impulse buying behavior. If enterprises can effectively connect online word-of-mouth with the product purchase process, when consumers have product desire due to the integration effect caused by online word-of-mouth, they can directly guide consumers to the purchase step, so that consumers can complete the purchase in a short time. Therefore, effectively linking the herd effect of online word-of-mouth with consumers' browsing word-of-mouth is an effective way for enterprises to stimulate herd consumers' impulse buying behavior. From a sequential perspective, this paper discusses the psychological process of consumers' impulse purchase and the role of regulatory variables under the background of the popularity of mobile Internet, and discusses the internal changes of positive and negative emotions in the process of consumers' impulse purchase. This is an in-depth study of online impulse buying behavior. Acknowledgements The work is supported by Science and Technology Planning Project of Henan Province of China (soft science research), grant number 212400410095.

Symmetric and Asymmetric Multiple Impulsive Constraints Without Friction and Their Characterization

We present two meaningful and effective non-ideal constitutive characterizations for a multiple impulsive constraints {mathcal {S}} comprising a finite number of non-ideal frictionless constraints of codimension 1, described in the geometric setup given by the space–time bundle {mathcal {M}} of a mechanical system in contact/impact with {mathcal {S}}. Thanks to the geometric structures associated to the elements of {mathcal {S}}, we introduce a symmetric characterization, that does not distinguish the elements forming {mathcal {S}} as regards mechanical behavior, and an asymmetric one that makes this distinction. Both the characterizations provide a generalization of the characterization of ideal multiple constraints presented in Pasquero (Q Appl Math 76(3):547–576, 2018). The iterative nature of these characterizations allows the introduction of two algorithms determining the right velocity of the system in case of single or multiple contact/impact with symmetric or asymmetric constraints {mathcal {S}}, once the elements forming {mathcal {S}} and the left velocity of the system are known. We show the effectiveness of the two possible choices with explicit implementations of these algorithms in two significant examples: a simplified Newton’s cradle system for the symmetric characterization and a disk in multiple contact/impact with two walls of a corner for the asymmetric one.

Relaxation of the attainability problem for a linear control system of neutral type

The problem of control of a linear system of neutral type with impulse constraints is developed. In addition, a given system of intermediate conditions is assumed. A setting is investigated in which a vanishingly small relaxation of the mentioned restrictions is allowed. In this regard, the attainability domain (AD) at a fixed time of the end of the process is replaced by a natural asymptotic analog, the attraction set (AS). To construct the latter, we use the construction of an extension in the class of finitely additive (f.-a.) measures used as generalized controls. It is shown that the AS coincides with the AD of the system in the class of generalized controls – f.-a. measures. The structure of the mentioned AS is investigated.

Trajectory-tracking control of a planar parallel robot using generalized predictive control with constraints

This paper presents the generalized predictive control with constraints, implemented to a planar parallel robot in order to calculate and track the desired trajectory of the end-effector of this robot. The manipulator is driven by three brushless direct current motors, and each one has an encoder to measure the velocity and rotation angles of the motors. Three constraints were considered to interact with the control law: control signal, terminal response and the over impulse constraints. The performance of the control law is evaluated in the simulation environment using Matlab/Simulink with the physic model developed through simscape multibody. The angular position and velocity errors for each of the three motors were calculated. Likewise, the output torques for each one were estimated. The results proved that the control law proposed with the constraints imposed for each motors has a good efficiency with a stable response time of the robot in performing the trajectory tracking, contributing to the scientific community a strategy of predictive optimization of control actions with multiple constraints applied on parallel robots.

Optimal two-impulse space interception with multiple constraints

We consider optimal two-impulse space interception problems with multiple constraints. The multiple constraints are imposed on the terminal position of a space interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations. Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is developed. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur; if two-impulse instants are free, then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.

Considering Link Flexibility in the Dynamic Synthesis of Closed-Loop Mechanisms: A General Approach

Abstract This paper has focused on the dynamic analysis of mechanisms with closed-loop configuration while considering the flexibility of links. In order to present a general formulation for such a closed-loop mechanism, it is allowed to have any arbitrary number of flexible links in its chain-like structure. The truncated assumed modal expansion technique has been used here to model link flexibility. Moreover, due to the closed nature of the mentioned mechanism, which imposes finite holonomic constraints on the system, the appearance of Lagrange multipliers in the dynamic motion equations obtained by Lagrangian formulation is unavoidable. So, the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations. In addition to the finite constraints, the impulsive constraints, which originate from the collision of system joints with the ground, have also been formulated here using the Newton's kinematic impact law. Finally, to stress the generality of the proposed formulation in deriving and solving the motion equations of complex closed-loop mechanisms in both the impact and non-impact conditions, the computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented.

