Search

This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient-based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real-world practical problem involving a bioreactor tank model is solved using the method proposed.

Yanyan Yin,1 Li Jiang,2 Lixin Xue3 1Department of Neurological Rehabilitation, Beijing Rehabilitation Hospital, Capital Medical University, Beijing, 100144, People’s Republic of China; 2Department of Critical Care Medicine, Xuanwu Hospital, Capital Medical University, Beijing, 100053, People’s Republic of China; 3Department of General Surgery, Fuxing Hospital, Capital Medical University, Beijing, 100038, People’s Republic of ChinaCorrespondence: Li Jiang, Department of Critical Care Medicine, Xuanwu Hospital, Capital Medical University, No. 45 Changchun Street, Xicheng District, Beijing, 100053, People’s Republic of China, Tel +8613601366055, Email jianglipaper@sina.comPurpose: To determine which frailty method can better improve the predictive ability of the Surgical Apgar Score combined with American Society of Anesthesiologists physical status classification (SASA).Patients and Methods: A prospective cohort study was conducted. A total of 194 elderly patients undergoing elective abdominal surgery were included. Preoperative frailty using FRAIL questionnaire, frailty index (FI), Clinical Frailty Scale (CFS) and SASA scores was assessed. Primary outcome was in-hospital Clavien-Dindo ≥grade II complications. Multiple logistic regression was used to examine the association between frailty and complications. Receiver operating characteristic curves were used to explore the predictive ability of frailty.Results: According to the FRAIL, FI and CFS criteria, the prevalence of frailty in the study population was 43.8%, 32.5%, and 36.6%, respectively. After adjusting for all covariates, frailty was significantly associated with postoperative complications in hospital by FRAIL [odds ratio: 5.11, 95% CI: 1.41– 18.44, P = 0.013], by FI [OR: 4.25, 95% CI: 1.21– 14.90, P = 0.024] and by CFS [OR: 5.10, 95% CI: 1.52– 17.17, P = 0.008]. The area under the curve (AUC) for SASA was 0.768 (95% CI: 0.702– 0.826). Addition of frailty assessment (FRAIL, FI and CFS) inc

The Franklin Institute In this paper, a new event-trigger based probabilistic controller is designed using a scenario optimization approach for the robust stabilization of uncertain systems subject to nonlinear and unbounded uncertainties. Sufficient probabilistic stabilization conditions are derived under which the closed-loop system is e level robust probabilistic stable. Based on these conditions, the design of the gains of the event-triggered state feedback controller is formulated and solved as an optimization problem involving linear matrix inequality. The applicability of theoretical results obtained is illustrated by a numerical example.

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. This paper studies the problem of H8 filtering for a class of uncertain discrete-time periodic Markov jump systems with partly unknown and periodic transition probabilities, which is described as a polytope. By using Lyapunov function, periodic H8 filter is designed, which ensures that the periodic dynamic system is stochastically stable and satisfies a prescribed H8 performance index. A numerical example is presented to illustrate the effectiveness of the proposed theoretical results.

© 2018 IEEE. In this paper, we investigate the consensus for heterogeneous multi-agent systems. The systems are composed of second-order linear and nonlinear agents with different nonlinear terms, which makes systems more general. A valid control law for each agent is given based on the communication with their neighbors. By employing LaSalle's invariance principle and Lyapunov stability theory, sufficient condition is established to achieve the consensus under the undirected connected topologies. Finally, we give a simulation example to illustrate the validity of the theoretical method.

This paper investigates the problem of consensus for second-order multi-agent systems with switching topologies and time-delays. The switching topologies and communication time-delays are described by Markov chains. By using a model transformation approach, sufficient conditions are established under which consensus is guaranteed. A numerical example is provided to verify the effectiveness of the proposed approach.

© 2018 Elsevier B.V. This paper addresses the problem of distributed leader-following consensus for a multi-agent system with an affine nonlinear term. The communication topology we adopt is an undirected connected graph and the leader sends its information to one or more followers. To make each follower asymptotically synchronize with the leader, a nonlinear distributed control protocol is proposed. Using a Lyapunov function and a matrix theory, we establish sufficient conditions which ensure the consensus of these nonlinear multi-agent systems. Finally, a numerical simulation is provided to verify the effectiveness and usefulness of the developed method.

