Output feedback control of discrete‐time systems with self‐triggered controllers

This paper is concerned with the self‐triggered output feedback control for discrete‐time systems, where an updating instants scheduler is implemented to determine when the controller is updated. For both the full‐order and reduced‐order observer cases, the updating instants are determined, respectively, where only the information of the estimated state at the current updating instant is required to obtain the next updating instant. It is shown that, with the proposed self‐triggered control schemes, not only the updating frequency is significantly reduced, but also the uniform ultimate boundedness of the closed‐loop system is guaranteed. Finally, a numerical example is used to verify the effectiveness and the merits of the proposed approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Higher order direct model reference adaptive control with generic uniform ultimate boundedness

This paper proposes a new higher order model reference adaptive control (HO-MRAC) approach following direct adaptive control philosophy, which estimates unknown time-varying parameters. This approach leads to a Lyapunov based conventional MRAC update law, augmented by an observer type parameter predictor dynamics. The predictor dynamics are composed of a stable known part, a feedback of the parameter error and unknown higher order parameters, which are updated using a Lyapunov based adaptive design. So, this HO-MRAC can cope with rapidly changing parameters, due to estimation of their time derivatives. Moreover, for stability analysis, a Lyapunov based generic ultimate boundedness theorem is presented, which allows for a computation of separate bounds for each state vector partition. Furthermore, this theorem formulates the explicit specification of transient and ultimate bounds, reaching time on the ultimate bounds and a set of admissible initial conditions. Two challenging illustrative examples demonstrate the effectiveness of the proposed approach.     

An auto-pole-placement self-tuning controller†

An explicit self-tuning controller is described that incorporates closed-loop pole location as the principal design criterion for the objective function of Clarke and Gawthrop. The algorithm includes several minor extensions to improve robustness : a variable dead-time compensator to deal with unknown or time-varying delay, and a method of treating steady-state offset that avoids retaining an integrator in the loop continuously. A new technique has been developed and included in the algorithm that enables the controller to be auto-tuning in the sense that the closed-loop pole(s) and sampling period can be determined on-line so as to optimize the system set-point step response, leaving the system designer to specify only internal model orders and noise characteristics on which to initiate retuning. The resulting controller is quite robust and can easily handle unstable, non-minimum phase systems in a single-loop configuration, as is demonstrated by several simulations including a non-linear model of a fixed-bed autothermal reactor operating over such a large range that auto-tuning of the poles is a necessity.     

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness (FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities (LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control (SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t)=c (c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.      

一个生态系统的有界性和稳定性

给出了一个多食性天敌与害虫系统的有界性和稳定性的充分条件，同时还阐述了它们的生态意义。     

Path tracking of underactuated ships with general form of dynamics

This article considers the path tracking problem for underactuated ships with general form of dynamics including uncertainties. By introducing certain two polar coordinate transformations, the ship's tracking kinematics and dynamics can be transformed into certain two-inputs–two-outputs nonlinear strict-feedback form. To avoid possible singularity problem in the backstepping control design, we introduce an asymptotic modification of orientation concept. Presented tracking scheme can guarantee the uniformly ultimately boundedness of closed-loop system in terms of polar coordinates. For the convenience of comparison with previous related works, where all tracking schemes were discussed in the Cartesian frame, we carry out some case studies to investigate the conditions under which the proposed tracking method can guarantee the same stability and convergence properties of tracking errors in the Cartesian frame. Numerical simulation studies are also carried out to demonstrate the effectiveness of presented tracking scheme.     

Robust input‐output finite‐time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities

In this paper, the robust input‐output finite‐time filtering problem is addressed for a class of uncertain Markovian jump nonlinear systems with partially known transition probabilities. Here, the disturbances, uncertainties, state delay, and distributed delays are all taken into account. Both the stochastic finite‐time boundedness and the stochastic input‐output finite‐time stability are introduced to the Markovian jump nonlinear systems with partially known transition probabilities. By constructing a reasonable stochastic Lyapunov functional and using linear matrix inequality techniques, sufficient conditions are established to guarantee the filtering error systems are stochastic finite‐time bounded and stochastic input‐output finite‐time stable, respectively. Finally, 2 examples are provided to illustrate the effectiveness of the proposed methods.     

Finite-region stability and boundedness for discrete 2D Fornasini–Marchesini second models

In this paper, the concepts of finite-region stability (FRS) and finite-region boundedness (FRB) are formulated for discrete two-dimensional (2D) Fornasini–Marchesini second (FMII) models, and then the analysis methods for FRS and FRB are proposed to investigate the transient behaviour of such discrete 2D FMII models. First, by building special recursive formulas, we develop a sufficient condition which guarantees the FRS of the system under solvable linear matrix inequalities (LMIs) conditions. Next, the FRB problem is addressed for the FMII model with exogenous disturbances and the corresponding criteria and LMIs conditions are reported. Finally, we apply the proposed FRS analysis method to consider the finite-region stabilisation problem of a chemical reactor thermal process, as well as some other numerical examples, to illustrate the validity of the proposed methods.     

Gain scheduling control of nonlinear singularly perturbed time-varying systems with derivative information

In this paper, we analyse the ultimate boundedness of nonlinear singularly perturbed time-varying systems and propose a control law using gain scheduling where the slow state and the exogenous signals are used as scheduling variables. In our control scheme, we have some flexibility in selecting the slow manifold of the system. Moreover, the derivative information can be properly engaged to manipulate the size of ultimate bound in tracking error of the controlled system.     

H∞ sliding mode control of discrete switched systems with time-varying delays

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.