Nonlinear Analysis-Hybrid Systems最新文献

This paper is devoted to the study of a large class of discrete-time backward Riccati equations arising in several linear quadratic (LQ) type control problems both in the deterministic and in the stochastic frameworks. The periodic time-varying case is considered. We propose existence and uniqueness conditions for a global special solution named stabilizing solution for such equations. Beside the stabilizability condition, the criterion derived in this paper is expressed based on some suitable properties of the characteristic multipliers of a discrete-time, periodic linear equation adequately constructed using the coefficients of the given equation. Our result englobes, as particular cases, several existing results in the literature.

This paper focuses on a class of functional diffusion systems with singularly perturbed regime switching, where the modulating Markov chain has a large state space and undergoes weak and strong interactions. By using the martingale method and weak convergence, this paper shows that the underlying system will weakly converge to a limit system, which is simpler than the original system. For a class of integro-differential diffusion system with singularly perturbed regime switching, as a class of special functional diffusion system, this paper demonstrates that if the limit system is moment exponentially stable, the original system with singular perturbation is also moment exponentially stable under suitable conditions. This result is interesting since the limit system is always simpler. Finally, an example is given to illustrate this result.

We propose a quantization-based distributed consensus tracking design to resolve the unknown control direction problem of uncertain switched nonlinear multiagent systems under a fully quantized environment. All feedback and communication signals for the local control design are quantized and the control coefficient functions and directions of agents are unknown. Differing from the previous literature results, the primary contribution of this work is to present a quantization-based distributed design solution to the unknown control direction problem of asynchronously switched agents in the consensus tracking field. The non-differentiability problem of virtual control laws using quantized feedback signals is addressed by employing the filter-based recursive method and developing the analysis technique of the quantization errors of Nussbaum functions. Quantization effects in local adaptive neural control laws are compensated via the adaptive tuning mechanism using quantized states. The practical stability of the overall closed-loop system is established by the common Lyapunov theory. Illustrative simulations verify the efficacy of the proposed quantization-based consensus tracking approach.

Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems. At each sampling instant, an STC mechanism determines not only the control inputs but also the next sampling instant. In this article, an STC approach for perturbed nonlinear systems is proposed. The approach uses a dynamic variable in addition to current state information to determine the next sampling instant, rendering the resulting STC mechanisms dynamic. Using dynamic variables has proven to be powerful for increasing sampling intervals for the closely related concept of event-triggered control, but has so far rarely been exploited for STC. Two variants of the dynamic STC approach are presented. The first variant can be used without further knowledge on the disturbance and leads to guarantees on input-to-state stability. The second variant exploits a known disturbance bound to determine sampling instants and guarantees asymptotic stability of a set containing the origin. In both cases, hybrid Lyapunov function techniques are used to derive the respective stability guarantees. Different choices for the dynamics of the dynamic variable, that lead to different particular STC mechanisms, are presented for both variants of the approach. The resulting dynamic STC mechanisms are illustrated with two numerical examples to emphasize their benefits in comparison to existing static STC approaches. Both variants are illustrated with a numerical example.

This article studies the problem of admissibility analysis for singular Markovian jump systems with time delay. Without introducing more variables, an augmented Lyapunov–Krasovskii functional (LKF) is presented, which does not require all matrices to satisfy the positive definite constraint. Inspired by free-matrix-based inequality, an improved version is proposed to obtain more accurate estimation of the integral term. Based on the novel LKF and the improved inequality, some relaxed stochastic admissibility criteria are proposed, which are less conservative. Finally, several examples are offered to verify the effectiveness of the proposed results.

In this paper, we consider the problem of multi-agent consensus in the presence of mobile adversaries. Faulty agents try to prevent the coordination among the regular agents and moreover are mobile in the sense that they can change their identities over time. Our approach towards resilient consensus is to extend the so-called mean subsequence reduced (MSR) algorithms to reduce the necessary communication based on three measures: (i) The information exchanged by the agents takes the form of ternary data in each message. (ii) A self-triggered method is first used so that agents avoid overreacting to DoS type attacks and maintain a certain communication rate. (iii) To enable the transmissions to terminate after reaching consensus, an event-triggered method is further introduced into the algorithm, resulting in a mixed protocol. Our study reveals that certain new features introduced in the protocols as well as in the conditions on network structures are critical to cope with potential attack strategies enabled by the mobile nature of the adversarial agents under ternary control. We verify the effectiveness of the proposed algorithm by means of a numerical example.

In this paper, the adaptive control via switching linear controllers is studied for a class of nonlinearly parameterized systems with unknown control directions. For the studied system, the parametric uncertainties entering the state equations nonlinearly can be fast time-varying or jumping at unknown time instants and the bounds of the parametric uncertainties are not required to know a priori and the control directions can be unknown. First, sufficient conditions for designing an adaptive stabilizer are derived. Then, the adaptive stabilizer is a switching-type one, in which a linear controller with two undetermined design parameters to be tuned is recursively designed by backstepping, and a switching mechanism is proposed to tune these parameters online for compensating the unknown control directions and the unknown bounds of the parametric uncertainties. The undetermined design parameters are based on the upper bound estimate of the unknown parameters existing not only in the nonlinear functions but also in the control directions functions. The proposed adaptive controller globally asymptotically stabilizes the system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed-loop system are bounded. Finally, an example is given to illustrate the effectiveness of the proposed method.

In this paper, the fault-tolerant tracking control problem is addressed for switched nonlinear systems subject to time-varying output constraints and dead-zone input under arbitrary switching signal. An improved output-dependent barrier function with weight factors is presented to handle the output constraint issue, which eliminates the conservative design that converts the output constraints into the tracking error related constraints and relaxes the requirements for the initial value of the systems output. Meanwhile, the barrier function presented in this paper can be used for the time-varying/constant symmetric/asymmetric output constraints and can tackle both constrained and unconstrained cases. Besides, the performance of the systems is ensured when actuator faults and dead-zone input occur simultaneously. By establishing the new coordinate transformations, together with command filter technique and the backstepping approach, the presented adaptive control strategy ensures that all signals of the closed-loop systems are bounded. Finally, the validity of the presented method is demonstrated via two simulation examples.

This paper studies the dwell-time-dependent stability analysis of impulsive systems by using a new time-square-dependent looped-functional. Based on the Lyapunov theory and two-sided looped-functional method, a time-square-dependent looped-functional is proposed, which fully utilizes the information of both the intervals $[t_k,t]$ and $[t,t_{k+1}]$. Then, by applying Jensen’s inequality and free-matrix-based inequalities to deal with integral terms in the functional derivatives, sufficient stability conditions in the form of linear matrix inequality are derived for periodic and aperiodic impulsive systems. Finally, numerical examples and simulation tests are given to illustrate the effectiveness and superiority of the proposed method.