Mode Transition Probabilities Research Articles

An adaptive synthetic method for long sequence radar mode recognition

AbstractRadar work mode recognition is crucial to analyse radar behaviour and intention. There are some challenges limiting the recognition of long sequences with multiple mode classes. First, the performance of recognition method relies on precise segregation of intercepted sequence, which is often unfeasible in reality. Second, the states at the boundaries of adjacent modes may create extraneous mode samples that intervenes the recognition. Third, current methods fail to deal with the scenarios where multiple modes share the same state sequence. To address these problems, a novel forward matching method (FMM) is proposed, comprising a shortest path method (SPM) for intra‐mode recognition, a matching strategy, and an adjustment mechanism. SPM is to provide potential recognition for short fragments of the given long sequence. The matching strategy is to assess the availability of current recognition. The adjustment mechanism tunes the segregation and improves the subsequent recognition. FMM offers several distinct advantages. First, the model can explicitly characterise the mode transition probability and is totally interpretable. Second, FMM can distinguish intentional ambiguities, alleviate mosaic ambiguity and probability deviation associated with inter‐mode recognition. Third, FMM is extendable to integrate with other intro‐mode recognition methods to cater to various scenarios.

Time-constrained Gaussian mixture model for clustering multi-modal chemical process data

Two novel unsupervised learning algorithms were developed for improved clustering of multi-modal time series data that are not separable in feature space, which are common characteristics of chemical process data. The algorithms are extensions of the conventional Gaussian Mixture Model (GMM) and K-means clustering. Both algorithms were adapted to account for the time-dependent nature of chemical process data and thus are termed time-constrained GMM (TCGMM) and time-constrained K-means (TCK-means). The algorithms are evaluated using autoregressive time series data with small step changes in the means and variances; a problem that confounds conventional clustering algorithms. In Case Study 1, step changes in the means and variances are implemented at specific time intervals to create two modes. TCGMM outperforms the other algorithms by obtaining a minimum of 85% accuracy in correctly identifying the modes. The TCGMM algorithm is also tested in a second case study where combinations of mean- and variance-shifts are randomly instantiated based on a conditional probability table (CPT). TCGMM outperforms conventional GMM by an average accuracy of 65.4% versus 46.6% and learns the CPT with an average difference in the main diagonal entries (probabilities of remaining in the same mode) of 1.89% and an average difference in the off-diagonal entries (mode transition probabilities) of 0.664%. Keywords: clustering, TCGMM, TCK-means

System identification in presence of undetectable packet losses in the actuation path

Identification of networked systems over communication links with packet losses is considered. It is assumed that there is no connection from the actuators to the system identifier such that no information is available on loss of data packets carrying the actuation signals. While the packet loss occurrences in the sensor links are naturally detectable by the system identifier as the receiving node, the packet loss occurrences in the actuation paths are not directly detectable. The existing system identification methods fail to be applicable without the information on packet loss occurrences. Presenting a solution for this issue is the objective of the present work. Two recursive algorithms are proposed to solve the problem in real time. For this purpose, ARMAX input–output representations of the system with Markovian jumping modes are developed. Then, filters are designed for estimation of the packet loss occurrences. The estimated mode is used in the recursive algorithms for identification of the whole system based on the maximum likelihood approach. A main algorithm and its simplified version are proposed that are capable of finding the various kinds of system parameters including the physical plant parameters and the communication mode transition probabilities. Effectiveness of the algorithms is verified through simulation examples where the system performance is evaluated and compared.

Adaptive Residual Useful Life Prediction for the Insulated-Gate Bipolar Transistors with Pulse-Width Modulation Based on Multiple Modes and Transfer Learning

Currently, residual useful life (RUL) prediction models for insulated-gate bipolar transistors (IGBT) do not focus on the multi-modal characteristics caused by the pulse-width modulation (PWM). To fill this gap, the Markovian stochastic process is proposed to model the mode transition process, due to the memoryless properties of the grid operation. For the estimation of the mode transition probabilities, transfer learning is utilized between different control signals. With the continuous mode switching, fractional Weibull motion (fWm) of multiple modes is established to model the stochasticity of the multi-modal IGBT degradation. The drift and diffusion coefficients are adaptively updated in the proposed RUL prediction model. In the case study, two sets of the real thermal-accelerated IGBT aging data are used. Different degradation modes are extracted from the meta degradation data, and then fused to be a complex health indicator (CHI) via a multi-sensor fusion algorithm. The RUL prediction model based on the fWm of multiple modes can reach a maximum relative prediction error of 2.96% and a mean relative prediction error of 1.78%. The proposed RUL prediction model with better accuracy can reduce the losses of the power grid caused by the unexpected IGBT failures.

