Multiple Piecewise Research Articles

Bumpless transfer control for switched time-delay systems with application to aero-engine control

For switched time-delay systems, the bumpless transfer control issue is investigated by utilizing the multiple piecewise Lyapunov–Krasovskii function approach. First, a time-delay-dependent bumpless transfer concept is put forward to depict the transient performance of switched time-delay systems, which restricts the bumps in the amplitude of the present state and the time-delay state, simultaneously. Second, a state-dependent switching signal with a prescribed time is designed to avoid switching frequently. A time-varying switching controller is developed to decrease control bumps. Third, under the premise of achieving asymptotic stability, a solvability condition ensuring a satisfactory bumpless transfer performance is derived through relaxing the traditional bumpless transfer condition. Finally, an instance of the aero-engine control system is used for exhibiting the validity of the presented method.

Finite-time bumpless transfer control problem for switched LPV systems with guaranteed switching frequency

For the switched linear parameter-varying (LPV) systems, the finite-time bumpless transfer control (FTBTC) issue is addressed by utilising the parameter-dependent multiple piecewise Lyapunov function method. First, for the switched LPV systems, a finite-time bumpless transfer performance is proposed, which only demands that bumpless transfer inequation holds in the activated interval in place of entire intervals. Second, a switching law depending on external parameters, system state, dwell time is designed to guarantee switching frequency. Third, a time-varying switching controller is designed, under which a solvable condition of the FTBTC issue is presented. It allows the FTBTC issue of each subsystem to be unsolvable. Finally, an aero-engine model is established to confirm the availability of the proposed scheme.

An exact model for enhancing/suppressing primordial fluctuations

Abstract Enhancements of primordial curvature fluctuations in single field inflation often involve departures from attractor trajectories in the phase space. We study enhancement/suppression of primordial fluctuations in one of the simplest models with exact background solutions for arbitrary initial conditions: a single field inflationary model with a piecewise exponential potential. We then present close to exact analytical solutions for primordial fluctuations in a general transition between two slow-roll attractors, valid whether the first slow parameter increases or decreases. The main features in the primordial spectrum are determined by the ratio of exponents of the potential. We also discuss the imprint of such features in the induced GW spectrum. Lastly, we apply the δN formalism to discuss non-Gaussianities and the tail of the probability distribution. We find that while non-Gaussianities are at most 𝒪(1) in the case of enhancement, they can be very large in the case of suppression. Our work can be easily generalized to multiple piecewise exponential potentials.

Activation Control of Multiple Piecewise Linear Neural Networks

Activation Control of Multiple Piecewise Linear Neural Networks

Adaptive fixed‐time neural control of nonlinear time‐varying state‐constrained systems

AbstractIn this paper, an adaptive fixed‐time neural control scheme is proposed for a class of nonlinear uncertain systems with full‐state constraints. A novel asymmetric hyperbolic barrier Lyapunov function (AHBLF) is first constructed to handle time‐varying constraints of all the system states. EspecialLy, the AHBLF can not only be applied to unconstrained, symmetric‐constrained and asymmetric‐constrained systems simultaneously, but also the fixed time control can be realized by incorporating the AHBLF into each step of the backstepping method to design controller. The adaptive controller is presented to guarantee that the tracking errors converge into the neighborhood around the equilibrium point in a fixed time and all the system states can be restricted within the predefined time‐varying boundaries. With the proposed control scheme, the singularity problem is avoided without constructing multiple piecewise functions, and no prior knowledge on the bound of gain functions is required in the controller design. Comparative simulations illustrate the effectiveness of the proposed control scheme.

Event‐triggered fault detection filter design for networked switched systems with all subsystems unstable and cyber attacks

SummaryThis article focuses on the issue of event‐triggered fault detection filters (FDF) design for networked switched systems. Compared with the existing fault detection literature, this article investigates the situation that all subsystems are unstable, and considers that stochastic cyber attacks will disrupt fault detection. An event‐triggered mechanism (ETM) that excludes Zeno behavior naturally is designed to economize limited network resources. Then considering the ETM‐induced delay term, the dynamics of the initial system combined with the ETM, fault detection filters, and the effects of cyber attacks are formulated as a new augment switched delayed residual model. Based on the constructed multiple piecewise discretized Lyapunov–Krasovskii function (MPDLKF) and the mode‐dependent dwell time (MDDT) method, sufficient conditions are obtained to guarantee globally mean‐square uniformly asymptotically stability of the new augment system. Moreover, a co‐design method of ETM matrices and FDF gains is proposed. Finally, simulation results are provided to verify the feasibility and effectiveness of the proposed method.

