Nonlinear Analysis-Hybrid Systems最新文献

This paper explores the problem of (generalized) Nash equilibrium search in multi-cluster games with heterogeneous dynamics and multiple constraints. Within this research framework, each agent acquires information solely through local interactions with its neighbors and forms clusters based on similarity of interests. These clusters manifest dual relationships of cooperation and competition: agents within the same cluster enhance decision-making capabilities through cooperation, while different clusters compete to maximize their respective benefits. To delve into these complex interactions among clusters and the learning and evolution processes among agents, four distributed control algorithms suitable for various scenario requirements are designed and implemented. These algorithms ensure that each agent converges to a Nash equilibrium (NE) or generalized Nash equilibrium (GNE) of the multi-cluster system within predefined time points. Finally, we apply these algorithms to the connectivity control problem of unmanned aerial vehicle swarms with diverse dynamics, validating the theoretical results through comprehensive simulations.

Sampled-data control linear systems subject to uniform input quantization are considered. Within this context, the design of a stabilizing sampled-data state feedback controller is proposed. The proposed controller guarantees uniform global asymptotic stability of an attractor containing the origin of the plant. Due to the interplay of continuous-time dynamics and instantaneous changes in the state, the closed-loop system is modeled as a hybrid dynamical system. By relying on a quadratic clock-dependent Lyapunov function, sufficient conditions in the form of bilinear matrix inequalities are provided to ensure closed-loop stability. These conditions are employed to devise an optimal controller design algorithm based on the use of convex–concave decomposition approach. This leads to an iterative design algorithm based on the solution to a sequence of semidefinite programs for which feasibility is guaranteed. Some illustrative examples show the effectiveness of the proposed results.

Kuramoto models (KMs) in scalar or high-dimensional form can describe the synchronization phenomenon for large populations of coupled oscillators in networks of dynamical systems such as power grids, satellite mobile sensing networks, etc. However, these models are developed based on continuous-time coupling among oscillators, which is not applicable to networks where the coupling between oscillators occurs only at impulsive instants. Herein, we propose for the first time a generalized high-dimensional Kuramoto oscillator network (HDKON) with variable-gain impulsive coupling on the unit sphere. The proposed HDKON can be reduced to a scalar form comprising a sinusoidal function, thereby generalizing the scalar KM in both temporal and spatial domains. Furthermore, we provide some variation coefficients of the synchronization errors for the oscillator pairs at impulsive instants, and derive a sufficient condition for the exponential synchronization of the HDKON with identical natural frequency. Moreover, we consider an HDKON with a central oscillator and demonstrate that peripheral oscillators almost globally exponentially synchronize to the central oscillator under a sufficient condition. Finally, numerical simulations are performed to verify the main theoretical results.

The effectiveness of reachability analysis often depends on choosing appropriate values for a set of tool-specific properties which need to be manually tailored to the specific system involved and the reachable set to be evolved. Such property tuning is a time-consuming task, especially when dealing with nonlinear systems. In this paper, we propose, instead, a methodology to automatically and dynamically choose property values for reachability analysis along the system evolution, based on the actual verification objective, i.e., the verification or falsification of a set of constraints. By leveraging an initial solution to the reachable set, we estimate bounds on the numerical accuracy required from each integration step to provide a definite answer to the satisfaction of the constraints. Based on these accuracy bounds, we design a cost function which we use, after mapping the property space to an integer space, to search for locally optimal property values that yield the desired accuracy. Results from the application of our methodology to the nonlinear reachability analysis tool Ariadne show that the frequency of correct answers to constraint satisfaction problems increases significantly with respect to a manual approach.