© 2018, ICIC International. All rights reserved. This paper investigates the problem of consensus for multi-agent systems with switching topologies and stochastic delays. The switching topologies and time-delays are governed by Markov chains. By using Lyapunov function approach, sufficient conditions are established such that consensus is achieved. A numerical example is provided to verify the effectiveness of the proposed approach.

© 2017 IEEE. This paper addresses the leader-following consensus issue for a type of nonlinear multi-agent systems with affine nonlinear term. A distributed control algorithm is constructed for each follower, and sufficient condition is obtained. The proposed control algorithm guarantees the state consensus of the multi-agent systems when the communication network among followers is an undirected and connected graph, and the leader sends its information to at least one follower. The effectiveness and usefulness of the theoretical results are illustrated by numerical simulation finally.

This paper addresses the problem of event-triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event-triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed-loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event-triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event-triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.

This paper investigates the problem of stability analysis for time-delay integral Markov jump systems with time-varying transition rates. Some free-weight matrices are addressed and sufficient conditions are established under which the system is stochastically stable. The bound of delay is larger than those in other results obtained, which guarantees that the proposed conditions are tighter. Numerical examples show the effectiveness of the method proposed.

This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markovian jumps, where the uncertainties are assumed to be norm bounded and the transition probabilities are time-varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time-varying transition probabilities inside a polytope, we establish conditions under which the closed-loop system is asymptotically stable. On the basis of these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by numerical examples including the application to a DC motor speed control example.

© 2017 ISSN 1881-803X. In this paper, the issue of stochastic stability and stabilization of periodic Markov jump systems with uncertain transition probabilities and parameters is investigated. The partially unknown transition probability matrix is described as a polytope with uncertain vertices. By constructing a Lyapunov function, sufficient conditions are established under which the system is stochastically stable. Numerical example is given to show the effectiveness of the method proposed.

© 2017 Technical Committee on Control Theory, CAA. The problem of robust fault detection (RFD) for nonlinear singular Markovian jump systems (NSMJLSs) with partly unknown transition probabilities is investigated in the paper. The RFD observer (RFDO) system and the dynamics of error generator are constructed. By Lyapunov function approach, the proposed method reduces the conservatism compared with the existing ones. Moreover, the performance index is proposed to minimize the influence of the unknown disturbances. Sufficient conditions on the existence of RFDO are established and given in terms of linear matrix inequalities(LMIs). Finally, a simulation example is given to illustrate that the proposed RFDO can detect the faults correctly and shortly after the occurrence.

The problem of system identification for nonlinear system is studied in this paper by using EM algorithm, and a stochastic scheduling parameter which follows a Markov jump process is considered. First, multi-model approach is addressed to describe the nonlinear process, where each linear parameter system is represented by an auto regressive exogenous model, and then, EM algorithm is used to do estimation with the help of stochastic scheduling parameter. A simulation example is given to illustrate the effectiveness of the approach proposed.

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed-loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.

© 2016 ISSN.A robust fault detection observer (RFDO) is designed to solve the robust fault detection problem of the nonlinear Markovian jump systems (NMJSs) with partly unknown transition probabilities. With the method of T-S fuzzy linearization, the original NMJSs are described as a set of local linear models. On this basis, free-connection weighting matrices are introduced to RFDO. A series of linear matrix inequalities which ensure the stochastic asymptotic stability of the system are obtained by using the constructed Lyapunov function. Furthermore, the design problem is formulated as a two-objective optimization algorithm. A simulation example is given to show that the designed RFDO can not only detect the fault sensitively, but have the robustness to unknown disturbances.

This paper focuses on delay-dependent robust fault detection (RFD) problem for continuous-time Markovian jump systems (MJSs) with partly unknown transition rates and time-varying delay. Free-connection weighting matrices are firstly addressed to robust fault detection filter design, which reduce the conservatism caused by fixed-connection weighting matrices. By considering Lyapunov stability theory, new delay-dependent stochastic stability criteria are eatablished in terms of linear matrix inequalities (LMIs). Based on this, sufficient conditions are given and proved to guarantee the existence of the robust fault detection filter system. Furthermore, an optimization design approach is derived with an improved cone complementarity linearization algorithm. Finally, a simulation example is given to show that the designed robust fault detection filter can detect the faults sensitively, and also respond robustly to unknown disturbances.

