Mode Transition Rate Research Articles

Fuzzy-model-based tracking control of Markov jump nonlinear systems with incomplete mode information

This paper considers the tracking control problem for nonlinear Markov jump systems based on T–S fuzzy model approach with incomplete mode information. It is assumed that the mode transition rate matrix is not a priori knowledge and only partial information is available. Moreover, the mode where the system stays when operating is not fully accessible to the designed controller. In this incomplete mode information scenario, a hidden Markov model based mechanism is modified to simulate the mode deficiency mapping. The incomplete transition rate matrix is well defined in the form of a polynomial. Based on this, by constructing a polynomially parameter-dependent Lyapunov matrices and linear matrix techniques, sufficient conditions are established to ensure the stochastic stability and a prescribed tracking performance. The controller design scheme are presented by solving a series of LMIs. Examples are given in the end to illustrate the effectiveness of our proposed results.

Observer-based controller design for nonlinear semi-Markov switched system with external disturbance

This paper focuses on the observer-based controller design problem for uncertain continuous-time nonlinear switched system with semi-Markov random switching signal. The mode transition rates (TRs) of switched system rely on the random sojourn-time instead of the constant. By considering the distribution of external disturbances, the nonlinear switched system is transformed into an augmented switched system, where the external disturbance is decoupled as a part of the state of the augmented system. Then, a stochastically switching observer is proposed to simultaneously estimate the state and external disturbance, and a sufficient condition on the stochastic stability of state estimation error dynamics is presented by constructing a semi-Markov Lyapunov function and using linear matrix inequality (LMI) technique. Furthermore, a stochastically switching controller is synthesized to guarantee the stochastic stability of the closed-loop switched system with external disturbance. Finally, an illustrative example is given to validate the effectiveness of the proposed approach.

Relaxed dissipative control of nonhomogeneous Markovian jump fuzzy systems via stochastic nonquadratic stabilization approach

Based on the stochastic nonquadratic stabilization approach, this paper proposes a method for designing dissipative controllers for continuous-time nonhomogeneous Markovian jump fuzzy systems such that performance enhancement and computational complexity reduction are simultaneously accomplished. First, the underlying stabilization conditions are formulated in terms of parameterized matrix inequalities depending on fuzzy basis functions, as well as on their time derivatives, and on mode-transition rates. Then, using our relaxation techniques that can impose stricter constraints on time-varying parameters, the stabilization conditions are converted into linear matrix inequalities (LMIs) that are less conservative and have lower computational complexity. The validity of this approach is shown by two illustrative examples.

Robust passivity analysis of Markov‐type Lotka–Volterra model with time‐varying delay and uncertain mode transition rates

This paper devotes to the global robust passivity problem for a novel Markovian switching Lotka–Volterra (LV) model with time‐varying delay. The Markovian switching with uncertain mode transition rates is first drawn into modeling the predator–prey system and the uncertainty of model parameters is also fully discussed, which can reflect the realistic practical significance. The robust passivity for the uncertain LV model with disturbance input and feedback control is studied by the passivity theories and inequality techniques. Some sufficient criteria are derived by the Lyapunov–Krasovskii functional, and the corresponding controllers are designed to ensure the passivity of the proposed closed‐loop uncertain LV model. Finally, a three‐specie two‐mode LV model is provided to illustrate effectiveness of the proposed theoretical results.

A Hybrid Sliding Mode Control Scheme of Markovian Jump Systems via Transition Rates Optimal Design

This article investigates the hybrid sliding mode control problem for the uncertain Markovian jump systems (MJSs) via the transition rates optimal design. The stability condition for the transition rates is first established to ensure the exponential mean-square (EMS) stability of the unforced uncertain MJSs. Then the hybrid design strategy on the sliding mode controller and transition rate matrix is presented to ensure the EMS stability of the controlled system. Moreover, the iterative optimization algorithms are developed to acquire the desirable transition rates, control gain, and decay rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> . Finally, some numerical simulation results are provided.

Mode switching and oscillations in PSR B1828–11

The young pulsar PSR B1828-11 has long been known to show correlated shape and spin-down changes with timescales of roughly 500 and 250 days, perhaps associated with large-scale magnetospheric switching. Here we present multi-hour observations with the Parkes and Green Bank Telescopes at multiple phases across the roughly 500-day cycle and show that the pulsar undergoes mode-changing between two stable, extreme profile states. The fraction of time spent in each profile state naturally accounts for the observed overall "shape parameter" (defined to be 0 for wide profiles and 1 for narrow ones); this and the variable rate of the mode transitions are directly related to the spin-down changes. We observe that the mode transition rate could plausibly function as an additional parameter governing the chaotic behaviour in this object which was proposed earlier by Seymour and Lorimer. Free precession is not needed to account for the variations.

Mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix

SummaryThis paper investigates mode feedback control strategy for continuous‐time Markovian jump linear systems with controllable mode transition rate matrix (MTRM). Based on the fact that system stability as well as its performance is dependent on MTRM, a mode feedback controller is proposed to perform control on MTRM such that system stability is achieved. Meanwhile, this strategy can help to improve system performance since it can adjust the occurrence probability of each subsystem. Firstly, taking into account that MTRM will totally determine system stability in absence of state feedback controller, the existence and restrictions on mode feedback controller are discussed where two cases are included. Then, based on a quadratic stabilization cost function that is a combination of state cost and control cost, a feasible solution of mode feedback control strategy is then obtained with its detailed algorithm given. Simulation results including comparisons with current state feedback mechanism are provided to illustrate the effectiveness of the proposed strategy.

Cluster and local mode‐dependent filtering for distributed Markovian jump systems in lossy multi‐sensor networks

This study addresses an H ∞ filtering problem for distributed Markovian jump systems (DMJSs) in multi-sensor networks with inaccessible global jumping modes, random data losses, random sensing topologies and incomplete mode transition rates (TRs). First, locally overlapped clusters are introduced to reformulate the DMJS to account for the scenario that the global modes of the DMJS are not accessible for filter design. Second, a new cluster and local mode-dependent H ∞ filtering framework is presented to incorporate the simultaneous presence of Markovian data losses and sensing topologies as well as incomplete mode TRs. The proposed H ∞ filters depend on only available information of cluster modes and local modes within this cluster, and thus eliminating the requirement of complete global modes. Third, criteria for designing desired filters are derived to preserve the stochastic stability of the resulting filtering error system under a prescribed H ∞ performance index. The proposed results are shown to be more general by covering some existing results as special cases. Finally, an F404 aircraft engine system is employed to demonstrate the effectiveness of the proposed filter design approach.

Jump linear quadratic Gaussian problem for a class of nonhomogeneous Markov jump linear systems

Summary This paper concerns with the jump linear quadratic Gaussian problem for a class of nonhomogeneous Markov jump linear systems (MJLSs) in the presence of process and observation noise. By assuming that mode transition rate matrices (MTRMs) are piecewise homogeneous whose variation is subjected to a high-level Markov process, two Markov processes are proposed to model the characteristics of nonhomogeneous MJLSs: the variation of system mode is governed by a low-level Markov process, while the variation of MTRM is governed by a high-level one. Based on this model, a mode-MTRM-based optimal filter is firstly given where filter gain can be obtained via coupled Riccati equations. Secondly, we extend the separation principle of the linear quadratic problem to the nonhomogeneous MJLSs case. An optimal controller is then designed to minimize the quadratic system cost. Finally, a potential application in solar boiler system is given to illustrate the developed theoretical methods. Copyright © 2016 John Wiley & Sons, Ltd.

Analytical Modeling of Mode Selection for Moving D2D-Enabled Cellular Networks

Device-to-device (D2D) communications have been proposed as a promising technology to improve network capacity and user experiences. In this letter, we make theoretical analyses on D2D mode selection with user mobility. Using the stochastic geometry, we deduced that the D2D communication range can be well represented by biased circles with varying radius. Besides, a tractable analytical framework considering both absolute movement and relative movement for mode selection in moving D2D scenarios is presented. Under the proposed model, the closed-form expressions of D2D mode transition rate and D2D mode residence time are derived, which are the key parameters for moving D2D mode selection performance.

Robust fuzzy control for stochastic Markovian jumping systems via sliding mode method

This paper considers the problem of sliding mode control for stochastic Markovian jumping systems by means of fuzzy method. The Takagi–Sugeno (T–S) fuzzy stochastic model subject to state-dependent noise is presented. A key feature in this work is to remove the restricted condition that each local system model had to share the same input channel, which is usually assumed in some existing results. The integral sliding surface is constructed for every mode and the connections among various sliding surfaces are established via a set of coupled matrices. Moreover, the present sliding mode controller including the transition rates of modes can cope with the effect of Markovian switching. It is shown that both the reachability of sliding surfaces and the stability of sliding mode dynamics can be ensured. Finally, numerical simulation results are given.

Decision-control mechanism for Markovian jump linear systems with Gaussian noise

Summary This paper investigates the decision–control mechanism for Markovian jump linear systems with Gaussian noise. The mechanism here consists of two parts: decision to govern the mode transition rate matrix and output-feedback controller to govern system state. Motivated by this, a joint index is put forward to evaluate system performance, which is a combination of traditional jump linear quadratic Gaussian cost and additional decision cost because extra expenses will be taken for adopting decision to mode transition rate matrix. For the minimization of joint index, the designing of optimal decision–control pair is deduced to the seeking of optimal decision. Meanwhile, the optimal decision can be obtained via an iterative with its convergence proved. Numerical examples illustrate the validity of the proposed mechanism. Copyright © 2015 John Wiley & Sons, Ltd.

