Nonlinear Analysis-Hybrid Systems最新文献

This article aims to provide a unified theoretical framework for studying the dynamic behavior of uncertain impulsive systems involving saturation structure and packet loss phenomenon. The concept named average packet loss interval (APLI) is developed to characterize the distribution of packet loss intervals. In this scenario, the traditional restrictions on the number, the proportion, or the upper bound of packet loss intervals can be significantly relaxed. By modeling the original systems as the asynchronous impulsive switched systems, some sufficient criteria are derived via the set invariant approach, addressing how to integrate the effects of impulsive and external disturbances into input-to-state stability (ISS) performance. It is also shown that the robustness of system performance against packet loss can be guaranteed ideally. Then, an optimization algorithm is designed with the hope of getting the maximum estimate of the domain of initial values. Finally, two examples are discussed to demonstrate the effectiveness of our proposed results.

In this paper, we study the regularity of the value function associated with a stochastic control problem involving two controls that act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a random clock. Whenever the random clock rings, the generator matrix is replaced by another, leading to a different dynamic for the finite state Markov chain of the modulated diffusion process. The second is a singular stochastic control that is executed on the process within each regime.

Iterative Learning Control (ILC) is commonly used for batch processes. However, it may face difficulties when dealing with non-repetitive disturbances and inconsistent initial states. In situations with non-repetitive disturbances, the output may disobey constraints and negatively impact tracking performance when using existing predictive ILC algorithms. This paper introduces a new model-predictive ILC incorporating feed-forward and feedback mechanisms. This new approach evaluates and attenuates the impact of non-repetitive disturbances on the output. As a result, constraints are guaranteed, and tracking performance is preserved and improved, even in the presence of non-repetitive disturbances. Furthermore, if the desired trajectory is unattainable, the proposed ILC can robustly track an optimal trajectory while still guaranteeing constraints. The convergence is proven rigorously. Finally, two examples are provided to demonstrate the effectiveness of this new approach.

Fault-tolerant control is a fundamental and challenging branch in the control community, and has wide applications in aerospace, automotive technology and nuclear engineering. Particularly, the study of faulty Boolean control networks (BCNs) is meaningful to the gene engineering. This paper focuses on the stuck-at fault occurring in BCNs, and investigates the controllability and observability of faulty BCNs. The basic mathematical tool is semi-tensor product (STP) of matrices, which is used to determine the algebraic formulation of BCNs subject to the meaningful stuck-at fault. Through the construction of faulty matrix, the relation between stuck-at fault and controllability of BCNs is presented. In addition, the observability of BCNs subject to stuck-at fault is discussed. Several new criteria are derived for the controllability and observability of BCNs subject to stuck-at fault, which have lower complexity than that of original BCNs. Finally, the obtained results are applied to analyze the controllability and observability of an faulty apoptosis network.

We propose new criteria, which are more general than those previously known in the literature, to guarantee the existence of global attractors for problems with state-dependent impulses. Our result on the existence of global attractors is proved for the case where the solutions on the underlying semiflow can possibly be nonunique, and it is even new for the case of solution uniqueness. Additionally, we provide collective versions of the proposed criteria, under which, as we prove, the global attractors exhibit upper-semicontinuity upon perturbation of the problem. The theory is illustrated through several examples of ODEs and PDEs.

This article is devoted to the analysis of fixed-time (FXT) and preassigned-time (PAT) output synchronization for T–S fuzzy complex networks (CNs). Firstly, to improve transmission efficiency of information, a kind of pure power-law control strategy with logarithmic quantization is designed and the power-law terms have only one free parameter. Then, by applying FXT stability theorem as well as inequality skills, some compact criteria are obtained to achieve FXT output synchronization of T–S fuzzy CNs, and the restriction on the output matrix with positive definite and diagonal form is removed. Furthermore, the PAT output synchronization of T–S fuzzy CNs is further explored by developing a quantized control scheme with power-law form. Three numerical examples in the end are given to attest the proposed control design and criteria.

We consider the problem of computing the maximal probability of satisfying an $\omega$-regular specification for stochastic, continuous-state, nonlinear systems evolving in discrete time. The problem reduces, after automata-theoretic constructions, to finding the maximal probability of satisfying a parity condition on a (possibly hybrid) state space. While characterizing the exact satisfaction probability is open, we show that a lower bound on this probability can be obtained by (I) computing an under-approximation of the qualitative winning region, i.e., states from which the parity condition can be enforced almost surely, and (II) computing the maximal probability of reaching this qualitative winning region.

The heart of our approach is a technique to symbolically compute the under-approximation of the qualitative winning region in step (I) via a finite-state abstraction of the original system as a $2\frac{1}{2}$-player parity game. Our abstraction procedure uses only the support of the probabilistic evolution; it does not use precise numerical transition probabilities. We prove that the winning set in the abstract $2\frac{1}{2}$-player game induces an under-approximation of the qualitative winning region in the original synthesis problem, along with a policy to solve it. By combining these contributions with (a) a symbolic fixpoint algorithm to solve $2\frac{1}{2}$-player games and (b) existing techniques for reachability policy synthesis in stochastic nonlinear systems, we get an abstraction-based algorithm for finding a lower bound on the maximal satisfaction probability.

We have implemented the abstraction-based algorithm in Mascot-SDS, where we combined the outlined abstraction step with our tool Genie (Majumdar et al., 2023) that solves $2\frac{1}{2}$-player parity games (through a reduction to Rabin games) more efficiently than existing algorithms. We evaluated our implementation on the nonlinear model of a perturbed bistable switch from the literature. We show empirically that the lower bound on the winning region computed by our approach is precise, by comparing against an over-approximation of the qualitative winning region. Moreover, our implementation outperforms a recently proposed tool for solving this problem by a large margin.

The problem of the finite-region passive control for 2-D Markov jump Roesser systems, in which the partial statistical information issues on Markov parameters and transition probabilities are considered simultaneously. To model this situation, a 2-D hidden Markov model with partial statistical information is established. The purpose of this paper is to design a controller based on the 2-D hidden Markov model such that both the horizontal states and vertical states of 2-D Markov jump Roesser systems are bounded in finite-time and a passive performance is met. Based on the Lyapunov function method, the criteria for the finite-region boundedness of 2-D Markov jump Roesser systems are established and the design method of the 2-D hidden Markov model-based asynchronous controller is presented. The effectiveness of the design method is verified by an illustrative example.

This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching controllers against $\omega$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called control sub-barrier certificates of subsystems, which are used to compositionally construct control barrier certificates of interconnected systems by imposing some dissipativity-type compositionality conditions. We propose a systematic approach to decompose high-level $\omega$-regular specifications into simpler tasks by utilizing the automata corresponding to the specifications. In addition, we formulate an alternating direction method of multipliers (ADMM) optimization problem in order to obtain suitable control sub-barrier certificates of subsystems while satisfying compositionality conditions. For systems with polynomial dynamics, we provide a sum-of-squares (SOS) optimization problem for the computation of control sub-barrier certificates and local controllers of subsystems. Finally, we demonstrate the effectiveness of our proposed approaches by applying them to a physical case study.

This article discusses a class of stochastic hybrid delayed coupled systems with multiple weights (SHDCSMW). Both white noise and telegraph noise are included in the coupled systems. By employing Kirchhoff’s Matrix-Tree Theorem, a global Lyapunov function is rebuilt indirectly, which is closely related to Markovian switching. Moreover, based on Lyapunov stability theory and stochastic analysis, several sufficient conditions with respect to asymptotic synchronization and topology identification of SHDCSMW are derived. Finally, the validity of theoretical results is proved by numerical examples.