The actual industrial process is usually an uncertain dynamic process. Probability constraints are appropriate for the industrial process modeling in uncertain environments, where constrained conditions do not require to be entirely satisfied or cannot be strictly satisfied. This paper models an energy dispatch strategy problem for hybrid power systems with renewable energy resources as a dynamic switching optimization problem with probability constraints. Finding an analytical solution of the probability constrained dynamic switching optimization problem (i.e., an infinite dimensional optimization problem) is usually very challenging because of the switching characteristic of its dynamic system and the complexity of probability constraints. To find a numerical solution, this problem is treated as a constrained nonlinear parameter optimization problem (i.e., a finite dimensional optimization problem) by using a relaxation approach, an improved sample approximation technique, two smooth approximation methods, and a control parameterization technique. The advantage of the proposed method is that the proposed method does not rely on the structure of the original problem and can be used to handle random variables with various distributions. Further, a penalty function-based intelligent optimization method is proposed for solving the resulting constrained nonlinear parameter optimization problem based on an improved limited-memory BFGS method and an improved intelligent optimization method. According to the convergence result, the penalty function-based intelligent optimization method has global convergence. Finally, two examples are adopted to demonstrate the effectiveness of the proposed approach. Numerical results show that compared with other methods, the proposed method not only can obtain a better solution with a smaller standard deviation, but also has relatively lower computational cost. Additionally, the proposed approach can achieve a stable and robust performance, when we consider the small noise disturbances in the initial system state. That is to say, an effective numerical optimization algorithm is proposed for solving the energy dispatch strategy problem for hybrid power systems with renewable energy resources. Further, a parameter setting method is also proposed by applying the sensitivity analysis approach to balance the calculation cost and the accuracy of obtained solutions.

Mean square exponential input-to-state stability (MSEISS) is studied for Markovian reaction–diffusion systems (MRDSs) with partial unknown transition probabilities. Firstly, the representation of the weak infinitesimal operator is derived for the partial differential system with Markovian switching. When transition probabilities are partially unknown, with the Lyapunov functional method, free constants and Wirtinger-type inequality, a sufficient condition is established to obtain the MSEISS for MRDSs where both the boundary input and in-domain input are considered. Then, the boundary controller is considered for MRDSs, and a sufficient criterion related to control gain is established to ensure the MSEISS and the effectiveness of controller is illustrated. In addition, the robust MSEISS is investigated for uncertain MRDSs. Finally, the derived results are illustrated via battery temperature management systems.

This paper studies static output-feedback stabilization of the second- and third-order (with relative degree 3) nonlinear systems by a fast-varying square wave dither with a high gain. Recently, a constructive time-delay approach to design such a fast-varying output-feedback controller for linear systems was suggested by using continuous measurements. In the present paper, we extend these results to the case where the measurements are sent to the controller via a communication network. The sampling intervals are expected to be small due to the rapidly oscillating high gains. To reduce the network load, we suggest a dynamic event-trigger (ET) via switching approach. We present the closed-loop system as a switching between the system under periodic sampling and the one under continuous event-trigger and take the maximum sampling preserving the stability as the lower bound of inter-event time. We construct appropriate coordinate transformations that cancel the high gains in the closed-loop system and apply the time-delay approach to periodic averaging of the system in new coordinates. By employing appropriate Lyapunov functionals, we derive linear matrix inequalities (LMIs) for finding efficient bounds on the dither frequencies and inter-event times that guarantee the stability of the original systems. Numerical examples illustrate the efficiency of the method.

This paper investigates the approximate synchronization of singular logical networks (SLNs) using algebraic representations. Different from complete synchronization, which requires the state trajectories of the drive-response SLNs to be completely consistent after a finite time, approximate synchronization allows for admissible errors between the state trajectories of the drive-response SLNs. A definition of approximate synchronization for SLNs is proposed. By analyzing the constructed admissible matrices, the solvability of SLNs is discussed. A criterion is provided for the approximate synchronization of SLNs. Self-triggered control is then introduced to address the approximate synchronization of SLNs. Based on this, an algorithm is presented to design the self-triggered state feedback control of approximate synchronization. The method presented in this paper can significantly reduce updating frequencies of controllers. Finally, obtained theoretical results are illustrated through a genetic regulatory network.

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.