Based on Gaussian Process (GP), a wavelength selection algorithm named Synergy Interval Gaussian Process (siGP) model is proposed in this paper by using near infrared spectroscopy technology. Full spectrum is divided into a series of unique and equal spacing intervals, before selecting optimal several intervals to establish GP model. Due to the GP model with nonlinear processing ability, the method reduces the disadvantages of nonlinear factor. Taking the near infrared spectrum data of moisture content and pH in solid-state fermentation of monascus as performance verification object of this new algorithm, the prediction correlation coefficient (R p ) of moisture content and pH are 0.956 4 and 0.977 3, respectively. The root mean square errors for prediction set (RMSEP) are 0.012 7 and 0.161 0, respectively. Data points participating in modeling decrease respectively from the original 1 500 to 225 and 375. In the prediction for independent samples, it shows good accuracy. Comparing with traditional synergy interval partial least squares (siPLS) algorithm, the results show that the siGP achieves the best prediction result. The prediction correlation coefficient of moisture content and pH in new algorithm has increased respectively by 3.37% and 3.51% under the model of Gaussian Process, with increases of 29.4% and 34.8% in the root mean square errors for prediction set. This study shows that the combination of siGP and GP model can select wavelength effectively and improves the prediction accuracy of the NIR model. This method is reference for realizing the online detection and optimization control.

© 2016 IEEE.This paper addresses the problem of robust stabilization for uncertain systems subject to input saturation and nonhomogeneous Markov jumps. The uncertainties are assumed to be norm bounded and the transition probabilities are time-varying and unknown. By expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws and the time-varying transition probabilities inside a polytope, we establish conditions under which the closed-loop system is asymptotically stable. Based on these conditions, the problem of designing the state feedback gains for achieving fast transience response with a guaranteed size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality (LMI) constraints. The results are then illustrated by a numerical example.

© 2016 TCCT.The problem of robust fault detection (RFD) for discrete-time Markovian jump linear systems (MJLSs) with partly unknown transition probabilities is investigated in the paper. The RFD observer (RFDO) system and the dynamics of error generator are constructed. By introducing some free-weighting matrices, the proposed method leads to less conservatism compared with the existing ones. Moreover, the H8 performance index is proposed to minimize the influence of the unknown disturbances. Sufficient conditions on the existence of RFDO are established and given in terms of LMIs. Finally, a simulation example is given to illustrate that the proposed RFDO can detect the faults correctly and shortly after the occurrence.

© 2016 IEEE.The problem of robust fault detection (RFD) for nonlinear discrete-time Markovian jump systems (MJSs) with partly unknown transition probabilities is investigated in the paper. With the method of T-S fuzzy linearization, the original systems are described as a set of local linear models. The RFD observer (RFDO) system and the dynamics of error generator are constructed. By introducing some free-weighting matrices, the proposed method leads to less conservatism compared with the existing ones. Moreover, the H8 performance index is proposed to minimize the influence of the unknown disturbances. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov-krasovskii function, then in the terms of linear matrix inequalities techniques, the sufficient conditions on the existence of RFDO are presented and proved. Finally, A simulation example is given to illustrate that the proposed RFDO can detect the faults correctly and shortly after the occurrence.

© 2015 IEEE.The problem of CSTR system identification is studied with a stochastic scheduling parameter. Multi-model approach is used to describe non-linear process, in which, each linear parameter system is represented by a ARX model. An expectation maximization (EM) algorithm is used for the identification of parameters which are unknown. Furthermore, scheduling variable corresponds to the operating conditions of the nonlinear process is considered as a stochastic parameter, which follows a Markov jump process.

