Nonlinear Analysis-Hybrid Systems最新文献

Investigating homoclinic trajectories and chaotic behaviors, is conducive to better understanding the fourteenth problem listed by Smale in his response to Arnold. This paper analytically detects coexisting homoclinic cycles without symmetry required in a class of three-dimensional (3D) piecewise systems, which is significantly different from the smooth case where a pair of homoclinic cycles with respect to one equilibrium point are generally symmetric. Moreover, it is rigorously shown that such coexisting cycles gives rise to chaos by means of analyzing a Poincaré map. An example finally is presented to illustrate the proposed results.

In this work, we study the convergence rate of the $N$-player Linear-Quadratic-Gaussian (LQG) game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second moments of the Mean Field Game equilibrium and applying the fixed point condition in Mean Field Game, we first provide the characterization of the equilibrium measure in Mean Field Game with a finite-dimensional Riccati system of ODEs. Additionally, with an explicit coupling of the optimal trajectory of the $N$-player game driven by $N$ dimensional Brownian motion and Mean Field Game counterpart driven by one-dimensional Brownian motion, we obtain the convergence rate $O\left(N^{-1/2}\right)$ with respect to 2-Wasserstein distance.

The finite-time stabilizing control design problem for discrete-time conewise linear systems is tackled in this paper. Such a class of systems consists of the union of ordinary linear time-invariant subsystems, whose dynamics are defined in prescribed conical regions, constituting a conical partition of the state space. By imposing some cone-copositivity properties to a suitable piecewise quadratic function, two sufficient conditions are preliminarily derived concerning the system’s finite-time stability. By building on them, novel results are then presented for the system’s finite-time stabilization through a piecewise linear output feedback controller. Such results are based on the solution of feasibility problems involving sets of Linear Matrix Inequalities (LMIs). A numerical example illustrates the effectiveness of the proposed approach.

This paper addresses the $H_{\infty }$ bumpless transfer control for switched nonlinear delayed systems with exogenous perturbations via the interval type-2 fuzzy model. We firstly establish a novel characterization of bumpless transfer performance, which provides a framework to the bumpless transfer control of switched nonlinear systems. By using the multiple Lyapunov-Krasovskii functionals and the state-dependent switching strategy, sufficient conditions for asymptotically stability with $H_{\infty }$ bumpless transfer performance are obtained. More incisively, different from the existing results where the $H_{\infty }$ bumpless transfer control design conditions do not involve the information of membership functions, we adopt the piecewise-linear-membership-function technique to remove this limitation. Correspondingly, novel membership-function-dependent $H_{\infty }$ bumpless transfer criteria are derived, under which the state-dependent switching law and $H_{\infty }$ bumpless transfer controllers are jointly designed. Finally, a tunnel diode circuit model is exploited to verify the applicability and validity of the developed method.

This paper deals with hybrid dynamical systems in the context of cybersecurity and Cyber–Physical Systems. It is shown how the design of a cipher, called self-synchronizing stream cipher, can be recast as control-theoretic issues, in particular left inversion, flatness and structural analysis. From an automatic control point of view, the main contribution lies in a methodology to construct generic flat LPV systems. Beyond pure control theoretic matters, the design also addresses computational complexity and security concerns. Those considerations motivate a hybrid architecture involving switched automata. A Proof-Of-Concept example illustrates the design of a statistical self-synchronizing stream cipher and the way how it operates to encrypt data flows.

The recent literature on event-triggered control has demonstrated the potential of dynamic periodic event-triggered control. Compared to continuous-time event-triggering rules, the benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon, which refers to the situation when there are an infinite number of updates in a bounded interval of time. The idea of periodic event-triggered control is to trigger the control law only at known allowable periodic sampling instants. In this paper, our objective is to relax the constraint on the periodicity of the allowable sampling instants and to adapt this framework to the dynamic event-triggered control, which has not been considered in the literature, as far as we are aware of. Following the successful efforts to assess the stability of aperiodic sampled-data control, here we propose a generic framework to emulate aperiodic dynamic event-triggered control law for linear systems, for which the allowable sampling instants are not necessarily equidistant. Such an analysis is made possible thanks to the looped-functionals framework, which gives the flexibility to consider the periodic/aperiodic static/dynamic event-triggered control in a single formulation. Finally, the efficiency of the proposed results is illustrated through the study of two academic examples.