Dynamic Event-Based Distributed Piecewise Filtering Over Sensor Networks Under Periodic DoS Attacks

In this article, the problem of distributed filtering for a class of linear discrete-time systems under periodic denial-of-service (DoS) attack is investigated. First, a cyclical and repeatable variable is introduced to characterize the behavior of a periodic DoS attack. Based on the introduced variable, a novel dynamic event-triggered scheme is designed to reduce the network transmission burden. Second, a cyclic switching estimation error model, which includes stable subsystems in the absence of a DoS attack and unstable subsystems in the presence of a DoS attack, is constructed. The global exponential stability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance is synthesized by utilizing multiple piecewise Lyapunov functions, and the gain matrix of the distributed filtering is derived in piecewise form. Third, the codesign algorithm of the dynamic event-triggered scheme and distributed piecewise filtering is proposed to make a tradeoff between network transmission burden and the performance of distributed filtering. Finally, an example is applied to verify the effectiveness of the proposed distributed piecewise filtering.

Output tracking and disturbance rejection control for switched systems under asynchronous switching

In this article, we discuss the output tracking and disturbance rejection problem for a class of switched systems with state time-varying delay under asynchronous switching. More precisely, proportional–integral control law is implemented to obtain the required tracking performance for the addressed systems. In addition, an improved equivalent-input-disturbance estimator is utilized to estimate and suppress the external disturbances. Further, the asynchronous switching phenomenon is considered between the proposed controller and the system mode. Setting a proper choice of multiple piecewise Lyapunov–Krasovskii functional, a group of required condition is established in the structure of linear matrix inequalities by using an average dwell time approach. At last, two numerical examples and their simulations including the DC motor driving model are displayed to justify the efficiency and applicability of the proposed control synthesis.

Adaptive Tracking Control of Hybrid Switching Markovian Systems with Its Applications

This paper focuses on the model reference adaptive tracking control problem of uncertain hybrid switching Markovian systems. The stochastic multiple piecewise Lyapunov function method is set up for designing a hybrid switching signal and a piecewise dynamic switching adaptive controller. The hybrid switching signal is presented to improve the adaptive tracking capability by providing plenty of adjusting time during the stochastic switching stage. A piecewise dynamic parameter projection adaptive control technique is developed, which provides more freedom in designing a model reference adaptive law. A set of piecewise dynamic switching adaptive controllers are designed such that all the signals of the tracking error system remain within a bounded region under the proposed hybrid switching signal, and the tracking error converges to a neighborhood of zero where the radius of the neighborhood can be made arbitrarily small by choosing the regulation parameters appropriately. Finally, the developed adaptive tracking control theory of uncertain hybrid switching Markovian systems is illustrated by using a numerical example and an application example of an electro-hydraulic model.

Time-Driven Adaptive Control of Switched Systems With Application to Electro-Hydraulic Unit.

This article focuses on the H∞ adaptive tracking problem of uncertain switched systems. A key point of the study is to set up a multiple piecewise Lyapunov function framework which provides an effective tool for designing an adaptive switching controller consisting of a state-feedback and time-driven switching signal and a time-driven adaptive law. The proposed switching signal guarantees the solvability of the H∞ adaptive tracking problem for uncertain switched systems. Significantly, it provides plenty of adjusting time for the adaptive tracking control strategy to damp the transient caused by switching and avoids frequent switching. A novel time-driven adaptive switching controller is established such that the tracking error asymptotically converges to zero and all the signals in the error dynamic system are bounded under an achieved disturbance attenuation level. The solvability criterion ensuring an H∞ adaptive tracking performance is established for the uncertain switched systems, where the solvability of the H∞ adaptive tracking problem for individual subsystems is not required. Finally, the proposed method is applied to the electro-hydraulic unit.

