Nonlinear Analysis-Hybrid Systems最新文献

In this paper, we inner-estimate the minimal domains of attraction of uncertain discrete-time switched systems under state-dependent switching, where the uncertain terms are described by bounded functions. At first, we introduce the uncertain parameter evolution to define the solution (or trajectory) of uncertain discrete-time switched system and then present the definitions of multi-step state subspaces, multi-step basins of attraction and multi-step Lyapunov-like functions. Then, based on using multi-step Lyapunov-like functions to iteratively compute multi-step basins of attraction, we establish an iterative framework to compute inner-estimations of the minimal domain of attraction. Especially, since certain multi-step state subspaces are empty sets, the corresponding constraints in the iterative framework are redundant. Therefore, we next realize the iterative framework by first finding out the non-empty multi-step state subspaces by the homotopy continuation method and then using S-procedure to under-approximately transform the iterative framework into a sum of squares programming. Moreover, we introduce a refinement method to improve our iterative method. At last, we apply our iterative method to four theoretical examples as well as a real-world example and present a short discussion on the results.

This paper investigates the stochastic safety analysis and synthesis issues for a class of linear human-in-the-loop (HiTL) systems based on hidden semi-Markov human behavior modeling and stochastic reachable set computation. Firstly, by considering the random property of human internal state (HIS) reasoning and the uncertainty from HIS observation, a hidden semi-Markov model (HS-MM) is employed to describe the HIS behavior. A discrete-time hidden semi-Markov jump system (HS-MJS) model is then constructed to depict the HiTL control system, which can integrate human model, machine model, and their interaction in a stochastic framework. The safety constraints are described through a polyhedral set of the machine state. Subsequently, based on the HS-MJS model, a sufficient condition for the stochastic safety of the HiTL control system is provided in terms of linear matrix inequalities (LMIs) via reachable set computation. A human-assistance safety control design is derived on the basis of LMIs. Moreover, for some given safe confidence level, a stochastic safety criterion and an LMI-based human-assistance controller synthesis method are proposed for the HiTL control system by computing the probabilistic reachable set. Finally, a lane-keeping assistance system is employed to verify the feasibility of the theoretical results.

This paper investigates the issues of data tampering attacks detection and system parameter identification in finite impulse response (FIR) systems with binary-valued observations. Without the need to acquire system-related prior information or perform operations such as adding watermarks or encryption to the data, a detection and identification joint algorithm is proposed using input design. This algorithm can detect potential data tampering attacks in the system while achieving consistent identification of system parameters. Subsequently, a pair of metrics for evaluating the detection performance of the algorithm, namely the missing detection rate and false detection rate, are introduced, and approximate expressions for both are provided, followed by a discussion on the impact of data length and detection threshold on these metrics. Finally, numerical simulations are conducted to validate the conclusions obtained and the results of the discussions.

For delayed generalized asynchronous Boolean networks with random disturbances, it is still uncertain about their robust controllability. This paper uses the semi-tensor product to transform these Boolean networks into linear representations to derive the dependence matrix of the network transition on the control mode. After that, three different control modes are utilized to define controllability. Each control mode provides both reachable trajectories set under a specific initial trajectory and an initial trajectory set under a specific target trajectory. It is also calculated for the likelihood of a transition between two states. Lastly, two concrete examples validate the theoretical findings under various control modes.

Given the cooperation and competition bi-directional mechanisms between subsystems, this paper aims at addressing bipartite quasi synchronization (BQS) of stochastic delayed cooperation–competition networks (SDCNs). We propose a gain-waving intermittent control policy, that includes more of the existing works, to assist the BQS, in an effort to cope with external interferences and the possibility of actuator damage caused by rapid switching. Intermittent gain is to be quantized legitimately via the postulate of waving average gain. Within this context, novel Lyapunov inequalities concerning bounded waving gain and unbounded one are advanced to ensure the BQS of SDCNs in conjunction with graph theory, since the present differential inequalities are incapable of being inoperative. Then we develop two kinds of BQS criteria and the bounds for the BQS error are estimated where the scenarios of bounded waving gain and unbounded one are involved separately. Besides, corresponding criteria about complete bipartite synchronization are presented and several design methods of gain-waving intermittent control are introduced by specific examples. Finally, the validity of the theoretical results is examined by an application on Chua’s circuit with numerical simulations being shown.

In this paper, we investigate the issue of almost sure stability (ASS) for a class of stochastic strict-feedback semi-Markov jump systems (SSSJSs) under periodic intermittent control (PIC). This control method and dynamic properties are studied for the first time in strict-feedback systems. First of all, based on the structural properties of the SSSJSs, virtual controllers are designed step by step and eventually deduced into the actual controller. Furthermore, by using stochastic analysis theory and multiple Lyapunov function method, we obtain sufficient conditions for ASS via PIC, which have a close relationship with control width and control period. By virtue of multiple Lyapunov functions that depend on the system states, the conservatism caused by mode-independent cases can be reduced effectively. Finally, the effectiveness of the presented results is illustrated by simulation examples.

The authors consider the stabilization of highly nonlinear switched stochastic systems with non-differentiable delay by delay feedback control. In this paper, switching signals of highly nonlinear switched stochastic systems are non-random which are different from the previous literature. Moreover, the time-varying delay of highly nonlinear switched stochastic systems is non-differentiable, while the time-varying delay of feedback control is constant or differentiable. By using the Lyapunov functional method and the mode-dependent average dwell time approach, we have established the delay-dependent stabilization criteria of highly nonlinear switched stochastic delay systems by delay feedback control. Finally, two numerical examples are provided to show the effectiveness of the developed theoretical results.

In this paper we consider the long time behavior for an $n$-dimensional population model driven by truncated $\alpha$-stable processes for interacting species. Some sufficient conditions for ergodicity or transience for our systems are given. This paper discloses the different jump measures impact on such pure-jumps population dynamics.

Self-cycling fermentation is an automated process used for culturing microorganisms. We consider a model of $n$ distinct species competing for a single non-reproducing nutrient in a self-cycling fermentor in which the nutrient level is used as the decanting condition. The model is formulated in terms of impulsive ordinary differential equations. We prove that two species are able to coexist in the fermentor under certain conditions. We also provide numerical simulations that suggest coexistence of three species is possible and that competitor-mediated coexistence can occur in this case. These results are in contrast to the chemostat, the continuous analogue, where multiple species cannot coexist on a single nonreproducing nutrient.

This study is dedicated to exploring the challenge of asynchronous resilient robust model predictive control (RMPC) for linear parameter-varying (LPV) systems operating under a stochastic communication protocol (SCP). In contrast to the conventional Markov-based SCP, a novel sojourn probability-based SCP is introduced to regulate packet transmissions. This innovative approach simplifies the determination of transition probabilities and lessens the computational burden. Acknowledging the challenges associated with observing sojourn probability information, a mode detector is employed to describe the connection between mode discrepancies. To address parameter uncertainties, a novel detected-mode-based resilient control law is formulated to ensure the mean-square stability of the LPV system within the resilient RMPC framework. Additionally, an online algorithm for resilient RMPC is presented, grounded in an auxiliary optimization problem. Ultimately, the effectiveness of the proposed control strategy is validated via a high-purity distillation process model.