Asynchronous stabilization for hidden Markov jump linear systems with complex transition probabilities

This study is intended to investigate the asynchronous stabilization problem for discrete-time Markov jump linear systems (MJLSs) with complex mode transition probabilities (C-TPs). A practical scenario is considered in this study. First, the system mode may not always be precisely detected in practice, therefore a hidden Markov model (HMM) is used to characterize the mismatched mode phenomenon. Second, some mode TPs associated with the Markov process of the original system may be unknown or inaccurate, rendering the C-TPs scenario. This issue could also exist in the conditional TPs associated with the joint process of the HMM. A mode separation strategy is proposed to separate the Markov process and the joint process such that we can deal with the C-TPs associated with them, respectively. Based on the above considerations, a unified controller design framework is established for MJLSs with or without C-TPs. Moreover, the results developed in this study can cover some existing works as special cases without introducing additional conservativeness. A DC motor device is used to demonstrate the effectiveness of the proposed design method.

Deep Learning Aided State Estimation for Guarded Semi-Markov Switching Systems With Soft Constraints

This paper investigates the problem of state estimation for guarded semi-Markov switching systems with soft constraints. We first construct the switching system in a multiple model manner and derive the recursive Bayesian filter compatible with the sojourn time and base state dependent mode transitions. To solve the intractable conditioned mode transition probabilities, we develop deep learning based classifiers with long short-term memory networks capturing the temporal dependencies. Various network structures are designed to handle different situations where knowledge of the transition probability matrix is available or deficient. Furthermore, we incorporate sequential Monte Carlo techniques into the multiple model framework to resolve the local filtering task. A novel particle refinement procedure exploiting the constraint information is proposed to improve the efficiency of particle propagation and prevent the exponential increase of particle number simultaneously. Simulations on a robotic manipulator and an autonomous vehicle tracking task validate the effectiveness of the proposed state estimation method.

Policy Synthesis for Switched Linear Systems With Markov Decision Process Switching

In this article, we study the synthesis of mode switching protocols for a class of discrete-time switched linear systems in which the mode jumps are governed by Markov decision processes (MDPs). We call such systems MDP-JLS for brevity. Each state of the MDP corresponds to a mode in the switched system. The probabilistic state transitions in the MDP represent the mode transitions. We focus on finding a policy that selects the switching actions at each mode such that the switched system is guaranteed to be stable. Given a policy in the MDP, the considered MDP-JLS reduces to a Markov jump linear system (MJLS). We consider both mean-square stability and stability with probability one. For mean-square stability, we leverage existing stability conditions for MJLSs and propose efficient semidefinite programming formulations to find a stabilizing policy in the MDP. For stability with probability one, we derive new sufficient conditions and compute a stabilizing policy using linear programming. We also extend the policy synthesis results to MDP-JLS with uncertain mode transition probabilities.

Stabilization and Optimization of Discrete-Time Markovian Jump Linear Systems via Mode Feedback Control

This article is devoted to a specific kind of discrete-time switched linear systems, where the switching signal is governed by a Markov chain, i.e., Markovian jump linear systems. For such systems, a mode feedback control mechanism is adopted to adjust the mode transition probability matrix, which is referred to as the switching law design, and the optimal mode feedback controller is sought to minimize a quadratic performance index containing both the system state and the mode feedback control input. First, the admissible set of the mode feedback control is investigated, and a sufficient condition is derived to ensure the desired stochastic stability. Second, under the assumption that the concerned system is mode-cost sequential, the original performance index is approximated into a new tractable one and a suboptimal mode feedback controller is then derived within the admissible set. Third, we consider a general situation where no specific requirements are imposed on the Markovian jump linear systems’ dynamics, derive the optimal mode feedback controller via a value-iteration-based algorithm, and prove the convergence of the obtained optimal controller. Finally, simulation results are provided to illustrate the validity of the proposed mode feedback control mechanism.

A novel system identification algorithm for nonlinear Markov jump system

System identification of nonlinear Markov jump systems (NMJSs) is crucial in modeling complex systems that contain unknown continuous and discrete states. In this system, the dynamics of continuous states is governed by the discrete states, which means the system can operate among different modes. The existing studies primarily identify the mode transition probability and noise model, whereas the parameters concerning the nonlinear continuous state transition function and observation function are commonly not considered. To identify all the parameters, a novel NMJSs identification algorithm based on a new particle system is proposed. The hidden state inference is implemented via an extended smoother that embodies the new particle system and Rao-Blackwellized particle Gibbs ancestor sampling kernel. The smoother not only estimates hidden state but also enables parameter update of the nonlinear functions. After inferencing the hidden states’ posterior density, a log-likelihood-based loss function is utilized to reduce the uncertainty of identifying the parameters related to the continuous state transition function. Then expectation–maximization and gradient descent are adopted to update the parameters. Finally, different experiments are conducted to verify the proposed algorithm. The results show that the proposed algorithm can approximate the parameter that well describes the data, and outperform other related approaches.

