Stability Analysis of Stochastic Interconnected Systems by Vector Lyapunov Function Method

Many modern control systems become gradually more complicated and, consequently, the approach to control design approaches is both difficulty and complex. Moreover, if such a complex interconnected system is subjected to non-smooth nonlinearities in the actuator, then unexpected difficulties, degradation or, even worse, instability will arise in the system performance. Therefore, a new decentralized sliding mode control (DSMC) approach for such a class of complex interconnected systems subjected to non-smooth (deadzone) nonlinearities is proposed in this paper. Based on sliding mode control (SMC) theory, the proposed DSMC laws guarantee the global reaching condition of the sliding mode in uncertain complex interconnected systems with deadzone nonlinearities, that is, they can ensure that the sliding mode is reached in finite time and with prescribed transient behavior. In the sliding mode, the investigated uncertain complex interconnected system with deadzone nonlinearities in the actuator still are insensitive to system uncertainties and external disturbances. The proposed DSMC laws can work effectively for uncertain complex interconnected systems either with or without deadzone nonlinearities in the actuator. However, this cannot be guaranteed by the traditional DSMC design for systems without input deadzone nonlinearities. Furthermore, the sliding motion can be controlled to converge within a specified exponential speed. Finally, two illustrative examples with a series of computer simulations are presented to demonstrate the effectiveness of the proposed DSMC laws.

Section: System Description and Preliminariesmentioning

confidence: 99%

Section: Exponential Stable Designmentioning

confidence: 99%

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Decentralized Sliding Mode Control for Multi‐Input Complex Interconnected Systems Subject to non‐smooth Nonlinearities

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2017

“…First, stability criteria were derived in by application of the scalar Lyapunov functions. A generalization of these criteria was proposed in where the vector Lyapunov function method was used.…”

Section: Introductionmentioning

confidence: 99%

Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Socha

2018

The problem of the exponential mean-square stability for nonlinear stochastic string hybrid system under parametric (multiplicative) Gaussian and external (additive) continuous non-Gaussian excitations is considered. The string hybrid system is treated as an infinite-dimensional family of strings (subsystems) with a switching rule that has the form of a right continuous Markov chain. It is described by infinite-dimension Ito stochastic differential equations. The excitations are assumed to be parametric Gaussian white noises and the continuous non-Gaussian processes modeled by polynomials of a Gaussian process. The nonlinear strings under external continuous non-Gaussian excitation are transformed to extended dimensional nonlinear strings with a special structure under a parametric Gaussian excitation. Using the methodology of the stability analysis of nonlinear hybrid systems with Markovian switchings the sufficient conditions of the exponential mean-square stability of nonlinear stochastic string systems under parametric Gaussian and external continuous non-Gaussian excitation with a Markovian switching are derived. The detailed calculations are given for linear systems.

Adaptive Control Scheme for Large‐Scale Interconnected Systems Described by Hammerstein Models

Elloumi

Kamoun

2017

This paper proposes an adaptive algorithm for the online control of discrete‐time large‐scale nonlinear systems, which reduces the noise effects acting on the system output (regulation problem) and allows the system output to keep track of a time‐varying trajectory (tracking problem). We consider a large‐scale nonlinear system that can be decomposed into single‐input single‐output (SISO) interconnected nonlinear subsystems with known structure variables (orders, delays) and unknown time‐varying parameters. Each interconnected subsystem is described by block‐oriented models, specifically a discrete‐time Hammerstein model. Parameter adaptation is performed using a recursive parametric estimation algorithm based on the adjustable model method and the least squares techniques. Simulation results of an interconnected petroleum process are provided to demonstrate the effectiveness of the developed control scheme.