Nonlinear Analysis-Hybrid Systems最新文献

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.

Despite the proposed results on the non-existing of finite time stable equilibria for fractional order systems (Shen and Lam, 2014), the commented paper (Wang et al., 2020) has shown finite time convergence of fractional order control systems via a couple of theorems. This comment demonstrates that the proofs of the given theorems in Wang et al. (2020) are incorrect.

This study focuses on the observer-based sliding mode control (SMC) for discrete stochastic switching models, where the semi-Markov kernel information is incomplete. Because the sensors do not always have direct access to the state vector in a complex environment, an observer-based output measurement is considered to estimate the system state. In contrast to previous works, the observer-based strategy is first investigated in studying the SMC for semi-Markov switching systems under the discrete framework. The sufficient condition for achieving mean-square stability is proposed to solve the desired observer and controller gains by utilizing the upper bound of sojourn time, along with the Lyapunov function that pertains to the system mode and the elapsed time. A mode-dependent SMC law is also constructed to ensure that the system state can reach the specified sliding region. Finally, the efficiency of the proposed method is demonstrated through the single-link robot arm model.

Applying jumping locomotion into autonomous mobile robot is an effective way for improving abilities to overcome barriers and pass through complex terrains. In this paper, based on the designed structural framework for bio-inspired quadruped jumping robot, dynamic model is established by utilizing port-Hamiltonian with dissipation (pHd) method, and a passivity-based control strategy for the robot joints trajectory tracking is presented. First, morphology and biomimetics knowledges of frogs (a kind of animals with excellent jumping skill) motivate us to complete a bio-inspired jumping robot framework based on frog’s motion mechanism and body structure with torsional springs as energy storage device. Then, combining system passivity and dissipation, port-Hamiltonian method is utilized to build a dynamic model for expressing the relationship of energy and force in the designed robot. Jumping process analysis of different stages is also designed for ensuring the robot to complete taking-off and landing stages successfully. Next, with the definition of extending feasible robotic joint trajectory by La Salle invariant set principle, interconnection and damping assignment passivity-based control (IDA-PBC) method is exerted to obtain a trajectory controller for realizing smoothly and stably trajectory tracking in joint space. At last, simulation results show the reasonableness of the designed framework. By comparing our method with state-feedback and sliding mode control, effectiveness of the dynamic model and trajectory controller is also verified.

In this paper, we consider a stochastic SIS epidemic model with vaccination in random switching environment. The system is formulated as a hybrid stochastic differential equation. We provide a threshold number that characterizes completely its longtime behavior. It turns out that if the threshold is negative, the number of the infected class converges to zero or the extinction happens. The rate of convergence is also obtained. In contrast, if the threshold is positive, the infection is endemic. We are able to obtain an algebraic formula for the threshold, which helps us to study some strategies for controlling the disease such as: (i) determining the minimum vaccination rate needed to keep the population from the disease and (ii) determining the strategy with minimum cost of vaccination and treatment. To illustrate the results, a number of mathematical simulations and numerical examples are also presented.

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the “angle” of the state at an event. This viewpoint allows us to analyze the inter-event times by studying the fixed points of the angle map, which represents the evolution of the “angle” of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. Following up on this, we further analyze the inter-event time behavior in the special case of threshold based event-triggering rule and we provide various conditions for convergence or non-convergence of inter-event times to a constant. We also analyze the asymptotic average inter-event time as a function of the angle of the initial state of the system. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, we consider a special case where the angle map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We illustrate the proposed results through numerical simulations.

In this paper we provide a positive answer for the C${}^0$-Closing Lemma in the context of $n$-dimensional piecewise smooth vector fields governed by the Filippov’s rules. So, given a model presenting a nontrivially recurrent point it is possible to consider a C${}^0$-close perturbation of it possessing a closed trajectory. Also, we conclude the paper proving the existence of a closed orbit around a T-singularity.

While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as the time step size. Manual tuning is especially problematic if one aims to verify that the system satisfies complicated specifications described by signal temporal logic formulas since the effect the tightness of the reachable set has on the satisfaction of the specification is often non-trivial to see for humans. We address this problem with a fully-automated verifier for linear systems, which automatically refines all parameters for reachability analysis until it can either prove or disprove that the system satisfies a signal temporal logic formula for all initial states and all uncertain inputs. Our verifier combines reachset temporal logic with dependency preservation to obtain a model checking approach whose over-approximation error converges to zero for adequately tuned parameters. While we in this work focus on linear systems for simplicity, the general concept we present can equivalently be applied for nonlinear and hybrid systems.

Event-triggered control has shown the potential for providing improved control performance at the same average sampling rate when compared to time-triggered control. While this observation motivates numerous event-triggered control schemes, proving it from a theoretical perspective has only been achieved for a limited number of settings. Inspired by existing performance analyses for the single-loop case, we provide a first fundamental performance comparison of time- and event-triggered control in a multi-agent consensus setting. For this purpose, we consider undirected connected network topologies without communication delays, a level-triggering rule for event-triggered control, and the long-term average of the quadratic deviation from consensus as a performance measure. The main finding of our analysis is that time-triggered control provably outperforms event-triggered control beyond a certain number of agents in our particular setting. We thereby provide an illustrative distributed problem setup in which event-triggered control results in a performance disadvantage when compared to time-triggered control in the case of large networks. Moreover, we derive the asymptotic order of the performance measure under both triggering schemes which gives more insights into the cost relationship for large numbers of agents. Thus, by presenting an analysis for a particular setup, this work points out that transferring an event-triggering scheme from the single-loop to the multi-agent setting can lead to a loss of the often presumed superiority of event-triggered control over time-triggered control. In particular, the design of performant decentralized event-triggering schemes can therefore pose additional challenges when compared to the analogue single-loop case.

This article presents a novel modeling and corrective control of switched asynchronous sequential machines (ASMs) with input/output submachines. In particular, the considered switched ASM is harnessed by the external switching signal that provokes arbitrary change of the mode or submachine. The existence of the external switching signal imposes unpredictable state drift opposite to model matching as well as ambiguity in determining the active submachine. We first present a state observer for state observation and identification of the active submachine. Based on the information delivered by the observer, we address the existence condition and design procedure for a corrective controller that matches the stable-state behavior of the closed-loop system to that of a reference model for every possible switching sequence. To demonstrate the validity and applicability of the proposed control scheme, we conduct hardware experiments on field-programmable gate array (FPGA) circuits for a space-borne digital system and provide convincing experimental results.