Catheterization Before Transperineal Ultrasound-guided Prostate Biopsy and the Risk of Urethrorrhagia

To investigate the efficacy of catheterization before transperineal ultrasound-guided prostate biopsy in reducing risk of urethrorrhagia. Currently, transperineal ultrasound-guided prostate biopsy (TPPB) is one of the most commonly used measures to help diagnose prostate cancer. However, whether the retention of catheterization before transperineal ultrasound-guided prostate biopsy is associated with the reduced risk of urethrorrhagia remains uncertain. A cohort study was conducted in our hospital from January 2021 to September 2021. This study included 93 patients who participated in transperineal ultrasound-guided prostate biopsy. We compared the risk of urethrorrhagia in patients who underwentindwelling catheterization before biopsy and those who did that after biopsy, and performed an unadjusted analysis. We also analyzed the use of related confounding factors to limit the cohort of men, and applied propensity-score adjustment to control potential confounders. Analyses that restricted the cohort men with the related confounding factors and that used propensity-score adjustment to control for potential confounders. A total of 93 men were recruited in the cohort study, and the numbers of patients in group 1 and group 2 were 64 and 29, respectively. There were 34 patients (53.1%) of urethrorrhagia in group 1, and 22 patients (75.8%) of urethrorrhagia in group 2. This was a significant difference between the 2 groups (P = .008). After adjusting for correlative factors, the preoperative catheterization is still a protective factor for postoperative urethrorrhagia through multivariate multiple piecewise linear regression analysis. The result of this cohort study suggested that preoperative catheterization can significantly reduce the risk of urethrorrhagia.

Fault-Tolerant Control of Switched LPV Systems: A Bumpless Transfer Approach

For switched linear parameter-varying (LPV) systems with possible actuator failures, the parameter-dependent multiple piecewise Lyapunov function is constructed to handle the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem. First, a generalized bumpless transfer concept is presented for switched LPV systems to describe the transient performance, for which only the local bumpless transfer condition is required. Second, an event-triggered switching law, depending on the system states, external parameters, and dwell time, is designed to ensure a time span among adjacent switchings. Third, a solvability condition of the <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> bumpless transfer fault-tolerant control problem is developed. A family of time-driven switching controllers with bumpless transfer constraint and fault-tolerant requirement are also designed. Finally, an application example of an aero-engine is given to verify the effectiveness of the developed methods.

Detection and computation of conservative kernels of models consisting of freeform curves and surfaces, using inequality constraints

We present an algorithm to compute a tight-as-needed conservative approximation of the kernel domain of freeform curves in R2 and freeform surfaces in R3. Inequality constraints to detect the interior of the kernel domain are formulated as multivariates, and solved with a subdivision-based approach to find the domains in R2 or R3 that satisfy the inequalities and are in the kernel. The convex hull of the computed domains is also included in the kernel, and adopted as the approximated kernel domain. We can apply the presented algorithm to detect the kernel domain of not only C1 continuous closed regular curves and surfaces, but also the kernel domains of multiple piecewise C1 continuous regular freeform curves and surfaces. Further, the presented algorithm can be applied to find the gamma-kernel as well as the kernel domain of open curves and surfaces, under some assumptions. We demonstrate our experimental result using various freeform curves and surfaces, and compare it with the kernel computation algorithm presented in Elber et al. (2006).

Multiple piecewise regression for trip generation models

Trip generation modelling is not a standard task as the relationship between the input and output variables is not exactly known and is often nonlinear. Furthermore, the input variables may have different types especially at the disaggregate levels. Accordingly, there is no single modelling technique that can be used for all trip generation cases. In this paper, a multiple piecewise regression technique is proposed to suit most trip generation cases. Thresholds can be identified at the discrete values in the case of categorical inputs; while, no thresholds are considered in the case of binary inputs. In addition, the locations of thresholds in case of continuous inputs are obtained to minimize the summation of squared errors and achieving the logical constraints. Thus, a broken hyperplane is determined using quadratic programming. The proposed technique is illustrated using a numerical example and then validated using three well-known examples. The results show that the proposed technique can fit the given data more accurately than the previous techniques. In addition, the proposed technique leads to more explicit and visualized models for practitioners. These findings will encourage researchers to apply the proposed technique in further applications such as trip distribution and mode choice models.

