Nonlinear Networked Control Systems Research Articles

Static-output feedback controller design for a class of nonlinear networked control systems with random delay and data packet dropout

ABSTRACTIn this paper, the problems of stability and stabilization are investigated for a class of nonlinear networked control systems (NCSs) in the presence of random delay. First, network-induced random delay is modelled as a Markov chain, and the resulting closed-loop system is transformed into a Markovian jump system. Then, sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via a new linear matrix inequalities (LMIs) formulation. Moreover, the stabilizing output feedback controller design is achieved by assuming some elements in the transition probability matrix to be unknown or unavailable because of the complexity of the network. Finally, numerical examples and simulations are carried out to show the usefulness of the designed controller.

Stochastic Optimal Regulation of Nonlinear Networked Control Systems by Using Event-Driven Adaptive Dynamic Programming.

In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.

Stability Analysis and Synthesis for Nonlinear Networked Control Systems

Abstract: The paper is concerned with stabilization of nonlinear networked systems which are described by the Takagi-Sugeno fuzzy systems. Based on Lyapunov-Krasovskii stability theorem, stability analysis and control design problems are considered. Novel Lyapunov-Krasovskii function and corresponding generalized controller allow to obtain less conservative conditions for the networked control system to be asymptotically stable. Furthermore, free matrix parameter method is introduced. This method is known to reduce the conservatism in control design conditions. With such novel controller and novel Lyapunov-Krasovskii function, a new controller design method is proposed. Resulting conditions for a controller to stabilize the networked control system are less conservative and are applicable for a wider class of nonlinear systems.

New reliable H∞ filter design for networked control systems with external disturbances and randomly occurring sensor faults

This paper deals with the reliable H∞-based filtering problem of nonlinear networked control systems in the presence of external disturbances and random sensor faults. More precisely, a random variable obeying the Bernoulli distribution is adopted to describe the failures of the network sensors. By employing the Lyapunov–Krasovskii functional method, delay-dependent criteria are developed to guarantee the existence of the designed filter with the prescribed H∞ performance. Then, a design method is given to calculate the desired reliable filter parameters. An illustrative example is provided to demonstrate the effectiveness and usefulness of the established theoretical results.

Predictive control of nonlinear continuous networked control systems with large time-varying transmission delays and transmission protocols

In this paper, we consider a class of globally Lipschitz nonlinear continuous networked control systems (NCS) incorporating large time-varying transmission delays and transmission protocols of communication networks with periodic sampling. To stabilize the NCS, we propose a new predictive control design scheme with plant outputs as the only available data. With uniformly globally exponentially stable (UGES) protocols, input-to-state stability of the entire NCS is ensured by small gain theory. In particular, the predictive controller can compensate transmission delays with any finite upper bound under the constraint that the sampling periods of the plant output and the observer output are small enough as well as the constraint that the predictor is accurate enough. The scheme is applied to a benchmark example to illustrate the effectiveness of our proposed method.

Interval Type-2 Fuzzy Model Predictive Control of Nonlinear Networked Control Systems

In this paper, the problem of fuzzy predictive control of nonlinear networked control systems subject to parameter uncertainties and defective communication links is studied. Stochastic variables with Bernoulli random binary distribution are used to represent the defective communication links with packets loss occurring intermittently between the controller and the physical plant. An interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model is employed to describe the nonlinear plant subject to parameter uncertainties, which can be captured with the lower and upper membership functions. The IT2 fuzzy model and IT2 fuzzy controller are not required to share the same lower and upper membership functions. In order to design the state-feedback fuzzy model predictive controller, an optimization problem which minimizes the upper bound of a quadratic objective function subject to input constraints and packets dropout is formulated and solved at every sampling instant in the finite time horizon. By introducing some slack matrices, less conservative conditions are developed for system stability analysis. Two examples are given to demonstrate the effectiveness and merits of the proposed new design techniques.

Robust nonlinear variable selective control for networked systems

ABSTRACTThis paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi–Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

Observer design for nonlinear networked control systems with variable transmission delays and protocols based on a hybrid system technique

In this paper, we address the stability problem of the observer system for networked control systems affected by transmission protocols and unknown variable delays. The transmission protocols are assumed to be uniformly globally exponentially stable (UGES). By the small gain theorem, we prove that the observation error converges to a small ball around the origin when the transmission intervals and transmission delays are small enough. In the sequel, an example is given to show the effectiveness of our conclusion.

