Nonlinear Analysis-Hybrid Systems最新文献

The presented research is to focus on the issue of fault alarm-based quantized hybrid control strategy for semi-Markov jump neural networks subject to multiple vulnerable factors, namely, actuator faults, quantization effects and time-varying delays. Particularly, the fault-based alarm signal with a threshold value is proposed for controller switching and also for preventing false alarms. Precisely, a logarithmic quantizer is incorporated in the control design to adjust the transmission of signals and to enhance better robustness on system performance. Besides, a mixed $H_{\infty }$ and passivity performance is employed in order to handle the traces of external disturbances. By proposing Lyapunov–Krasovskii functional involving time delays along with Wirtinger based integral inequality, the anticipated control gain parameters that confirm the stochastic stability of the addressed system can be determined with the assistance of linear matrix inequality. The excellent dynamic performances of the proposed control scheme are clarified through two numerical examples, whereas the stability of the system is restrained with the timely alert performance of the configured alarm signal.

To simulate a more realistic and uncertain system model, this paper innovatively studies the output feedback control strategy to stabilize probabilistic Boolean control networks (PBCNs). This is the first time that output feedback method is used to solve stability problems in PBCNs. Compared with the traditional state feedback, observing output states is more direct and efficient. Firstly, a condition for the output-feedback stabilization in the sense of minimum time is explored. A sufficient and necessary condition is then provided to determine time-invariant output-feedback stabilizers. Afterwards, two constructive algorithms for design time-invariant output-feedback controllers are proposed. To comprehensively solve the output feedback stabilization problems, this paper explores two sufficient conditions for obtaining stabilizers under time-varying feedback control inputs, which provides more feasibility and significance for solving biomedical problems.

This paper is devoted to numerically solving a class of optimal stopping problems for stochastic hybrid systems involving both continuous states and discrete events. The motivation for solving this class of problems stems from quickest event detection problems of stochastic hybrid systems in broad application domains. We solve the optimal stopping problems numerically by constructing feasible algorithms using Markov chain approximation techniques. The key tasks we undertake include designing and constructing discrete-time Markov chains that are locally consistent with switching diffusions, proving the convergence of suitably scaled sequences, and obtaining convergence for the cost and value functions. Finally, numerical results are provided to demonstrate the performance of the algorithms.

This article investigates an event-triggered strategy to deal with the bipartite consensus issue for stochastic multiagent systems (SMASs) in a communication noisy environment. The communication network can be modeled by a random signed graph and the communication noise is compound noises (additive noise and multiplicative noise). The stochastic event-triggered bipartite consensus control protocol for SMASs with compound noises is presented by the stochastic approximation (SA) method. Due to the control gain is time-varying and agent-dependent, the implementation of event-triggered control protocol may cause out-sync of the control gain. Meanwhile, the coexistence of stochastic antagonistic information and compound noises causes it hard to turn the noises term into an error equation, which leads to the fact that the traditional error transition method is invalid for our underlying system. To deal with these challenges, the state’s boundedness for each agent is first constructed by the Lyapunov method, and then the event-triggered bipartite consensus can be demonstrated via a new semi-decomposition technique. Finally, the effectiveness of the proposed SA controller is verified by two examples.

This paper focuses on observer-based asynchronously intermittent decentralized control of large-scale linear systems. The controller and observer of each subsystem are assumed to work and rest simultaneously, whereas the controllers and observers in different subsystems have independently and asynchronously intermittent working/resting time. By designing a piece-wise continuous auxiliary timer and using it to construct a switching vertex-Lyapunov function for each subsystem, we provide linear matrix inequality (LMI) conditions to determine the minimal allowable control rate of the intermittent controller that preserves the stability of the closed-loop system. We also present the design of an observer-based decentralized controller via LMIs. Finally, a simulation example illustrates the validity of the results.