© 2015 IEEE.This paper studies the problem of disturbance rejection controller design for a class of nonhomogeneous Markov jump systems, in which the nonhomogeneous Markov jump process is described as a polytope set. To compensate the disturbance, a disturbance observer is considered, and based on which the state-feedback control law is designed. Under the designed controller, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically stable and a prescribed H8 performance index is satisfied. Finally, a simulation example is given to illustrate the effectiveness of the developed techniques proposed.

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.In this paper, a robust fault detection and diagnosis (FDD) method is proposed for multiple-model systems with modeling uncertainties. A compensation step is introduced to modify the mixed states and their variances obtained through the interacting multiple model (IMM) approximation and to solve the uncertainty problem. The degree of compensation is governed by a modification parameter determined by the orthogonality principle, which means that the estimation error calculated in the sub-filter using the true system models should be orthogonal to the residual error vector. To avoid over compensation in the unmatched models, a minimization procedure is used to derive the overall modification parameter. When the modification parameter is equal to one, the proposed method reduces to the IMM algorithm. An experiment is conducted through the ball and tube system to demonstrate the effectiveness of the proposed method.

© 2015 Technical Committee on Control Theory, Chinese Association of Automation.This study is concerned with model predictive control (MPC) for a class of discrete-time Markov jump system with disturbances. A synthesis method to design robust model predictive controller is proposed by considering H2/H8 performance index, a serious of sufficient conditions are obtained which guaranteeing the stability of system, meanwhile satisfying the constraints. Finally, a numerical example is presented to illustrate the effectiveness of the developed results.

A linear full-order robust fault detection observer is designed to solve the robust fault detection problem of Markovian jump systems with partly unknown transition probabilities. Free-connection weighting matrices are introduced to robust fault detection observer design, which reduces the conservatism caused by fixed-connection weighting matrices. A series of linear matrix inequalities (LMIs) which ensure the system's stochastic asymptotic stability are obtained by using the constructed Lyapunov function. Based on that, a sufficient condition for the existence of the robust fault detection observer system is given and proved. Furthermore, an optimization design approach is also derived. A simulation example is given to show that the designed robust fault detection observer can not only detect the faults quickly and sensitively, but also respond robustly to unknown disturbances.

In this paper, we propose a method for designing continuous gain-scheduled H1 controller for a class of stochastic nonlinear systems with unknown information. The stochastic nonlinear system under study is governed by a finite-state Markov process, but with partially known jump rate from one mode to another. Initially, gradient linearization procedure is applied to describe such nonlinear systems by several model-based linear systems. Next, H8 controllers are established for each linear model in terms of linear matrix inequalities. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear controllers for the whole nonlinear jump system. A numerical example is given to illustrate the effectiveness of the developed techniques. © ICIC International 2014.

This paper is concerned with the optimal linear estimation for a class of direct-time Markov jump systems with missing observations. An observer-based approach of fault detection and isolation (FDI) is investigated as a detection mechanic of fault case. For systems with known information, a conditional prediction of observations is applied and fault observations are replaced and isolated; then, an FDI linear minimum mean square error estimation (LMMSE) can be developed by comprehensive utilizing of the correct information offered by systems. A recursive equation of filtering based on the geometric arguments can be obtained. Meanwhile, a stability of the state estimator will be guaranteed under appropriate assumption. © 2014 Qing Sun et al.

A simplified model predictive control algorithm is designed for discrete-time Markov jump systems with mixed uncertainties. The mixed uncertainties include model polytope uncertainty and partly unknown transition probability. The simplified algorithm involves finite steps. Firstly, in the previous steps, a simplified mode-dependent predictive controller is presented to drive the state to the neighbor area around the origin. Then the trajectory of states is driven as expected to the origin by the final-step mode-independent predictive controller. The computational burden is dramatically cut down and thus it costs less time but has the acceptable dynamic performance. Furthermore, the polyhedron invariant set is utilized to enlarge the initial feasible area. The numerical example is provided to illustrate the efficiency of the developed results. © 2014 Yanyan Yin et al.

This paper studies the problem of robust H8 controller design for a class of uncertain Markov jump systems with time-varying transition probabilities, which follows nonhomogeneous jump processes. The time varying transition probability matrix is described as a polytope set. By Lyapunov function approach, under the designed controller, a sufficient condition is presented to ensure that the resulting closed-loop system is stochastically stable and that a prescribed H8 performance index is satisfied. Finally, an application of a DC motor device is addressed to demonstrate the effectiveness of developed techniques. © 2014 The Franklin Institute.