Introduction

This issue of Lexis apprehends humor in its wider sense, including, for instance, comedy, irony, satire, parody, sarcasm, to name but a few of its many variations. Within this framework, it aims to approach it via the paradigm of lexical creation, meant as a tool used to provoke laughter. Indeed, humorists enjoy playing on words, but also playing with words, which implies a taste for lexical creativity. How are such humorous effects achieved with the lexicon? Derivation, compounding and blending mechanisms, phoneme or letter inversion processes, paronymic neologisms, among many other lexicogenic operations, although revealing the great creativity of their enunciators, obey lexical and morphological rules. If such rules were not followed, they would not work, be efficient and understood by their addressees. The Bergsonian precept [1914: 37], used to describe one of the mechanisms initiating laughter – “something mechanical encrusted on the living” – applies to language indeed: the double tension between creative impulse and linguistic constraints is paramount to the reflections of the thirteen international researchers who have contributed to this thematic issue.

Lyapunov–Krasovskii‐type criteria on ISS and iISS for impulsive time‐varying delayed systems

This study investigates the problem of input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive time-varying delayed systems. Some Lyapunov–Krasovskii-type criteria on ISS and iISS which are effective for destabilising impulses and stabilising impulses are derived from advanced linear dissipation inequalities under average impulsive interval constraints. The conditions which require the coefficients of the linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be constants in the existing results on ISS/iISS of impulsive delayed systems are weakened. In this study, with the aid of the notions of uniformly exponentially stable function and average impulsive interval, the results allow the coefficients of the developed linear dissipation inequalities on the Lyapunov–Krasovskii functionals to be time-varying functions which can take both positive and negative values, and the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and enough big upper bound simultaneously. Two examples are presented to illustrate the effectiveness of the results.

Dynamic modeling of planar closed-chain robotic manipulators in flight and impact phases

This paper presents a systematic procedure for the dynamic modeling of a closed-chain robotic system in both the flight and impact phases. In the proposed approach, first, a planar closed-chain system constructed of n rigid links and n+1 revolute joints is virtually converted to an open kinematic chain. Then, a recursive algorithm based on the Gibbs–Appell principle is applied to reduce the computational load of the developed model, which contains finite constraints. The normal impact phase of this closed-chain robotic system, which includes impulsive constraints, is modeled based on the Newton's kinematic impact law. Finally, computer simulations of a hexagonal closed-chain robotic system in both the flight and impact phases are carried out. This work is actually an extension of the previous investigation of the authors, which was restricted to the study of an open kinematic chain. So, in order to avoid duplication, only the necessary modifications in converting open kinematic chains to closed-chain robotic manipulators are presented here. To the best of our knowledge, this is the first time that a combination of finite and impulsive constraints in a closed-chain mechanical system has been recursively formulated. Since experimental verification of the proposed model is not easy to achieve in this case and no well-defined benchmark problems could be found to validate the model, the findings of this work are compared with the results obtained by simulating the same system in the “Working Model” computer software.

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian–Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge–Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space–time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization.The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier–Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.

On an asymptotic analysis problem related to the construction of an attainability domain

Problems of constructing and analyzing the properties of attainability domains play an important role in control theory and its applications. In particular, this applies to control under impulse constraints that reflect the energetics of a process. The situation is complicated by the possible instability of the process under variation (in particular, under relaxation) of constraints related to boundary and intermediate conditions. Stability of the problem is also missing, in general, under relaxation of state constraints. In these cases, it is natural to focus on the asymptotic variant of the statement; this is especially expedient when one has to deal with initially asymptotic requirements. In all these cases, it seems expedient to use analogs of J. Warga’s approximate solutions. At the same time, to seek necessary approximate (and, in fact, asymptotic) solutions, it is natural to use generalized modes. For problems with impulse constraints and discontinuity in the coefficients of control actions, such modes lead to phenomena described by products of discontinuous functions and generalized functions even in the class of linear systems. In a large series of his studies, to overcome the arising difficulties, one of the authors used constructions of extension in the class of finitely additive measures. The present paper follows this approach and is ideologically relevant to the engineering problem of controlling the thrust of an engine under conditions of a given program of variation of its orientation; it is postulated that energy resources are completely consumed in a natural (for a number of impulse control problems) mode of short-duration impulses: the set of time instants at which the instantaneous control is different from zero can be embedded in an interval of vanishingly small length. Within these short periods of time, the engine should consume all energy resources while obeying some other constraints (making the sense of moment constraints) to a high degree of accuracy. In addition, one should take into account the possible discontinuity of the functions defining the coefficients of control actions. As a natural analog of the attainability domain, we use an attraction set, whose construction, together with the subsequent study of its main properties, constitutes the goal of the present study.

