Stochastic Sampling Periods Research Articles

Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables. The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets. For this purpose, a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities. Then, an asynchronous fuzzy sampled-data controller, featuring distinct premise variables from the active suspension system, is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership. Furthermore, novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous H2 and H∞ performance requirements. Finally, the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Sampled-Data Stabilization for Boolean Control Networks With Infinite Stochastic Sampling.

Sampled-data state feedback control with stochastic sampling periods for Boolean control networks (BCNs) is investigated in this article. First, based on the algebraic form of BCNs, stochastic sampled-data state feedback control is applied to stabilize the considered system to a fixed point or a given set. Two kinds of distributions of stochastic sampling periods are considered. First, the distribution of sampling periods is assumed to be independent identically distributed (i.i.d.) in the range of any positive integers and the second distribution of sampling periods is assumed to follow an infinite Markov process. A BCN with infinite stochastic sampling periods proves to be equivalent to a finite stochastic switched system, based on which, necessary and sufficient conditions are given to guarantee the stabilization and set stabilization of the BCN with stochastic sampling periods. For the first one, two algorithms are given to guarantee the stabilization and set stabilization of the considered system. For the second one, necessary and sufficient conditions are all presented in the linear programming form. Examples are listed to show the effectiveness of our results.

Improved result on state estimation for complex dynamical networks with time varying delays and stochastic sampling via sampled-data control

This paper investigates state estimation for complex dynamical networks (CDNs) with time-varying delays by using sampled-data control. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling state estimator is transformed into a continuous time-delay system with stochastic parameters in the system matrices, where the purpose is to design a state estimator to estimate the network states through available output measurements. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) containing triple and fourth integral terms and applying Wirtinger-based single and double integral inequality, Jenson integral inequality technique, delay-dependent stability conditions are established. The obtained conditions can be readily solved by using the LMI tool box in MATLAB. Finally, a numerical example is provided to demonstrate the validity of the proposed scheme.

Stability analysis of the linear discrete teleoperation systems with stochastic sampling and data dropout

This paper addresses the stability conditions of the sampled-data teleoperation systems consisting continuous-time master, slave, operator, and environment with discrete-time controllers over general communication networks. The output signals of the slave and master robots are quantized with stochastic sampling periods which are modeled as being from a finite set. By applying an input-delay method, the probabilistic sampling system is converted into a continuous-time system including stochastic parameters in the system matrices. The main contribution of this paper is the derivation of the less conservative stability conditions for linear discrete teleoperation systems taking into account the challenges such as the stochastic sampling rate, constant time delay and the possibility of data packet dropout. The numbers of dropouts are driven by a finite state Markov chain. First, the problem of finding a lower bound on the maximum sampling period that preserves the stability is formulated. This problem is constructed as a convex optimization program in terms of linear matrix inequalities (LMI). Next, Lyapunov–Krasovskii based approaches are applied to propose sufficient conditions for stochastic and exponential stability of closed-loop sampled-data bilateral teleoperation system. The proposed criterion notifies the effect of sampling time on the stability-transparency trade-off and imposes bounds on the sampling time, control gains and the damping of robots. Neglecting this study undermines both the stability and transparency of teleoperation systems. Numerical simulation results are used to verify the proposed stability criteria and illustrate the effectiveness of the sampling architecture.

$$\mathcal {H}_{\infty }$$ H ∞ filtering for sample data systems with stochastic sampling and Markovian jumping parameters

This paper deals with the problem of $$\mathcal {H}_{\infty }$$ filtering for sample data systems that possess random jumping parameters described by a finite-state Markov process with stochastic sampling. Multiple stochastic sampling periods are considered in which each sampling period is assumed to be time varying that switches between two different values in a random way with given probability. The aim of this paper is to design a filter such that the filtering error system is stochastically stable with a prescribed $$\mathcal {H}_{\infty }$$ disturbance attenuation level. Sufficient conditions for the existence of $$\mathcal {H}_{\infty }$$ filters are expressed in terms of linear matrix inequalities (LMIs), which can be solved by using Matlab LMI toolbox. Numerical examples are given to illustrate the effectiveness of the proposed result including a realistic Transmission Control Protocol network model.

Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

In this article, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.

Sampled-data H∞ control for a class of Markovian jump systems with input saturation via stochastic sampling design

This paper deals with the problem of [Formula: see text] control for a stochastic sampling Markovian jump system subject to input saturation. The stochastic sampling we address is a Bernoulli distribution and two different sampling periods are considered whose occurrence probabilities are known constants. Actually the control method in this paper can be applied to a system with multiple stochastic sampling periods. By transforming the original stochastic sampling Markovian jump system into a continuous Markovian jump delayed systems, the plant can be stabilized by a state-feedback controller with input saturation. By applying an appropriate Lyapunov–Krasovskii function, some sufficient conditions for the stabilization of the system and the [Formula: see text] controller design are derived in terms of linear matrix inequalities. Finally, in order to validate the efficiency of the approach mentioned above, a simulation example is provided.

Robust probabilistic sampling [formula omitted] output tracking control for a class of nonlinear networked systems with multiplicative noises

In this paper, the problem of robust sampled-data H∞ output tracking control is investigated for a class of nonlinear networked systems with probabilistic sampling, multiplicative noises and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H∞ output tracking design.

Robust H ∞ output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noise

In this paper, the problem of robust sampled-data H ∞ output tracking control is investigated for a class of fuzzy networked systems with stochastic sampling, multiplicative noise and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and they can be extended to the case with multiple stochastic sampling periods. By using an input-delay method, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality(LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H ∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H ∞ output tracking design.

A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks

In this paper, the problem of distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering in sensor networks using a stochastic sampled-data approach is investigated. A set of general nonlinear equations described by sector-bounded nonlinearities is utilized to model the system and sensors in networks. Each sensor receives the information from both the system and its neighbors. The signal received by each sensor is sampled by a sampler separately with stochastic sampling periods before it is employed by the corresponding filter. By converting the sampling periods into bounded time-delays, the design problem of the stochastic sampled-data based distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters amounts to solving the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of stochastic nonlinear systems with multiple bounded time-delays. Then, by constructing a new Lyapunov functional and employing both the Gronwall's inequality and the Jenson integral inequality, a sufficient condition is derived to guarantee the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance as well as the exponential mean-square stability of the resulting filtering error dynamics. Subsequently, the desired sampled-data based distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters are designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering scheme.

Stabilizing composite control for a class of linear systems modeled by singularly perturbed Ito differential equations

In this paper, the problem of robust H∞ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H∞ performance. Moreover, an H∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.

Robust sampled-data [formula omitted] control with stochastic sampling

In this paper, the problem of robust H ∞ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input-delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H ∞ performance. Moreover, an H ∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.