Competition is a common biological relationship in nature, especially for some fish species. For different situations and different purposes in a two populations competitive system, we propose three novel mathematical models of two-fish competition with linear correlation feedback control. The first scenario considers undesirable competition in the system, and the purpose of control is to avoid the extinction of the inferior population. By discussing the existence and stability of the order-1 periodic solution, an effective method is provided for the realization of the fixed-period control and stabilization of the system, and the parameter optimization design is realized with the goal of minimizing the control cost. The second scenario considers the coexistence of two fish populations, and the purpose of control is transformed into harvesting of both populations. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamic characteristics and complexity of the control system are enriched, and the optimal design of parameters is realized with the goal of maximizing the economic benefits. The third scenario considers the phenomenon of equal competition between the two populations. The purpose of control is to avoid the extinction of one of the populations due to the large number of one population. By analyzing the existence of the order-1 and order-2 periodic solutions, the dynamical characteristics of the system are further enriched. Finally, numerical simulations are carried out for the three scenarios to illustrate the theoretical results and the feasibility of the control. The control strategy based on linear dependent feedback proposed in this paper provides an effective way to realize the coexistence of two populations competing systems.

In this paper, we investigate the problem of mitigating epidemics by applying an event-triggered control strategy. We consider a susceptible–infected–removed–susceptible (SIRS) model, which builds upon the foundational SIR model by accounting for reinfection cases. The event-triggered control strategy is formulated based on the condition in which the control input (e.g., the level of public measures) is updated only when the fraction of the infected subjects changes over a designed threshold. To synthesize the event-triggered controller, we leverage the notion of a symbolic model, which represents an abstracted expression of the transition system associated with the SIRS model under the event-triggered control strategy. Then, by employing safety and reachability games, two event-triggered controllers are synthesized to ensure a desired specification, which is more sophisticated than the one given in previous works. The effectiveness of the proposed approach is illustrated through numerical simulations.

This note investigates the H_∞ filtering for a kind of discrete-time switched systems ruled by cyclic switching regularities. By virtue of the cyclic manipulation of dwell-time (DT) switching and average dwell-time (ADT) switching reported in the literature, an innovative switching strategy of cycle-dependent persistent dwell-time (CPDT) property is first developed referring to the original persistent dwell-time (PDT) scheme. Further, to overcome the cycle-dependent DT constraint appearing in the CPDT switching, cycle-dependent ADT is sub-regionally injected into the suffering areas, which is different from the full-regional injection of ADT into the PDT switching in the literature. In this way, the CPDT switching is advanced to the cycle-dependent average persistent dwell-time switching, which can bring more flexibility to the switching design. Based on the newly introduced switching mechanisms, quasi-time-dependent (QTD) stability and l₂-gain criteria are formulated for discrete-time cyclic switched systems to guide the design of intended QTD full-order filters, through which the produced filter error systems perform as expected in terms of the stability and H_∞ noise attenuation capability. At last, the validities and advantages of the obtained filtering solutions are expounded by specific illustrative examples.

This paper presents a distributed fault detection filter (FDF) for positive semi-Markovian jump systems (PSMJSs) based on an adaptive event-triggered mechanism (AETM) scheme. A novel AETM is first proposed for the systems. A weighted fault model is introduced to assist the estimation of the original fault. Utilizing stochastic copositive Lyapunov function (CLF), a distributed FDF whose parameters are designed by virtue of linear programming (LP), is proposed. Under the designed filter, the positivity and stochastic stability with $L_1/L\text{\_}$-gain performance of a fault detection system is reached. The contribution of this paper contains three aspects: (i) An AETM is constructed for the considered systems, (ii) A distributed FDF is designed for the systems, and (iii) The hybrid $L_1/L\text{\_}$-gain performance is achieved with respect to the disturbance and the fault. Two illustrative examples are given for verifying the validity of the results.