Reliable Decentralized Supervisors for Discrete‐Event Systems Under Communication Delays: Existence and Verification

A reliable decentralized supervisory control framework for discrete‐event systems is proposed to deal with possible actuation failures and communication delays. We mainly focus on the existence of such a controller that the control performance can be guaranteed even in face of local supervisor failures and communication delays. Especially, the existence of k‐reliable decentralized supervisors under communication delays is characterized by the notion of k‐reliable together with . In addition, the verification for k‐reliable decentralized supervisors is investigated by developing a constructive methodology to test the k‐reliable . It is shown that for a given number of distributed components, the existence of such k‐reliable decentralized supervisors can be checked with a polynomial complexity in the size of the state space.     

Robust Partially Mode Delay‐Dependent ℋ∞ Output Feedback Control of Discrete‐Time Networked Control Systems

In this paper, a methodology for designing an output feedback controller for discrete‐time networked control systems has been considered. More precisely, network‐induced delays between the sensor and the controller is modelled by a Markov chain with transition probabilities which are not assumed to be fully known. The systems parameter uncertainties are assumed to be norm‐bounded and possibly time‐varying. To the best of the authors knowledge, the problem of designing a partially mode delay‐dependent output feedback controller for NCSs with partially known transition probability matrix has not been investigated in the literature. Based on the Lyapunov‐Krasovskii functional approach, sufficient conditions for the existence of a robust partially mode delay‐dependent output feedback controller are given in terms of bilinear matrix inequalities which can be solved using a cone complementarity linearization algorithm. The proposed design methodology differs from the existing design methodologies in that dynamic output feedback controllers are parameterized by both modes and transition probabilities, as opposed to the existing design approaches which parameterize controllers by modes only. The results obtained reduce to the existing results on fully known transition matrices when transition probabilities are fully known. It is shown that the proposed methodology can be applied to real world systems. The proposed design methodology is verified by using a DC servo motor system where the plant and the controller are connected via a cellular network with partially known transition probability matrix.     

Robust Adaptive Dynamic Surface Control for a Class of MIMO Nonlinear Systems with Unknown Non‐Symmetric Dead‐Zone

This paper is devoted to adaptive output tracking for a class of multi‐input multi‐output nonlinear systems with unknown non‐symmetric dead‐zone. With the aid of a matrix factorization and a similarity transformation, a robust adaptive dynamic surface control scheme is proposed and the difficulty caused by the control gain matrix and the dead‐zone is circumvented. By introducing a surface error modification and an initialization technique, we show that the performance of the tracking errors can be guaranteed. Moreover, the proposed scheme contains only one updated parameter at each design step, which significantly reduces the computational burden. It is proven that all signals of the closed‐loop system are semi‐globally uniformly bounded. Simulation results on coupled inverted double pendulums are presented to illustrate the effectiveness of the proposed scheme.     

The Mixed Robust /FTS Control Problem Analysis and State Feedback Control

In this paper we deal with the mixed  /finite‐time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input‐output finite‐time stability with an  bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state‐feedback. The property of quadratic input‐output finite‐time stability with an  bound implies that the system under consideration satisfies an  performance bound between the disturbance input and the controlled output and, at the same time, is input‐output finite‐time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time‐varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.     

Disturbance Observer‐Based Elegant Anti‐Disturbance Control for Stochastic Systems with Multiple Disturbances

Disturbance observer‐based elegant anti‐disturbance control (DOBEADC) scheme is proposed for a class of stochastic systems with nonlinear dynamics and multiple disturbances. The stochastic disturbance observer based on pole placement is constructed to estimate disturbance which is generated by an exogenous system. Then, composite DOBC and controller is designed to guarantee the composite system is mean‐square stable and its performance satisfies a prescribed level. Finally, simulations on an A4D aircraft model show the effectiveness of the proposed approaches.     

Robust Stochastic Stability and Control for Uncertain Singular Markovian Jump Systems with Multiplicative Noise

This paper focuses on the problems of robust stability and stabilization and robust control for uncertain singular Markovian jump systems with (x,v)‐dependent noise. The parameter uncertainties appearing in state, input, disturbance as well as diffusion terms are assumed to be time‐varying but norm‐bounded. Based on the approach of generalized quadratic stability, the memoryless state feedback controller is designed for the robust stabilization problem, which ensures that the resulting closed‐loop system has an impulse‐free solution and is asymptotically stable in the mean square. Furthermore, the results of robust control problem are derived. The desired state feedback controller is presented, which not only meets the requirement of robust stabilization but also satisfies a prescribed performance level. The obtained results are formulated in terms of strict LMIs. What we have obtained can be viewed as corresponding extensions of existing results on uncertain singular systems. A numerical example is finally given to demonstrate the application of the proposed method.     

