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In this article, an extended state observer‐based finite‐region control scheme is presented for two‐dimensional Markov jump systems with unknown mismatched disturbances. The mathematical model of the two‐dimensional Markov jump systems is built on the well‐known Roesser model. By establishing special recursive formulas and utilizing the 2‐D Lyapunov function theory, sufficient conditions are obtained, which prove that the resultant system is finite‐region bounded, if some linear matrix inequalities are achieved. Then, we provide an algorithm to solve the extended state observer‐based controller gains. With the proposed control scheme, the external disturbances can be actively rejected from the system outputs. To conclude, a numerical example based on the Darboux equation is provided to demonstrate the validity and effectiveness of the devised control scheme. [ABSTRACT FROM AUTHOR]

Summary: Joint estimation of states and time‐varying parameters of linear stochastic systems is of practical importance for fault diagnosis and fault tolerant control. The known fact is that measurements have outliers. They can significantly degrade the properties of linearly recursive algorithms, which are designed to work in presence of Gaussian noises. This article proposes two kinds of strategies for joint parameter‐state robust estimation of linear stochastic models in presence of all possible faults and non‐Gaussian noises. In the form of Theorem, joint robust algorithm for systems with sensor and component faults, as well as the algorithm for systems with parameter faults are proposed. Because of their good features in robust filtering, Masreliez‐Martin filter represents a cornerstone for realization of the proposed robust algorithms for joint state‐parameter estimation. The good features of proposed robust estimation algorithms, in relation to algorithms based on other widely‐used filters, are illustrated by simulation results. On the other side, intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which a lot of important details cannot be included in the model. Also, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the abovementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The good practical values of the proposed robust joint algorithm to identification of the pneumatic cylinder are illustrated by experimental results. [ABSTRACT FROM AUTHOR]

A new online iterative algorithm for solving the H ∞ control problem of continuous-time Markovian jumping linear systems is developed. For comparison, an available offline iterative algorithm for converging to the solution of the H ∞ control problem is firstly proposed. Based on the offline iterative algorithm and a new online decoupling technique named subsystems transformation method, a set of linear subsystems, which implementation in parallel, are obtained. By means of the adaptive dynamic programming technique, the two-player zero-sum game with the coupled game algebraic Riccati equation is solved online thereafter. The convergence of the novel policy iteration algorithm is also established. At last, simulation results have illustrated the effectiveness and applicability of these two methods. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An online adaptive optimal control problem for a class of nonlinear Markov jump systems (MJSs) is studied. It is worth noting that the dynamic information of MJSs is partially unknown. Applying the neural network linear differential inclusion techniques, the nonlinear terms in MJSs are approximately converted to linear forms. By using subsystem transformation schemes, we can transfer the nonlinear MJSs to N new coupled linear subsystems. Then a new online policy iteration algorithm is put forward to obtain the adaptive optimal controller. Some theorems are given afterward to ensure the convergence of the new algorithm. At last, a simulation example is provided to verify the applicability of the algorithm. [ABSTRACT FROM AUTHOR]