Nonfragile passivity and passification of nonlinear singular networked control systems with randomly occurring controller gain fluctuation

In this article, the nonfragile passivity and passification problems are investigated for a class of nonlinear singular networked control systems (NCSs) with network‐induced time‐varying delay. In particular, the randomly occurring controller gain fluctuation is taken into consideration by introducing the stochastic variable satisfying the Bernoulli random distribution. By constructing proper Lyapunov–Krasovskii function, delay‐dependent sufficient conditions are established to guarantee the passivity of the singular NCSs. Based on the derived results, the nonfragile passification controller is further designed in terms of linear matrix inequalities. Finally, a numerical example is provided to illustrate the applicability and effectiveness of our theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 200–210, 2016

Global -exponential stabilisation of a class of nonlinear networked control systems

abstractIn this paper, we investigate global -exponential stabilisation of a class of nonlinear networked control systems. The network-induced delays are assumed to be random and significantly smaller than the sampling period. First, sufficient conditions are presented to ensure global -exponential stability for a class of hybrid systems with time delay. Then, the networked control systems are modelled as the hybrid systems with time delay. By the techniques of adding a power integrator and a recursive argument, a sampled-data state feedback control law is presented. Sufficient conditions are given to ensure global -exponential stability of the closed-loop system by constructing a Lyapunov–Krasovskii function. Finally, a numerical example is presented to show the validity of the new methods.

Design of observer-based controller for T–S fuzzy systems with intermittent measurements

This paper studies the problem of observer-based fuzzy control for a class of nonlinear networked control systems (NCSs) in the framework of interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model. Both imperfect communication channels and parameter uncertainties are taken into consideration. Bernoulli random distribution is used to describe such unreliable communication environment. Nonlinear NCSs are modeled via the IT2 T–S fuzzy model, in which membership functions with lower and upper bounds can capture and express parameter uncertainties. The observer is designed to observe unmeasurable state variables. Moreover, based on these techniques, sufficient conditions are derived to guarantee the resulting closed-loop system to be stochastically stable and possess the property of external disturbance attenuation. Finally, a numerical example is provided to illustrate the effectiveness of the approach proposed in this paper.

A new compensation for fuzzy static output-feedback control of nonlinear networked discrete-time systems

This paper investigates the problem of static output-feedback control of discrete-time nonlinear networked control systems with data packet dropouts on the basis of the fuzzy-model-based Takagi-Sugeno (T-S) approach. The nonlinear system is modeled via T-S fuzzy model. Both imperfect sensor-to-controller (S/C) and controller-to-actuator (C/A) links are considered via a novel data model. Some slack matrices are introduced to reduce the conservativeness. By constructing fuzzy Lyapunov function, the sufficient conditions are derived to guarantee the resulting closed-loop system to be stochastically stable as well as the predefined H∞ performance index. Finally, some simulation results are given to demonstrate the effectiveness of the proposed results.

On Feedback Passivity of Discrete-Time Nonlinear Networked Control Systems With Packet Drops

We analyze the feedback passivity of a networked control system in which the control packets may be dropped by the communication channel. Specifically, we consider a discrete-time switched nonlinear system with relative degree zero that switches between two modes. At the instants when the communication link transmits the packet successfully, the system evolves in closed-loop and the increase in storage function is bounded below the energy supplied by the control input. At the instants when a packet drop occurs, the system evolves in open loop according to the free dynamics of the closed-loop mode and the increase in storage function is not necessarily bounded by the supplied energy. The literature on passivity of switched systems seems to consider only the case when all the modes are passive, which is not the case here. We prove that if the ratio of time steps for which the system evolves in closed-loop versus in open loop is lower bounded by a critical number, the system is locally feedback passive in a suitably defined sense. This generalized definition of feedback passivity is useful since it preserves two important properties of classical passivity—that feedback passivity implies asymptotic stabilizability for zero state detectable systems and that feedback passivity is preserved in parallel and negative feedback interconnections.