Joint decision and control strategy for a class of nonhomogeneous Markovian jump systems with input constraints

This paper is concerned with the joint decision and control strategy for a class of nonhomogeneous Markovian jump systems subject to input constraints. By assuming the mode transition rate matrix (MTRM) of Markovian jump systems is piecewise homogeneous instead of homogeneous, a higher-level Markov chain represented by the higher-level mode transition rate matrix (HMTRM) is introduced to describe the variation of MTRM. Based on this, taking into account the minimization of system cost, a novel joint decision and control strategy is proposed in the presence of input constraints. This strategy consists of two sections: decisions are applied to the HMTRM such that the occurrence probability of subsystems is adjusted ultimately; next on the basis of altered HMTRM, controller is designed in view of input constraints. In comparison with conventional control method, this strategy not only guarantees the stability of the considered system well, but also decreases the system cost effectively. Numeral examples along with comparisons are put forward to illustrate the effectiveness of the proposed strategy.

Stability Analysis of A Class of Hybrid Stochastic Retarded Systems Under Asynchronous Switching

The stability of a class of hybrid stochastic retarded systems (HSRSs) with an asynchronous switching controller is investigated. In this model, the controller design relies on the observed jumping parameters, which are however delayed and thus can not be measured in real-time precisely. This delayed time interval, referred to as the “asynchronous switching interval”, is Markovian and dependent on the actual switching signal. The sufficient conditions under which the system is either stochastically asymptotic stable or input-to-state stable are obtained by applying the extended Razumikhin-type theorem to the asynchronous switching interval. These results are less conservative as it is only required that the designed Lyapunov function is non-decreasing. It is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying Markov process, which is a conclusion similar to that in asynchronous deterministic switched systems. The effectiveness and correctness of the obtained results are finally verified by a numerical example.

Robust stability and stabilization of linear stochastic systems with Markovian switching and uncertain transition rates

This paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching. The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix. New criteria for testing the robust stability of such systems are established in terms of bi-linear matrix inequalities (BLMIs), and sufficient conditions are proposed for the design of robust state-feedback controllers. A numerical example is given to illustrate the effectiveness of our results.

Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates

This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. Based on linear matrix inequalities, the quantized state-feedback controller is formulated to ensure the closed-loop system is stable in mean square. Finally, a numerical example is presented to verify the validity of the developed theoretical results.

H∞Control for Stochastic Systems with Markovian Switching and Time-Varying Delay via Sliding Mode Design

This paper addresses the problem ofH∞control for a class of uncertain stochastic systems with Markovian switching and time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties and an unknown nonlinear function in the state. An integral sliding surface corresponding to every mode is first constructed, and the given sliding mode controller concerning the transition rates of modes can deal with the effect of Markovian switching. The synthesized sliding mode control law ensures the reachability of the sliding surface for corresponding subsystems and the global stochastic stability of the sliding mode dynamics. A simulation example is presented to illustrate the proposed method.

Control and decision strategy for a class of Markovian jump systems in failure prone manufacturing process

This study investigates control and decision strategy for the failure prone manufacturing process, which is modelled as a two-mode Markovian jump system (MJS). Considering the historical effects on the system, the mode transition rate matrix (MTRM) is time-varying instead of homogeneous. A piecewise homogeneous MJS is thus proposed to characterise this phenomenon, in which the MTRM is homogeneous during certain time intervals but non-homogeneous for the whole time interval. By regarding each homogeneous MTRM as one event, all the MTRMs over the whole time interval will take values in an event set and be governed by a higher-level Markov chain. To ensure such system operates normally with high probability, the decisions including preventive maintenance and corrective maintenance are introduced to adjust the higher-level Markov chain. Motivated by this, a new joint performance, consisting of both cost function for decision making and controller design, is developed. Optimal decisions are obtained by an iterative algorithm whose convergence is proved, as well as an optimal controller is designed. The effectiveness of this method is demonstrated by simulations.

Robust control of uncertain singular stochastic systems with Markovian switching via proportional–derivative state feedback

This study focuses on the problem of robust control for a class of uncertain singular stochastic Markovian jump systems via proportional–derivative state feedback controllers (PDSFCs). The uncertainties are not only in system matrices, such as state, input and derivative matrices, but also in mode transition rate matrix. New sufficient conditions for the existence of mode-dependent PDSFC are derived as linear matrix inequalities (LMIs) such that the closed-loop singular stochastic system is quadratically normal and quadratically stochastically stable (QNQSS). Especially, another PDSFC referred to be partially mode dependent is also given by a mode-dependent Lyapunov function. Numerical examples are used to show the effectiveness of the proposed methods.

Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

This article investigates the problem of robust ℋ∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ℋ∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ℋ∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov–Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.