Optimal decision strategy for discrete-time Markovian jump linear systems

This paper investigates the discrete-time Markovian jump linear systems (MJLSs) whose mode transition probability matrix (MTPM) can be adjusted by decisions. Motivated by switching law design in switched systems, the optimal decision strategy is proposed for stabilisation and optimisation of such MJLSs where decision cost is taken into account. First, aiming at system stability, the feasible domain of decision is given for stable and unstable MJLSs with initial MTPM. Second, a generalised performance index is put forward which contains both state cost and decision cost, and we obtain the quantitative relationship between the index and decision via stochastic dynamic programming. Finally, for the optimisation of the performance index, a value iteration algorithm is proposed with its convergence proof. This algorithm, searching for the optimal decision within the feasible domain, achieves superior performance on the basis of ensuring stability. Simulation results illustrate the effectiveness of the proposed optimal decision strategy.

Multiple‐model Gaussian mixture probability hypothesis density filter based on jump Markov system with state‐dependent probabilities

The Gaussian mixture probability density (GM-PHD) filter has become a popular approach to solve the multiple-target tracking (MTT) problem because it can effectively and efficiently estimate the number of targets and target states that change over time from noisy measurements. In the GM-PHD filter, the target detection and survival probabilities, and the birth rate are assumed to be constant, irrespective of the target state. However, in some applications, for example, when the target follows the planned trajectory, the detection, survival and birth of the target depend on its state. Besides, when the target reaches a waypoint along the planned trajectory, it will take a manoeuvre to go to the next waypoint, but the GM-PHD filter does not accommodate manoeuvring targets that switch between several motion models. To address this, we propose a multiple-model GM-PHD filter with state-dependent probabilities, which can explicitly consider the mode transition probabilities, the probabilities of detection and survival, and the birth rate as a function of the target state. The performance of the proposed algorithm is demonstrated by illustrative MTT scenarios which include target manoeuvres during occlusion.

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

AbstractThis paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

Mean stability for a class of discrete-time non-homogeneous positive Markov jump linear systems

This paper investigates the mean stability and stabilisation problem for a class of discrete-time positive Markov jump linear systems where the Mode Transition Probability Matrix (MTPM) is a stochastic process instead of time invariant. By assuming the jump of system mode is governed by a low-layer Markov chain and the variation of corresponding MTPM is governed by a high-layer one, a non-homogeneous positive Markov jump linear system model with two Markov chains is then proposed. Based on this, the necessary and sufficient conditions of mean stability for this concerned model are addressed via analysing the time evolution of the first-order moment of state variables. Second, a mode-MTPM-dependent state feedback controller can then be designed according to the given stability conditions which is solvable in terms of linear programming problems. Finally, a numerical example is provided to show the effectiveness of the presented control strategy.

Nonfragile $l_{2}$ –$l_{\infty}$ Fault Estimation for Markovian Jump 2-D Systems With Specified Power Bounds

This paper addresses the nonfragile sensor fault estimation problem for a class of two-dimensional (2-D) nonlinear systems. The underlying system is described by the well-known Fornasini–Marchesini model. The system parameters are subject to abrupt changes regulated by the Markovian process for which the entries of the mode transition probability matrix are partially accessible. A novel 2-D nonfragile state estimator is constructed to achieve the sensor fault estimation where the estimator gains are allowed to be randomly perturbed. Then, together with the Lyapunov stability theory, the stochastic analysis techniques are employed to derive the sufficient conditions that guarantee the following three performance requirements: 1) the exponential stability of the estimation error dynamics; 2) the prespecified constraint on the energy-to-peak gain; and 3) the prespecified restriction on the prescribed power bound. Moreover, the estimator gains are parameterized by using the convex optimization method. Finally, a numerical example is provided to illustrate the effectiveness of the addressed estimation algorithm.

Extended dissipative asynchronous filtering for T–S fuzzy switched systems with partial transition descriptions and incomplete measurements

This paper analyzes the problem of extended dissipative asynchronous filtering for Markov jump T–S fuzzy systems (MJTSFSs) with sensor failures and incomplete measurements. The highlight of this work lies in the fact that we introduce an asynchronous filter (AF) in which mode transition probability matrix (TPM) is non-homogeneous. “Asynchronous” means that the switching of the filters to be designed may be different from that of the systems. Thanks to this AF, partial information of system modes can be fully utilized to achieve the improved and extended dissipative performance including the dissipativity, passivity, H∞ performance and l2−l∞ performance. Specifically, we first attempt to show that the transition probability information (TPI) of the two different Markov chains is not fully known, which can be regarded as an extension of existing work. In the meantime, this is also an arduous problem to be solved in this article. Additionally, with respect to the asynchronous filtering of MJTSFSs, we not only consider that sensor failures occur randomly in the filter systems, but also that research that the measured output is assumed to be quantized by the logarithmic quantizer. Then, an AF is designed for MJTSFSs with sensor failures and incomplete transition probability (ITP) for the first time. Finally, through three examples, the effects of sensor failures, quantizers, and degrees of asynchronism on system performance are examined.

