Network‐based robust event‐triggered control for continuous‐time uncertain semi‐Markov jump systems

This article investigates the event‐triggered (ET) states feedback robust control problem for a class of continuous‐time networked semi‐Markov jump systems (S‐MJSs). An ET scheme, which depends on semi‐Markov process, is presented to design a suitable controller and save communication resources. To cope with the network transmission delay phenomenon, a time‐delay S‐MJSs model under the ET scheme is introduced to describe this phenomenon. Then, it is assumed that the communication links between event detector and zero‐order holder are imperfect, where the signal quantization and the actuator fault occur simultaneously. The sufficient conditions are derived by means of linear matrix inequalities approach, which guarantees the stochastic stability of the constructed time‐delay S‐MJSs in an optimized performance level. Based on these criteria, the parameters of controller under the ET scheme are readily calculated. Some simulation results with respect to F‐404 aircraft engine system for two kinds of ET parameters are given to validate the proposed method.     

An iterative approach for the discrete‐time dynamic control of Markov jump linear systems with partial information

The , and mixed dynamic output feedback control of Markov jump linear systems in a partial observation context is studied through an iterative approach. By partial information, we mean that neither the state variable x(k) nor the Markov chain θ(k) are available to the controller. Instead, we assume that the controller relies only on an output y(k) and a measured variable coming from a detector that provides the only information of the Markov chain θ(k). To solve the problem, we resort to an iterative method that starts with a state‐feedback controller and solves at each iteration a linear matrix inequality optimization problem. It is shown that this iterative algorithm yields to a nonincreasing sequence of upper bound costs so that it converges to a minimum value. The effectiveness of the iterative procedure is illustrated by means of two examples in which the conservatism between the upper bounds and actual costs is significantly reduced.     

Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

This paper presents techniques to linearly combine the sensor measurements and/or actuator inputs of a linear time‐invariant system to obtain a new system that is interior conic with prescribed bounds. In the optimal sensor combination problem, a desired system output is defined, and in the optimal actuator combination problem, a desired system input is defined, along with a frequency bandwidth in which the desired system input or output should be matched. The simultaneous optimal sensor and actuator combination problem includes desired system outputs and inputs. In all cases, the weighted or norm of the difference between the system with linearly combined sensors or actuators and the desired system is minimized while rendering the new system interior conic with prescribed bounds. The weighting transfer matrix used in the ‐ or ‐optimization problem is determined by the frequency bandwidth of interest. The individual sensor and actuator combination methods involve linear matrix inequality constraints and are posed as convex optimization problems, whereas the combined sensor and actuator method is an iterative procedure composed of convex optimization steps. Numerical examples illustrate superior tracking performance with the proposed sensor and actuator combination techniques over comparable techniques in the literature when implemented with a simple feedback controller. Robust asymptotic stability of the closed‐loop system to plant uncertainty is demonstrated in the numerical examples.     

A multilevel sampled‐data approach for resilient navigation and control of autonomous systems

Autonomous systems are rapidly becoming an integrated part of the modern life. Safe and secure navigation and control of these systems present significant challenges in the presence of uncertainties, physical failures, and cyber attacks. In this paper, we formulate a navigation and control problem for autonomous systems using a multilevel control structure, in which the high‐level reference commands are limited by a saturation function, whereas the low‐level controller tracks the reference by compensating for disturbances and uncertainties. For this purpose, we consider a class of nested, uncertain, multiple‐input–multiple‐output systems subject to reference command saturation, possibly with nonminimum phase zeros. A multirate output‐feedback adaptive controller is developed as the low‐level controller. The sampled‐data (SD) design of this controller facilitates the direct implementation on digital computers, where the input/output signals are available at discrete time instances with different sampling rates. In addition, stealthy zero‐dynamics attacks become detectable by considering a multirate SD formulation. Robust stability and performance of the overall closed‐loop system with command saturation and multirate adaptive control are analyzed. Simulation scenarios for navigation and control of a fixed‐wing drone under failures/attacks are provided to validate the theoretical findings.     

