Adaptive Control for Stochastic Switched Nonlower Triangular Nonlinear Systems and Its Application to a One-Link Manipulator

Summary This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous L2 bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and L2 gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

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“…Example Consider the following nonlinear one‐link flexible robot:

\begin{matrix} lefttrue \\ {\overset{x}{true}}_{m} (t) & = x_{italicwm} (t), \\ {\overset{x}{true}}_{italicwm} (t) & = \frac{k}{J_{m}} x_{L} (t) - \frac{k}{J_{m}} x_{m} (t) - \frac{B}{J_{m}} x_{italicwm} (t) + \frac{K_{a}}{J_{m}} {scriptN}_{italicsat} (u (t)), \\ {\overset{x}{true}}_{L} (t) & = x_{italicwL} (t), \\ {\overset{x}{true}}_{italicwL} (t) & = - \frac{k}{J_{L}} x_{L} (t) + \frac{k}{J_{L}} x_{m} (t) - \frac{italicMgL}{J_{L}} \sin (x_{L} (t)), \end{matrix}

where x m ( t ) is the angular position of the motor rotor, x L ( t ) represents the angular position of the link,

{\dot{x}}_{m} ((), t)

symbolizes the angular velocity of the motor rotor, and

{\dot{x}}_{L} ((), t)

is the angular velocity of the link. J m denotes the inertia of the motor rotor, and J L signifies the inertia of the link.…”

Section: Simulation Resultsmentioning

confidence: 99%

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Hussain

Rehan

Ahn

et al. 2019

Intl J Robust & Nonlinear

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“…On another research frontier, with the rapid technological developments in computer science, communication, and electronics, it is necessary to investigate the RMPC problem for networked control systems . In networked control systems, components such as sensors and controllers are connected to networks subject to a limited bandwidth . In such a case, data collision and network congestion might occur during data transmission via a shared communication network.…”

Section: Introductionmentioning

confidence: 99%

“…[18][19][20][21][22] In networked control systems, components such as sensors and controllers are connected to networks subject to a limited bandwidth. [23][24][25][26][27][28] In such a case, data collision and network congestion might occur during data transmission via a shared communication network. In order to avoid these unexpected network-induced phenomena, some communication protocols such as the round-robin 29 protocol, the try-once-discard (TOD) protocol, and the stochastic communication protocol, [30][31][32][33] have been increasingly introduced to orchestrate the date transmission order, where only a subset of components obtaining the privilege has an access to the shared network.…”

Section: Introductionmentioning

confidence: 99%

Resilient RMPC for polytopic uncertain systems under TOD protocol: A switched system approach

Zhu

Song

Ding

2018

Intl J Robust & Nonlinear

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Summary This paper addresses the resilient robust model predictive control (RMPC) problem for a class of polytopic uncertain systems under the try‐once‐discard (TOD) protocol. At each transmission instant, only one sensor node obtains the privilege to access the shared communication network in order to prevent the data from collision. The measurements transmission order of the sensor nodes is orchestrated, and a switched system is constructed according to the underlying TOD protocol. The aim of this paper is to design a set of desired resilient dynamic output feedback controllers in the framework RMPC such that the switched system with the underlying TOD protocol is exponentially stable. By taking the influence of the TOD protocol into account, sufficient conditions are provided to guarantee the recursive feasibility of the RMPC strategy and the stability of the established closed‐loop system in terms of the average dwell time method. Moreover, the effective resilient controllers in RMPC framework are derived by solving an online constrained optimization problem. Finally, a network‐based direct current motor example is utilized to illustrate the effectiveness of the proposed model predictive control strategy.

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“…Owing to such complicated behaviors and due to the complex nature of the switched systems, the problem of control and stabilization of switched systems has become as an interesting research topic in the last decades. Accordingly, many remarkable research studies have been dedicated to the stability synthesis and control performance of switched systems –…”

Section: Introductionmentioning

confidence: 99%

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

Aghababa

2018

Intl J Robust & Nonlinear

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Summary In this study, the problem of finite‐time practical control of a class of nonlinear switched systems in the presence of input nonlinearities is investigated. The subsystems of the switched system are considered as complex nonlinear systems with a cascade structure. Each subsystem is fluctuated by lumped uncertainties. Moreover, some parts of the system's dynamics are considered to be unknown in advance. This paper sets no restrictive assumption on the switching logic of the system. Therefore, the aim is to propose a controller to work under any arbitrary switching signals. After providing a smooth sliding manifold, a simple adaptive control input is developed such that the system trajectories approach the prescribed sliding mode dynamics in finite‐time sense. The adopted control signal does not use the upper bounds of the lumped uncertainties, and it is robust against unknown nonlinear parts of the subsystems. It is proved that the origin is the (practical) finite‐time stable equilibrium point of the overall closed‐loop system. Subsequently, the proposed control rule is modified to handle the same switched system with no input nonlinearities. Computer simulations via 2 chaotic electric direct current machines demonstrate the robust performance of the derived variable structure control algorithm against system fluctuations and nonlinear inputs.

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Adaptive Control for Stochastic Switched Nonlower Triangular Nonlinear Systems and Its Application to a One-Link Manipulator

Cited by 152 publications

References 57 publications

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Resilient RMPC for polytopic uncertain systems under TOD protocol: A switched system approach

Stabilization of a class of cascade nonlinear switched systems with application to chaotic systems

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