Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.     

Finite-time stability and instability of stochastic nonlinear systems

This paper presents a new definition of finite-time stability for stochastic nonlinear systems. This definition involves stability in probability and finite-time attractiveness in probability. An important Lyapunov theorem on finite-time stability for stochastic nonlinear systems is established. A theorem extending the stochastic Lyapunov theorem is also proved. Moreover, an example and a lemma are presented to illustrate the scope of extension. A useful inequality, extended from Bihari’s inequality, is derived, which plays an important role in showing the Lyapunov theorem. Finally, a Lyapunov theorem on finite-time instability is proved, which states that almost surely globally asymptotical stability is not equivalent to finite-time stability for some stochastic systems. Two simulation examples are given to illustrate the theoretical analysis.     

Local-homogeneity-based global continuous control for mechanical systems with constrained inputs: finite-time and exponential stabilisation

A global continuous control scheme for the finite-time or (local) exponential stabilisation of mechanical systems with constrained inputs is proposed. The approach is formally developed within the theoretical framework of local homogeneity. This has permitted to solve the formulated problem not only guaranteeing input saturation avoidance but also giving a wide range of design flexibility. The proposed scheme is characterised by a saturating-proportional-derivative type term with generalised saturating and locally homogeneous structure that permits multiple design choices on both aspects. The work includes a simulation implementation section where the veracity of the so-cited argument claiming that finite-time stabilisers are faster than asymptotical ones is studied. In particular, a way to carry out the design so as to, indeed, guarantee faster stabilisation through finite-time controllers (beyond their finite-time convergence) is shown.     

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.     

Geometric homogeneity with applications to finite-time stability

This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider finite-time stability of homogeneous systems. The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems.     

Finite-time observers for multi-agent systems without velocity measurements and with input saturations

This paper is devoted to the distributed finite-time observers for multi-agent systems, where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback. An effective framework through defining a class of coordinated saturation functions is introduced, under which both a first-order finite-time observer and a high-order finite-time observer are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers. With mild modifications of our control strategies, the foregoing results are then extended to the distributed finite-time containment control problem, where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders. Numerical simulations are presented to demonstrate the efficiency of our methods.     

Frequency-dependent performance of an endoreversible Carnot engine with a linear phenomenological heat-transfer law

On the basis of an endoreversible Carnot heat-engine model, the frequency-dependent performance of the engine is analyzed when the heat transfers between the working fluid and the heat reservoirs obey a linear phenomenological heat-transfer law, i.e., Q ∝ (ΔT⁻¹). The relations among average power-output, efficiency, available temperature-drop, cycle frequency and ratio of the heat-transfer times are derived. They are different from those obtained with Newton’s law. The results can provide guidance for selecting the appropriate working points of heat engines.     

Reciprocating heat-engine cycles

The performance of a generalized irreversible reciprocating heat-engine cycle model consisting of two heating branches, two cooling branches and two adiabatic branches with heat-transfer loss and friction-like term loss was analyzed using finite-time thermodynamics. The relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the efficiency of the cycle are derived. Moreover, analysis and optimization of the model were carried out in order to investigate the effect of the cycle process on the performances of the cycles using numerical examples. The results obtained herein include the performance characteristics of irreversible reciprocating Diesel, Otto, Atkinson, Brayton, Dual and Miller cycles.     

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.