Congestion Control for Nonlinear TD-SCDMA Discrete Networks Based on TCP/IP

A successive approximation approach (SAA) is developed to obtain a new congestion controller for the nonlinear TD-SCDMA network control systems based on TCP/IP. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term that is the limit of the solution sequence of the adjoint vector differential equations. By using the finite-time iteration of nonlinear compensation term of optimal solution sequence, we can obtain a suboptimal control law for TD-SCDMA network control systems based on TCP/IP.

Multirate Output Feedback Control of Nonlinear Networked Control Systems

This technical note studies output feedback stabilization of nonlinear networked control systems (NCSs) under multirate sampling. Network induced constraints are modeled as norm-bounded uncertainties and a general framework for multirate nonlinear NCS design is established. Under standard continuity and consistency assumptions, we analyze dissipativity of the proposed multirate output feedback structure in the presence of channels uncertainties and disturbance inputs. Our result is then applied to preserve input-to-state stability (ISS) in a semiglobal practical sense and also to derive sufficient conditions that guarantee exponential stability of the uncertain multirate NCS in the absence of disturbances.

Emulation-based stabilization of networked control systems implemented on FlexRay

We investigate the emulation controller design approach for nonlinear networked control systems (NCS) with FlexRay. FlexRay is a deterministic communication protocol which is increasingly used in the automotive industry as it provides a high bandwidth and allows for safety critical applications. It is characterized by pre-set communication cycles that are subdivided into static and dynamic segments; the data transmissions are scheduled by different rules depending on the segment. We propose for the first time a hybrid model of NCS with FlexRay for this purpose. We show, under reasonable assumptions, that the asymptotic stability property ensured by the controller in the absence of communication constraints is preserved when the latter is implemented over FlexRay with sufficiently frequent data transmission. In particular, we assume that on each communication segment, the data transmissions are governed by uniformly globally exponentially stable protocols. This covers the case when the round-robin protocol is implemented on the static segment and the try-once-discard protocol is implemented on the dynamic segment. We provide explicit maximum allowable transmission interval bounds that guarantee stability.

Fuzzy-Model-Based Quantized Guaranteed Cost Control of Nonlinear Networked Systems

This paper is concerned with the problem of guaranteed cost control for a class of continuous-time networked control systems based on the Takagi–Sugeno fuzzy model approach. In this study, network-induced transmission delays and packet dropouts are taken into simultaneous consideration. By the improved Lyapunov–Krasovskii functionals, a less-conservative delay-dependent condition is proposed for the stability analysis of the resulting closed-loop system. Furthermore, the sufficient condition under which the guaranteed cost controller exists is formulated in terms of linear matrix inequalities, and the suboptimum solution is obtained by a cone complementarity linearization algorithm. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

Fault detection for a class of non‐linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

In this study, the problem of fault detection for a class of discrete-time non-linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full-order mode-dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H ∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality-based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method.

Sampled‐data control of nonlinear networked systems with time‐delay and quantization

SummaryIn this paper, the stabilization problem of a class of nonlinear networked systems with time‐delay and quantization through sampled‐data control is investigated. With sampled‐data control, sufficient conditions to guarantee the trivial solution of the nonlinear networked system to be asymptotically stable without any quantization or with uniform quantization are derived. Finally, an example of a continuous‐time nonlinear system controlled through a digital controller and a communication channel is given to illustrate the effectiveness of the proposed control methods. Copyright © 2015 John Wiley & Sons, Ltd.

Fault detection for a class of non‐linear networked control systems with data drift

In this paper, the fault detection problem is studied for a class of non-linear discrete-time networked control systems (NCSs). An individual stochastic variable satisfying a certain probabilistic distribution is utilised to describe the data drift of each sensor. The random transmission delays with the upper bound and the data drift phenomena are taken into account in a unified framework. By augmenting the states of the original non-linear NCS and the constructed full-order fault detection filter, the resulting fault detection dynamics is converted into an H ∞ filtering problem of a non-linear time-delay system. A sufficient condition for the existence of the designed fault detection filter is given in terms of a feasible linear matrix inequality, guaranteeing that the fault detection dynamics is stochastically stable and attains the prescribed H ∞ attenuation level. Finally, a numerical example is presented to show the effectiveness of the proposed method.