The Output FeedbackH∞Control Design for the Linear Stochastic System Driven by Both Brownian Motion and Poisson Jumps: A Nonlinear Matrix Inequality Approach

2012 ◽  
Vol 15 (4) ◽  
pp. 1139-1148 ◽  
Author(s):  
Xiangyun Lin ◽  
Weihai Zhang ◽  
Xiangrong Wang
Keyword(s):  
Brownian Motion ◽  
Stochastic System ◽  
Control Design ◽  
Matrix Inequality ◽  
Poisson Jumps ◽  
Linear Stochastic System ◽  
Nonlinear Matrix Inequality ◽  
Nonlinear Matrix

Design and experimental realization of a backstepping nonlinear H∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach

2017 ◽  
Vol 40 (11) ◽  
pp. 3390-3403 ◽  
Author(s):  
Subhasish Mahapatra ◽  
Bidyadhar Subudhi
Keyword(s):  
Control Algorithm ◽  
Autonomous Underwater Vehicle ◽  
Vertical Plane ◽  
Underwater Vehicle ◽  
Matrix Inequality ◽  
Parameter Uncertainties ◽  
Experimental Realization ◽  
State Dependent ◽  
Nonlinear Matrix Inequality ◽  
Nonlinear Matrix

This paper focuses on the development of a nonlinear [Formula: see text] control (NHC) algorithm for an autonomous underwater vehicle (AUV) in the vertical plane. A three-degree-of-freedom AUV depth model is developed in terms of a nonlinear affine form which is used to design the control algorithm. The depth is controlled using a backstepping technique which generates a desired pitch angle for the NHC algorithm. The nonlinear control is designed using the [Formula: see text]-gain analysis which is transformed into a Hamilton–Jacobi–Isaacs (HJI) inequality. Further, the HJI inequality is presented in terms of a nonlinear matrix inequality structure in order to find a solution for the NHC problem using the concept of convex optimization. Hence, we desire to test the convex property of the nonlinear system before the realization of the control algorithm. The robust behaviour of the NHC algorithm is realized by ensuring the performance of the proposed control algorithm in the face of model and parameter uncertainties. A comparison between the NHC algorithm and the state-dependent Riccati equation is made in order to show the efficacy of the developed control algorithm. Furthermore, an experimental study of the proposed control scheme has been pursued to analyse the effectiveness of the developed control algorithm.

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