Finite-time stabilization of continuous-time switched positive delayed systems

This paper deals with the problems of finite-time stability and stabilization for continuous-time switched positive linear time-delay systems under mode-dependent average dwell time switching signals. First, finite-time stability conditions are established by constructing an multiple piecewise copositive Lyapunov–Krasovskii functional. Then, finite-time stabilization is achieved by designing a state-feedback controller in the form of linear programming. This numerical construction approach proposed for controller cancels the restriction of the multiple piecewise copositive Lyapunov–Krasovskii functional on controllers, which can decrease the conservatism. Finally, two numerical examples are given to show the advantages of our methods.

Connectivity-preserving-based distributed adaptive asymptotically synchronised tracking of networked uncertain nonholonomic mobile robots with actuator failures and unknown control directions

This brief addresses a distributed adaptive asymptotically synchronous tracking problem based on guaranteed connectivity for networked uncertain nonholonomic mobile robots (NMRs) with actuator failures and unknown control directions. First, a radial basis function (RBF) neural network is used to approximate the unknown nonlinear functions, and a distributed nonlinear error surface is introduced to achieve synchronous tracking between NMRs and maintain the initial connectivity patterns. Then, a conditional inequality that allows multiple piecewise Nussbaum functions to achieve robust control is proposed to solve the problem of unknown actuator failures and unknown control directions. Moreover, the proposed protocol ensures that all signals in the closed-loop system are globally bounded and the tracking errors converge asymptotically to zero. Finally, a simulation example verifies the effectiveness of the proposed adaptive laws.

Stochastic stability of positive Markov jump linear systems with fixed dwell time

This paper studies the stochastic stability of positive Markov jump linear systems with a fixed dwell time. By constructing an auxiliary system that originated from the initial system with state jumps, sufficient and necessary conditions of stochastic stability for positive Markov jump linear systems are obtained with both exactly known and partially known transition rates. The main idea in the latter case is applying a convex combination to convert bilinear programming into linear programming problems. On this basis, multiple piecewise linear co-positive Lyapunov functions are provided to achieve less conservative results. Then state feedback controller is designed to stabilize the positive Markov jump linear systems by solving linear programming problems. Numerical examples are presented to illustrate the viability of our conclusions.

Prediction of limit cycle oscillations in piecewise linear systems with multiple piecewise nonlinearities

Prediction of limit cycle oscillations in piecewise linear systems with multiple piecewise nonlinearities

H∞ Tracking Control of Uncertain Markovian Hybrid Switching Systems: A Fuzzy Switching Dynamic Adaptive Control Approach.

This article investigates the H∞ stochastic tracking control problem for uncertain fuzzy Markovian hybrid switching systems by using a fuzzy switching dynamic adaptive control approach. The long and the short is to construct multiple piecewise stochastic Lyapunov functions which provide an effective tool for designing hybrid switching law and fuzzy switching dynamic adaptive law. A hybrid switching law, including both stochastic switching and deterministic switching, is designed to represent more general switching scenarios, which can improve the H∞ adaptive tracking performance through offering a running time before stochastic switching for the adaptive control strategy to work well. A fuzzy switching dynamic adaptive control technique is developed such that all signals of the tracking error equation are bounded, and the system state trajectory tracks the reference model state trajectory under a disturbance attenuation level as closely as possible. Finally, an application study verifies the effectiveness of the acquired methods.

Bumpless Transfer H∞ Anti-Disturbance Control of Switching Markovian LPV Systems Under the Hybrid Switching.

This article focuses on the bumpless transfer H∞ anti-disturbance control problem for switching Markovian LPV systems under a hybrid switching law. A parameter-dependent multiple piecewise disturbance observer-based bumpless transfer control strategy is put forward to reject multiple disturbances and reduce switching bumps. First, a hybrid switching law making full use of determinacy and randomness is proposed to improve the bumpless transfer anti-disturbance level by introducing a fixed dwell time in random switching. Second, a generalized bumpless transfer anti-disturbance specification is given to describe the switching quality at the switching points of switching Markovian LPV systems. Third, a solvability condition is established for the bumpless transfer H∞ anti-disturbance control problem, and a parameter-dependent multiple piecewise disturbance observer-based bumpless transfer controller is designed. Finally, an application example has been supplied to demonstrate the availability of the developed method.