Non‐Fragile Observer‐Based Control for Uncertain Neutral‐Type Systems via Sliding Mode Technique

This paper is concerned with the problem of observer‐based control for a class of uncertain neutral‐type systems subjected to external disturbance by utilizing sliding mode technique. A novel sliding mode control (SMC) strategy is proposed based on the state estimate and the output. A new sufficient condition of robust asymptotic stability with disturbance attenuation level for the overall systems composed of the original system and error system in the sliding mode is derived in terms of a linear matrix inequality (LMI). Then, a new adaptive controller is designed to guarantee the reachability of the predefined sliding surface in finite‐time. Finally, numerical examples are provided to verify the effectiveness of the proposed method.     

r‐consensus control for higher‐order multi‐agent systems with digraph

This paper studies a consensus problem for lth (l ≥ 2) order multi‐agent systems with digraph, namely, for a fixed r (0 ≤ r ≤ l ? 1), the rth derivative of the states x_i of agents are convergent to a constant value and, for every k (0 ≤ k ≤ l ? 1), are convergent to zeros. A new concept of r‐consensus is introduced and new consensus protocols are proposed for solving such an r‐consensus problem. A sufficient and necessary condition for r‐consensus is obtained. As special cases, criteria for third‐order systems are given, in which the exact relationship between feedback gains is established. Finally, an illustrative example is given to demonstrate the effectiveness of these protocols.     

Dynamic Output‐Feedback Control for T‐S Fuzzy Systems with Input Time‐Varying Delay

This paper considers the problem of the control for T‐S fuzzy systems with input time‐varying delay via dynamic output feedback. Firstly, by applying the reciprocally convex approach, new delay‐dependent sufficient condition for performance analysis is obtained. Then, a less conservative condition for the existence of the controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in the considered system, the time‐delay term is included in the measured output. This results in the difficulty in designing the controllers being increased and the obtained results being applied to a wider class of fuzzy systems than the most existing ones. The main contribution of this work lies in the application of the reciprocally convex inequality and the time‐delay term included in the measured output. Finally, the advantages and effectiveness of the present results are shown by several numerical examples.     

Low Frequency Sensitivity Function Constraints for Nonlinear ‐stable Networked Control

The paper derives a robust networked controller design method for systems with saturation where the delay is large and uncertain, as in one‐directional data flow‐control. A classical linear H_∞ criterion is first formulated in terms of the sensitivity and complementary sensitivity functions. A new asymptotic constraint is then derived, which specifies the minimum amount of low frequency gain that is needed in the sensitivity function to conclude on non‐linear closed loop ‐stability using the Popov criterion. This result guides the selection of the design criterion, thereby adjusting the linear controller design for better handling of delay and saturation. The controller design method then uses gridding to pre‐compute a subset of the stability region. Based on the pre‐computed region, a robust ‐stable controller can be selected. Alternatively, an adaptive controller could recompute ‐stable controllers on‐line using the pre‐computed region. Simulations show that the controller meets the specified stability and performance requirements.     

Robust Sliding Mode Control Design for Mismatched Uncertain Systems with a Performance

This paper presents an optimal design of sliding mode controller with a constraint for a general class of uncertain systems. The method proposed here takes into account nonmatching disturbance signals and nonmatching system model uncertainties. Without requiring any transformation or restriction on the input matrix, our approach leads to a straightforward design which can be easily solved by using linear matrix inequality (LMI) technique. By solving the problem of optimal sliding motion design with some quadratic constraints based on LMIs, a mixed approach is presented to reduce the effect of uncertainties and disturbances on the sliding motion. Finally, we give simulation results for controlling a chemical reactor to illustrate the applicability of the proposed scheme for uncertain time‐delay systems or mismatched uncertain systems.     

Quantized Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information

This paper investigates the problem of quantized filtering for a class of continuous‐time Markovian jump linear systems with deficient mode information. The measurement output of the plant is quantized by a mode‐dependent logarithmic quantizer, and the deficient mode information in the Markov stochastic process simultaneously considers the exactly known, partially unknown, and uncertain transition rates. By fully exploiting the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for quantized performance analysis is first derived, and then two approaches, namely, the convex linearization approach and iterative approach, to the filter synthesis are developed. It is shown that both the full‐order and reduced‐order filters can be obtained by solving a set of linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). Finally, two illustrative examples are given to show the effectiveness and less conservatism of the proposed design methods.     

