Adaptive asymptotic stabilization of switched parametric strict‐feedback systems with switched control

This paper is concerned with the problem of adaptive stabilization for a class of switched linear‐parametric nonlinear systems under arbitrary switching. The traditional adaptive backstepping control is successfully extended to switched systems from nonswitched ones where the asymptotic regulation of system state is not destroyed due to rapid or abrupt changes of switching parameters. A new switched adaptive controller is designed by exploiting a common high‐order Lyapunov function with a σ‐modification mechanism, which can reflect sufficiently the changes of plant by designing different adaptive laws and control laws for different subsystems. An explicit formula for constructing a continuous and piecewise virtual control function is given to remove the restriction where some bound functions have to be constructed blindly by designers in the existing results, which may be somewhat too strict to be applied. A numerical example is provided to validate the proposed approach.     

Adaptive control for a class of high‐order switched nonlinearly parameterized systems

The problem of adaptive stabilization is studied for a class of high‐order switched nonlinearly parameterized systems; none of subsystems is assumed to be adaptively stabilizable. By exploiting the multiple Lyapunov functions method and the adding a power integrator technique, a switched adaptive control technique is set up. Meanwhile, in order to reduce the conservativeness caused by adoption of a common update law for all subsystems, different update laws of individual subsystems are designed. Also, we simultaneously construct a switching law and adaptive state‐feedback controllers of subsystems to achieve global stability in the sense of Lyapunov of the closed‐loop system and global asymptotic regulation of the system states. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

Output feedback passification of saturated switched systems

This paper addresses the passivity and feedback passification of the saturated switched systems. A switching law and output feedback controllers are designed such that the corresponding closed-loop systems are with the passivity and disturbance tolerance capacity. The switching law satisfies a maximal dwell time (DT) condition, which avoids too high switching frequency. More importantly, under the switching law, the storage function is allowed to be increased during the DT and then decreased due to the drop of itself at the mixed time/state-dependent switching instants. This releases the performance requirement of existing results where the storage function must be non-increasing all the time. Finally, the existence of the upper bound of DT and output feedback controllers is guaranteed by solving some linear matrix inequalities. Two examples are given to show the effectiveness of the proposed method.     

切换自治系统的动态输出反馈镇定

本文研究离散时间切换线性自治系统的输出反馈镇定问题. 在切换系统可观测的假设下, 设计具有多线性 时变增益的动态观测器, 实现有限时间状态估计. 在此基础上, 设计多路径动态输出反馈切换策略, 实现闭环系统指 数收敛.     

Adaptive finite‐time stabilization of nonlinearly parameterized systems subject to mismatching disturbances

This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme.     

一类非线性参数化系统的自适应鲁棒控制

针对一类含有非线性参数化不确定项的非线性系统,本文提出了一种基于浸入和不变流形的自适应鲁棒控制器.由于浸入和不变流形方法将调节函数引入到参数估计律的设计中,增加了控制器设计自由度,保证对系统中未知参数的渐近估计,使得设计出的自适应鲁棒控制器在克服非线性参数化不确定项和外界扰动影响的同时,保证了良好的动态和稳态性能.最后通过仿真实例验证了所提算法的有效性.     

Passivity and feedback passification of switched discrete-time linear systems

This paper focuses on the passivity analysis and feedback passification for switched discrete-time linear systems using multiple storage functions under a certain switching law. Controllers and switching laws are designed based on complete and partial state measurements, respectively. Conditions for strict passivity of a switched discrete-time system are obtained without the requirement of strict passivity of subsystems. In the case of partial state measurements, dynamic output feedback controllers for subsystems are designed, and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed-loop switched system. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical results.     

Incremental passivity and output regulation for switched nonlinear systems

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.     

Differential Riccati equation‐based adaptive stabilization for switched linear systems

In this paper, a novel adaptive control design is proposed to stabilize a class of switched linear systems with parametric uncertainties and disturbances. In particular, a family of differential Riccati equations that holds for the finite switching intervals are established, of which the closed‐form solutions are exploited to develop the Lyapunov function for the closed‐loop system. This Lyapunov function is imposed to be decreasing at and between two arbitrary switching instants by solving a group of matrix inequalities, based on which the adaptive controllers for switched linear system with and without disturbances are proposed, respectively. In the nondisturbed setting, asymptotic stability of the adaptive switched linear system is achieved, while the system is bounded in a mean square sense in the disturbed setting. A numerical example of flight control for F4E fighter aircraft is used to illustrate the proposed adaptive control methodology.     

Finite-time stabilization of output-constrained planar switched systems via output feedback

Finite-time stabilization (FTS) problem of output-constrained planar switched systems via output feedback is investigated in this paper. State feedback control laws are constructed in a systematic way by combining the revamped adding a power integrator technique (APIT) with the elaborately designed logarithm-type barrier Lyapunov function (BLF). By merging the constructed variable-gain switched observers, finite-time output-feedback stabilization, then, is achieved with the output constraint meets too. At the end, simulations are presented to show the effectiveness of the proposed method.     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

Adaptive finite‐time stabilization of a class of quantized nonlinearly parameterized systems

This paper deals with the problem of adaptive control of a class of strict‐feedback nonlinearly parameterized systems with quantized input signal. A hysteretic type of quantizer is used to avoid chattering. By using a power integrator technique, a new controller is designed to ensure the global finite‐time stability of the nonlinear system. Finally, two simulation examples are given to demonstrate the effectiveness of our design method. Copyright © 2017 John Wiley & Sons, Ltd.     