In this paper, a robust H8 controller is designed for saturated Markov jump systems with uncertainties and time varying transition probabilities. The time-varying transition probability uncertainty is described as a polytope set. Stochastic stability is analyzed for the underlying systems by Lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed-loop system is stochastically stable and a prescribed H8 performance is also achieved. Furthermore, the attraction domain of this Markov jump system is estimated and evaluated. A simulation example is given to show the effectiveness of the developed techniques. © 2013 Elsevier Inc. All rights reserved.

In this paper, an observer-based H8 controller is designed for a class of extended Markov jump systems subject to time-delay and actuator saturation nonlinearity. Gradient linearization procedure is employed to describe such nonlinear systems by several linear Markov jump systems. Next, a mode-dependent Lyapunov function is constructed for these linear systems, and a sufficient condition is derived to make them stochastically stable, and then, a continuous gain-scheduled approach is applied to design a continuous nonlinear observer-based controller on the entire extended nonlinear jump system. A simulation example is given to illustrate the effectiveness of developed techniques. © 2013 The Franklin Institute.

In this article, we propose a method for designing continuous gain-scheduled robust H 8 controller for a class of stochastic time-varying neutral systems subject to time-varying delay and actuator saturation. Initially, at different selected time points, one can obtain a series of time-constant neutral system models with Markov jumping parameter. Subsequently, H 8 controller is designed for each constant stochastic neutral system which guarantees exponential stochastic stabilisation of the system. Lastly, continuous gain-scheduled controller design method is employed, and an entire time-varying controller is designed for the whole working region. Simulation example is given to illustrate the effectiveness of developed techniques. © 2013 Taylor and Francis Group, LLC.

The problem of constrained model predictive control on a class of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficient matrices for the time variant system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic system, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon, stability of the system is guaranteed by searching a state feedback control law. Finally, constraints on both inputs and outputs are considered for such system and predictive controller is designed in terms of linear matrix inequality. Simulation example shows the validity of this method. © ISSN 1349-4198.

In this paper, we propose a method for designing continuous gain-scheduled worst-case controller for a class of stochastic nonlinear systems under actuator saturation and unknown information. The stochastic nonlinear system under study is governed by a finite-state Markov process, but with partially known jump rate from one mode to another. Initially, a gradient linearization procedure is applied to describe such nonlinear systems by several model-based linear systems. Next, by investigating a convex hull set, the actuator saturation is transferred into several linear controllers. Moreover, worst-case controllers are established for each linear model in terms of linear matrix inequalities. Finally, a continuous gain-scheduled approach is employed to design continuous nonlinear controllers for the whole nonlinear jump system. A numerical example is given to illustrate the effectiveness of the developed techniques. © 2012 Springer Science+Business Media, LLC.

In this paper, we propose a method for designing continuous gain-scheduled robust H 8 observer on a class of extended stochastic nonlinear systems subject to time delay and actuator saturation. Initially, gradient linearization procedure is applied to describe such extended nonlinear systems into several model-based linear systems. Next, a robust linear H 8 observer is designed to such linear stochastic models. Subsequently, a convex hull set is investigated and sufficient condition is derived in terms of feedback observer to determine whether a given initial condition belongs to an ellipsoid invariant set. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear observers on the entire extended nonlinear jump system. A simulation example is given to illustrate the effectiveness of developed techniques. © 2012 AACC American Automatic Control Council).

The problem of receding horizon predictive control of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of linear parameter varying system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficients matrices for the time variable system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic convex polyhedron linear parameter varying systems, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon, stability of the system is guaranteed by searching a state feedback control law. Finally, receding horizon predictive controller is designed in terms of linear matrix inequality for such system. Simulation example shows the validity of this method. © 2012 IEEE.