Impulsive practical tracking synchronization of networked uncertain Lagrangian systems without and with time-delays

This paper presents a procedure for studying tracking synchronization of networked Lagrangian systems via impulsive control, where each agent is allowed to be nonidentical, even uncertain dynamics. Some algebraic criteria for tracking synchronization without and with time-delays are established respectively. It turns out that these criteria can provide a novel impulsive control strategy to synchronize globally networked Lagrangian systems to a given time-varying target trajectory with a desired tracking error bound (called as practical tracking synchronization). A distinctive feature of the developed control strategy is fully to take into account the effects of impulsive constraints, and thereby to yield impulsive synchronization motion of networked Lagrangian systems, provided that each agent instantaneously interacts with its neighbors only at some discrete moments. As a direct application of the theoretical results, practical tracking synchronization of nonidentical 3-DOF mobile robots without and with time-delays is discussed in detail. Simulation results illustrate and visualize the effectiveness and feasibility of the proposed control technique.

Shock analysis and optimization of two-layered cellular materials subject to pulse loading

We present the method of characteristics with mass, momentum, and energy conservation to solve the nonlinear wave equation with shock formation in a two layer one-dimensional rod made of cellular material. We show that the rigid-perfectly-plastic-locking model cannot predict shock formation at a material interface, so we propose an elastic–plastic-densifying model to describe the stress–strain behavior of the cellular materials. The conditions for shock formation at a material interface are provided. We conduct a two-layer analysis to gain insights into the behavior of two layer cellular systems and to determine which material properties are most important for design. Finally, we optimize the significant parameters to reduce the length of one and two layered cellular systems with impulse and mass constraints subject to pulse loading. The results reinforce the concept of sandwich structures and show that two layer systems can achieve a 30% reduction in length over single layer ones.

Impulsive synchronization motion in networked open-loop multibody systems

This paper presents a procedure for studying impulsive synchronization motion in networked open-loop multibody systems formulated by Lagrange dynamics. Impulsive motion occurs when the networked systems are physically subject to either direct or indirect impulsive effects, or when subjected to both simultaneously. The impulsive effects are usually caused by impulsive forces or impulsive constraints. The governing equations of networked open-loop multibody systems are developed from Lagrange formulation. The procedure automatically incorporates a preliminary feedback control and the effects of impulsive constraints through its analysis. Some generic criteria on exponential synchronization of the system output with respect to generalized coordinates and its velocities over, respectively, undirected fixed and switching network topologies, are derived analytically. The procedure shows that impulsive synchronization motion in networked open-loop multibody systems can achieve by impulsive constraints strategies. Two examples and simulations are used to demonstrate and validate the analysis procedure.

An Eigenvalue Problem for the Analysis of Variable Topology Mechanical Systems

Mechanical systems with time-varying topology appear frequently in natural or human-made artificial systems. The nature of topology transitions is a key characteristic in the functioning of such systems. In this paper, we discuss a concept that can offer possibilities to gain insight and analyze topology transitions. This approach relies on the use of impulsive constraints and a formulation that makes it possible to decouple the dynamics at topology change. A key point is an eigenvalue problem that characterizes several aspects of energy and momentum transfer at the discontinuous topology transition.

Extension of a Problem of the Game Control

The terminal game problem of control of the linear system with a discontinuity in coefficients under controlling influences and impulse constraints is considered. In the class of finitely additive measures with the property of the weak absolute continuity with respect to the restriction of the Lebesgue measure to some “sufficient” measurable structure, the generalized game problem of control is constructed.