Stormwater detention ponds are essential stormwater management solutions that regulate the urban catchment discharge towards streams. Their purposes are to reduce the hydraulic load to avoid stream erosion, as well as to minimize the degradation of the natural waterbody by direct discharge of pollutants. Currently, static controllers are widely implemented for detention pond outflow regulation in engineering practice, i.e., the outflow discharge is capped at a fixed value. Such a passive discharge setting fails to exploit the full potential of the overall water system, hence further improvements are needed. We apply formal methods to synthesize (i.e., derive automatically) optimal active controllers. We model the stormwater detention pond, including the urban catchment area and the rain forecasts with its uncertainty, as hybrid Markov decision processes. Subsequently, we use the tool Uppaal Stratego to synthesize using Q-learning a control strategy maximizing the retention time for pollutant sedimentation (optimality) while also minimizing the duration of emergency overflow in the detention pond (safety). These strategies are synthesized for both an off-line and on-line settings. Simulation results for an existing pond show that Uppaal Stratego can learn optimal strategies that significantly reduce emergency overflows. For off-line controllers, a scenario with low rain periods shows a 26% improvement of pollutant sedimentation with respect to static control, and a scenario with high rain periods shows a reduction of overflow probability of 10%–19% for static control to lower than 5%, while pollutant sedimentation has only declined by 7% compared to static-control. For on-line controllers, one scenario with heavy rain shows a 95% overflow duration reduction and a 29% pollutant sedimentation improvement compared to static control.

In the paper the problem of state estimation of the nonlinear spatially-distributed system described by semilinear wave equations over the limited capacity communication channel is considered under the assumption that the boundary derivative is measured with the sampling and the external boundary control input is perfectly known. The Luenberger-type observer is designed based on the Speed-gradient method with an energy-like objective functional. An upper bound for the observer error in terms of the data transmission error and channel data rate (capacity) is derived and two data transmission procedures are numerically studied to find the admissible data transmission bounds. The key contribution of this paper is the extension of the previously existing results to the cases when the measurements and signal transmission in the control system cannot be available instantly and the finite capacity of the communication channels should be taken into account. The study of such cases is important for the observation and control of PDEs since the instant processing of infinite dimensional PDE data is problematic. The novelty of the results is threefold. Firstly, the state observer for distributed systems described by semilinear wave equations under limited channel data rate (capacity) is designed. Secondly, first time analytic bound for estimation error is obtained. Thirdly, first time the adaptive coding procedure is introduced and numerically studied for distributed systems.

In this paper, the partial synchronization of general Boolean Networks is studied from the perspective of nodes and states by using the semi-tensor product of matrices. First, by introducing the Hamming distances and its algebraic expression, the partial synchronization of general Boolean Networks can be transformed into an ensemble stability problem. Second, through optimizing the pinning strategy, the conditions for achieving partial synchronization of general Boolean Networks are developed, and the algorithm for finding the optimal pinning nodes is given. Subsequently, to further simplify the above condition, the related pinning node strategy is further optimized and combined by introducing state-flipped mechanism, which makes the general Boolean Networks partially synchronous under no condition, and requires the less number of nodes to be pinned compared to the previous works. Meanwhile, the corresponding algorithm for seeking the optimal pinning nodes is designed in the context of flipping the state only once. Finally, the obtained results are validated by several specific numerical examples. In summary, the current work can further enrich and improve the study of partial synchronization problems in Boolean Networks.

In this work, we develop an ordinary differential equation (ODE) model with impulsive sanitation of cholera. The sanitation interventions are classified into three types in this article. The first two types are human sanitation, with type-1 sanitation focused on the prevention of direct and indirect transmissions and type-2 focused on prevention of bacterial shedding. The third type refers to pathogen sanitation where interventions are performed in contaminated water environment via disinfection. For the developed impulsive model, we introduce the basic production number $R_0$ and show that $R_0$ remains a sharp disease threshold parameter despite the incorporation of impulsive sanitation. We numerically investigate the impact of impulsive sanitation on the prevention and control of the disease. Our numerical results indicate that type-1 sanitation tends to bear the longest time window between subsequent interventions among all the three types of sanitation provided the same level of sanitation efficacy. Particularly, when the sanitation efficacy is 50% under 90% compliance, type-1 sanitation can be implemented about every 7 months for the purpose of disease control, whereas type-2 and type-3 sanitation will have be performed on a daily basis and every three weeks or so, respectively.

We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinuous right-hand side. For piecewise affine systems, a normalization of the propagated probability distribution at every time step allows us to analytically compute the expectation integrals of the mean and covariance dynamics while explicitly taking into account the discontinuity. This leads to a natural smoothing of the discontinuity such that for relevant levels of uncertainty the resulting ODE can be integrated directly with standard schemes and it is neither necessary to prespecify the switching sequence nor to use a switch detection method. We then show how this result can be employed in the more general case of piecewise smooth functions based on a structure preserving linearization scheme. The resulting dynamics can be straightforwardly used within standard formulations of stochastic optimal control problems with chance constraints.