State and mode feedback control strategy for discrete‐time Markovian jump linear systems with time‐varying controllable mode transition probability matrix

SummaryIn this article, the state and mode feedback control strategy is investigated for the discrete‐time Markovian jump linear system (MJLS) with time‐varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode‐dependent state feedback controller is designed to stabilize the MJLS based on the time‐invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time‐varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value‐iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.

Hidden Markov Model Based Fault Detection for Networked Singularly Perturbed Systems

Based on a hidden Markov model (HMM), the issue of fault detection (FD) is investigated for singularly perturbed systems with their measurements transmitted over a bandwidth-limited communication network. A homogeneous Markov chain is adopted to model packet dropouts and time delays simultaneously, whose mode transition probabilities are assumed to be partially unknown. The discrepancies between the Markov modes and their observed ones have been noted, which are reflected by a hidden Markov process. An HMM-based FD filter (FDF) is aimed to be designed such that the stochastic stability and prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance are ensured for the resulting filtering error dynamics of FD. A new Lyapunov-Krasovskii functional is constructed, which is with the Markov mode and the singular perturbation parameter (SPP). With the aid of up-to-date techniques in handing time delays, a sufficient condition based on linear matrix inequalities (LMIs) is derived which provides a design scheme of such an FDF. The FDF parameters are given and the SPP's admissible bounds are evaluated when the LMIs have feasible solutions. The performance of the designed FDF is demonstrated by two examples.

Intent Inference Based Trajectory Prediction and Smooth for UAS in Low-altitude Airspace with Geofence

In order to meet the higher accuracy requirement of trajectory prediction for Unmanned Aircraft System (UAS) in Unmanned Aircraft System Traffic Management (UTM), an Intent Based Trajectory Prediction and Smooth Based on Constrained State-dependent-transition Hybrid Estimation (CSDTHE-IBTPS) algorithm is proposed. Firstly, an intent inference method of UAS is constructed based on the information of ADS-B and geofence system. Moreover, a geofence layering algorithm is proposed. Secondly, the Flight Mode Change Points (FMCP) are used to define the relevant mode transition parameters and design the guard conditions, so as to generate the mode transition probability matrix and establish the continuous state-dependent-transition model. After that, the constrained Kalman filter (CKF) is applied to improve State-dependent-transition Hybrid Estimation (SDTHE) algorithm by applying equality constraint to the velocity of UAS in the straight phase and turning phase, respectively, and thus the constrained state-dependent-transition hybrid estimation (CSDTHE) algorithm is constructed. Finally, the results of intent inference and hybrid estimation are used to make trajectory prediction. Furthermore, each flight segment of trajectory is smoothed respectively by Rauch-Tung-Striebel (RTS) backward smooth method using the proposed CSDTHE-RTS algorithm, so as to obtain more accurate trajectory prediction results. The simulation shows that the proposed algorithm can reduce the errors of trajectory prediction and the time delay of intent inference.

Gain Scheduled State Feedback Synthesis for Markovian Jump Systems with Mode Transition Probabilities Depending on Time-Varying Parameters

Gain Scheduled State Feedback Synthesis for Markovian Jump Systems with Mode Transition Probabilities Depending on Time-Varying Parameters

State and mode feedback control for discrete-time Markovian jump linear systems with controllable MTPM

In this note, the state and mode feedback control problems for a class of discrete-time Markovian jump linear systems &#x0028 MJLSs &#x0029 with controllable mode transition probability matrix &#x0028 MTPM &#x0029 are investigated. In most achievements, controller design of MJLSs pays more attention to state &#x002F output feedback control for stability, while the system cost in practice is out of consideration. In this paper, we propose a control mechanism consisting of two parts: finite-path-dependent state feedback controller design with which uniform stability of MJLSs can be ensured, and mode feedback control which aims to decrease system cost. Differing from the traditional state &#x002F output feedback controller design, the main novelty is that the proposed control mechanism not only guarantees system stability, but also decreases system cost effectively by adjusting the occurrence probability of system modes. The effectiveness of the proposed mechanism is illustrated via numerical examples.