Passivity and output feedback passification of switched continuous-time systems with a dwell time constraint

This paper is concerned with the passivity analysis and output feedback passification for a class of switched continuous-time systems. A switching law and control units are designed to guarantee the passivity of closed-loop switched systems. Different from the exist results in state-dependent switching framework, we construct a novel switching law such that the switched system obeys a minimal dwell time between any two consecutive switchings. This avoids the possible arbitrarily fast switching caused by state-dependent switching law. Moreover, the switching law uses only the lower bound of the dwell time and partial measurable states of the closed-loop system, which is applicable in output feedback framework. Using multiple discretized storage functions, the controllers working on different time intervals are obtained, which ensure the closed-loop system is passive under the switching law. Finally, two examples are provided to illustrate the effectiveness of the developed results.     

Adaptive state feedback control for switched stochastic high‐order nonlinear systems under arbitrary switchings

This paper studies the adaptive state feedback control for a class of switched time‐varying stochastic high‐order nonlinear systems under arbitrary switchings. Based on the common Lyapunov function and using the inductive method, virtual controllers are designed step by step and the form of the input signal of the system is constructed at the last. The unknown parameters are addressed by the tuning function method. In particular, both the designed state feedback controller and the adaptive law are independent of switching signals. Based on the designed controller, the boundness of the state variables can be guaranteed in probability. Furthermore, without considering the Wiener process or with the known parameter in the assumption, adaptive finite‐time stabilization and finite‐time stabilization in probability can be obtained, respectively. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

Adaptive disturbance rejection for strict‐feedback switched nonlinear systems using multiple Lyapunov functions

This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict‐feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non‐switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Quadratic stabilization of switched systems

We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched system is quadratically stabilizable via switched state feedback for all uncertainties.     

Positive stabilization for switched linear systems under asynchronous switching

This paper is concerned with the positive stabilization for a class of switched systems under asynchronous switching signals. Because it inevitably takes some time to identify the active subsystem in the real systems and activate the corresponding controller, the switching of controllers lags behind that of subsystems, which arises the problem of the asynchronous switching. By analyzing the solution of dynamic systems, the mode‐dependent controllers are designed to guarantee the positivity and exponential stability for the resultant closed‐loop switched linear systems under asynchronous switching signals in continuous‐time and discrete‐time cases, respectively. Sufficient conditions for the existence of admissible state‐feedback controllers are developed, and the corresponding switching signals are designed. Furthermore, a synchronous switching phenomenon is discussed as a special case. Finally, numerical examples are given to illustrate the effectiveness of the results. Copyright © 2015 John Wiley & Sons, Ltd.     

An algorithm for the robust exponential stabilization of a class of switched systems

In this paper, we consider continuous‐time switched systems whose subsystems are linear, or, more generally, homogeneous of degree one. For that class of systems, we present a control algorithm that under certain conditions generates switching signals that globally exponentially stabilizes the switched system, even in the case in which there are model uncertainties and/or measurement errors, provided that the bounds of that uncertainties and errors depend linearly on the norm of the state of the system and are small enough in a suitable sense. We also show that in the case in which the measurement errors and the model uncertainties are bounded, the algorithm globally exponentially stabilizes the system in a practical sense, with a final error which depends linearly on the bounds of both the model uncertainties and the measurement errors. In other words, the closed‐loop system is exponentially input‐to‐state‐stable if one considers the perturbations and output measurements bounds as inputs. For switched linear systems, under mild observability conditions, we design an observer whose state‐estimation drives the control algorithm to exponentially stabilize the system in absence of perturbations and to stabilize it in an ultimately bounded way when the perturbations and the output measurement errors are bounded. Finally, we illustrate the behavior of the algorithm by means of simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

关于自适应非线性镇定的某些结果

不确定非线性系统的反馈控制一直是控制科学的中心问题之一,迄今已经取得很大进展。然而,目前现有大部分工作所研究的反馈控制规律,或是连续时间形式的,或是采样反馈形式但需要采样频率充分快,或是离散时间反馈形式,但需要被控离散时间系统的非线性函数增长速度不超过线性。要消除或减弱这些约束条件,一般来讲是相当困难的。这就促使我们探究反馈机制的最大能力和根本局限。尽管近年来在这个方向有许多重要进展,但仍有许多非平凡的重要问题有待研究。例如,在反馈通道中有时滞情形,或者系统状态是高维的情形。在本文中,我们将探索两类比较特殊的离散时间不确定非线性动力系统的控制问题,给出关于全局自适应反馈镇定的某些初步结果。