Composite Disturbance‐Observer‐Based Control and Control for High Speed Trains with Actuator Faults

To guarantee the position and velocity tracking performance of high speed trains (HSTs) with actuator faults, a composite control algorithm consisting of the disturbance‐observer‐based control (DOBC) and control is proposed. Based on the multiple point‐mass model, the dynamics of HSTs is established by a cascade of carriages which are connected by flexible couplers, during the procedure of which, the running resistance, actuator faults and multiple disturbances are taken into account. The multiple disturbances are composed of two parts, one of which is the ramp resistance due to the track slope, the other is unknown gusts which can be modeled as a harmonic disturbance with time‐varying frequency. The unknown gusts is estimated and rejected via the DOBC methodology, meanwhile, the running resistance and the ramp resistance are attenuated by the control methodology. According to the Lyapunov stability analysis and LMI‐based algorithms, main results are derived such that the closed‐loop system is asymptotically stable and the desired performance can be guaranteed. Compared with the numeral simulation results with the single control method, it is demonstrated that the proposed control methodology is more effective and the system has a higher precision of position and velocity tracking.     

Spline Based Pseudo‐Inversion of Sampled Data Non‐Minimum Phase Systems for an Almost Exact Output Tracking

This paper considers the problem of achieving a very accurate tracking of a pre‐specified desired output trajectory , for linear, multiple input multiple output, non‐minimum phase and/or non hyperbolic, sampled data, and closed loop control systems. The proposed approach is situated in the general framework of model stable inversion and introduces significant novelties with the purpose of reducing some theoretical and numerical limitations inherent in the methods usually proposed. In particular, the new method does not require either a preactuation or null initial conditions of the system. The desired and the corresponding sought input are partitioned in a transient component ( and u_t(k), respectively) and steady‐state ( and u_s(k), respectively). The desired transient component is freely assigned without requiring it to be null over an initial time interval. This drastically reduces the total settling time. The structure of u_t(k) is a priori assumed to be given by a sampled smoothing spline function. The spline coefficients are determined as the least‐squares solution of the over‐determined system of linear equations obtained imposing that the sampled spline function assumed as reference input yield the desired output over a properly defined transient interval. The steady‐state input u_s(k) is directly analytically computed exploiting the steady‐state output response expressions for inputs belonging to the same set of .     

Non‐Fragile Extended Dissipativity Control Design for Generalized Neural Networks with Interval Time‐Delay Signals

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile performance, non‐fragile performance, non‐fragile passive performance, non‐fragile mixed and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system.     

Quasi‐Time‐Dependent Controller for Discrete‐Time Switched Linear Systems With Mode‐Dependent Average Dwell‐Time

This paper is concerned with the stability and stabilization problem of a class of discrete‐time switched systems with mode‐dependent average dwell time (MDADT). A novel Lyapunov function, which is both mode‐dependent (MD) and quasi‐time‐dependent (QTD), is established. The new established Lyapunov function is allowed to increase at some certain time instants. A QTD controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed performance index. The new QTD robust controller designed in this paper is less conservative than the mode independent one which is frequently considered in literatures. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the developed results.      

Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems

This paper proposes a new scheme for estimating the actuator and sensor fault for Lipschitz nonlinear systems with unstructured uncertainties using the sliding mode observer (SMO) technique. Initially, a coordinate transformation is introduced to transform the original state vector into two parts such that the actuator faults only appear in the dynamics of the second state vector. The concept of equivalent output error injection is then employed to estimate the actuator fault. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Furthermore, the proposed actuator fault estimation method is extended to sensor fault estimation. Finally, the effectiveness of the proposed scheme in estimating actuator and sensor faults has been illustrated considering an example of a single‐link flexible joint robot system.     

Controllability of Semilinear Systems of Parabolic Equations with Delay on the State

In this paper we prove the approximate controllability of the following semilinear system parabolic equations with delay on the state variable where Ω is a bounded domain in is a n × n non diagonal matrix whose eigenvalues are semi‐simple with non negative real part, the control u belongs to and B is a n × m matrix. Here τ≥0 is the maximum delay, which is supposed to be finite. We assume that the operator L:L²([?τ,0];Z)→Z is linear and bounded with and the nonlinear function f:[0,r] × IRⁿ×IR^m→IRⁿ is smooth and bounded.     

Robust Control of Discrete‐time Singular Systems via Integral Sliding Surface

In this paper, the sliding mode control for a class of uncertain discrete‐time singular system with performance constraint is studied. By taking the singular matrix E into consideration, a new type of integral sliding mode surface is firstly introduced, based on which a sufficient condition is derived to guarantee the sliding mode dynamics admissible with a given γ‐level disturbance attenuation of the unmatched disturbance. A controller law is also given to keep the system trajectory staying in a neighborhood of the ideal sliding surface. Finally, a numerical example is given to show the effectiveness of the proposed approach.     

Improved Adaptive Controller Synthesis of Piecewise‐Affine Systems

This paper considers the adaptive control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptive control of PWS can be reduced to the control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.