In this paper, global exponential stochastic stability based continuous gain-scheduled robust L-two-L-infinity filtering problem is studied for a class of stochastic neutral systems subject to time-varying parameters. First, the stochastic time-varying neutral systems are described by a series of stochastic time-constant systems at some selected time points, then based on stochastic Lyapunov-Krasovskii functional approach, a new globally exponentially stochastically stabilizable criterion is derived for each of the jumping system by means of linear matrix inequalities. Subsequently, L-two-L-infinity filtering systems are designed for such linear jump systems. Finally, continuous gain-scheduled approach is employed to design time-varying filter systems for the whole working region. A simulation example shows the effectiveness and potential of the developed techniques. © 2012 South China University of Technology, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

In this paper, the problem of continuous gain-scheduled fault detection (FD) is studied for a class of stochastic nonlinear systems which possesses partially known jump rates. Initially, by using gradient linearization approach, the nonlinear stochastic system is described by a series of linear jump models at some selected working points. Subsequently, observer-based residual generator is constructed for each jump linear system. Then, a new observer-design method is proposed for each re-constructed system to design H8 observers that minimize the influences of the disturbances, and to formulate a new performance index that increase the sensitivity to faults. Finally, continuous gain-scheduled approach is employed to design continuous FD observers on the whole nonlinear stochastic system. Simulation example is given to show the effectiveness and potential of the developed techniques. © 2011 Elsevier Ltd. All rights reserved.

In this paper, we propose a method for designing continuous gain scheduled H-infinity observer for uncertain nonlinear continuous stirred-tank reactor system subject to time-delay and actuator saturation. Initially, gradient linearization procedure is applied to describe such nonlinear system into several linear systems. Next, a convex hull set is investigated in order to transform the actuator constraints into several linear constraints, and then, a set of H-infinity observers is designed for these linear models, which guarantees the system states belong to an ellipsoid invariant set. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear observer on the entire uncertain nonlinear system. A simulation example is given to illustrate the effectiveness of developed techniques. © 2012.

This paper studies the problem of continuous gain-scheduled PI tracking control on a class of stochastic nonlinear systems subject to partially known jump probabilities and time-varying delays. First, gradient linearization procedure is used to construct model-based linear stochastic systems in the vicinity of selected operating states. Next, based on stochastic Lyapunov stabilization analysis, sufficient conditions for the existence of a PI tracking control are established for each linear model in terms of linear matrix inequalities. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear PI tracking controllers on the entire nonlinear jump system. Simulation example is given to illustrate the effectiveness of the developed design techniques. © 2011 The Franklin Institute © 2011 Published by Elsevier Ltd. on behalf of The Franklin Institute.

In this paper, an observer-based finite-time continuous gain-scheduled control is designed for a class of stochastic bioreactor systems with partially known jump rates. By using gradient linearization approach, the nonlinear stochastic systems are described by a series of linear jump models at some selected working points, then based on stochastic Lyapunov-Krasovskii functional approach, a new robust stochastic finite-time stabilizable criterion is derived to ensure robust finite-time stabilization of the each jump linear system by means of linear matrix inequalities. This method is then extended to provide observer-based finite-time state feedback H8 controllers for such linear jump systems. Lastly, continuous gain-scheduled approach is employed to design observer-based continuous H8 controllers for the whole bioreactor jump systems. Simulation examples show the effectiveness and potential of the developed techniques. © 2010 Springer Science+Business Media, LLC.

This paper studies the problem of continuous gain-scheduled robust fault detection (RFD) on a class of time-delay stochastic nonlinear systems with partially known jump rates. By means of gradient linearization procedure, stochastic linear models and filter-based residual signal generators are constructed in the vicinity of selected operating states. Furthermore, in order to guarantee the sensitivity to faults and robustness against unknown inputs, an RFD filter (RFDF) is designed for such linear models by first designing H 8 filters that minimize the influences of the disturbances and modeling uncertainties and then a new performance index that increases the sensitivity to faults. Subsequently, a sufficient condition on the existence of RFDF is established in terms of linear matrix inequality techniques. Finally, a continuous gain-scheduled approach is employed to design continuous RFDFs on the entire nonlinear jump system. A simulation example is given to illustrate that the proposed RFDF can detect the faults correctly and shortly after the occurrences. © 2011 IEEE.