Characterization and optimization of the smoothed spectral abscissa for time‐delay systems

We introduce a new robust stability measure for systems with multiple pointwise delays, which is called smoothed spectral abscissa, consistently with the existing measure for delay‐free systems. Its main characteristics are that it is smooth with respect to the system parameters and it provides a trade‐off between the decay rate of the system solution and the norm of a transfer matrix related with the system. The smoothed spectral abscissa is implicitly defined in terms of the norm of an auxiliary system, and its computation is based on the so‐called delay Lyapunov matrix. We show that these features make the smoothed spectral abscissa suitable for the design of robust controllers by using standard gradient‐based optimization techniques and exploiting a novel characterization of the derivatives of the delay Lyapunov matrix with respect to the system parameters.     

Robust nonfragile observer‐based control of switched discrete singular systems with time‐varying delays: A sliding mode control design

This paper is devoted to the robust sliding mode control issue for a type of switched discrete singular systems with time‐varying delays under arbitrary switching. Since the system states are not available, the nonfragile observer strategy is used to generate the state estimation. By designing a novel sliding surface function, which is established on the estimation, new sufficient conditions via linear matrix inequalities are derived so that the closed‐loop system is admissible with an disturbance attenuation level γ. Furthermore, sliding mode controllers are given to guarantee the reachability of the quasi‐sliding mode and weaken the chattering. At last, examples are presented to verify the validity of our provided approach.     

A new -gain analysis framework for discrete-time switched systems based on predictive Lyapunov function

The work proposes the pre--gain analysis framework based on the newly raised nonweighted pre--gain performance index and predictive Lyapunov function, which is devoted to nonweighted -gain analysis and relevant control of discrete-time switched systems under mode-dependent average dwell time. This also provides new ideas for other disturbance-related studies. To begin with, the predictive Lyapunov function is established for switched nonlinear systems in the sense of better reflecting future system dynamics and future external disturbances. Hence, it is achievable to develop less conservative stability and nonweighted pre--gain criteria for switched linear systems. Further, a new disturbance-output expression is devised to match with the nonweighted pre--gain, whose function is to estimate and optimize the traditional nonweighted -gain of the underlying system through discussions. Then, a solvable condition is formulated to seek the piecewise time-dependent gains of switching controller in a convex structure, ensuring the global uniform exponential stability with nonweighted pre--gain and thereby attaining much smaller non-weighted -gain. Finally, the simulation comprised of a circuit system and a numerical example manifests the impressive potential of the obtained results for the purpose of preferable disturbance attenuation performances.     

Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.     

Quasi‐time‐dependent asynchronous filtering for discrete time switched systems via the event triggering mechanism

This article is concerned with the quasi‐time‐dependent asynchronous filter design problem for a class of discrete‐time switched systems via the event‐triggering mechanism. Applying the quasi‐time‐dependent Lyapunov functions and the mode‐dependent average dwell time technique, an asynchronous filter is designed with a weighted performance index; the filter parameter matrices are quasi‐time‐dependent in each event‐triggering‐dependent sampling interval; both cases (Case 1: no more than one switching, Case 2: multiple switchings) are taken into account in this sampling interval, by which the assumption, that the maximal asynchronous period is not larger than the minimal dwell time, is relaxed in this article. Simulation examples are given to show the less conservatism and effectiveness of the proposed results.     

On the dual linear periodic time‐delay system: Spectrum and Lyapunov matrices,with application to analysis and balancing

We present novel theoretical concepts for linear time‐periodic systems with multiple delays, which are closely related to the spectral properties and Lyapunov matrices. At the basis of the main results is the associated dual system, constructed by transposition of the systems matrices and affine transformations of their arguments. We introduce, for the first time, the concepts of the norm and the dual Lyapunov matrix of periodic systems with delays. We show that the primal and dual system have the same norm, characterized by primal and dual delay Lyapunov equations, which extend the well‐known results for time‐invariant systems with delays, and periodic systems without delays. Having at hand the pair of primal‐dual Lyapunov matrices, along with some energy interpretations, allow us to generalize the concept of position balancing and explore its potential for model reduction. The obtained results are illustrated by several examples, including the delayed Mathieu equation.     

Stability and stabilization for singularly perturbed systems with Markovian jumps

This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ?_i‐free but involving its bound are developed by constructing an ?_i‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.     

A less conservative approach to handle time‐varying parameters in discrete‐time linear parameter‐varying systems with applications in networked control systems

This article proposes a new strategy to deal with linear parameter‐varying discrete‐time systems, whose time‐varying parameters can be written as solutions (such as exponential, trigonometric, or periodic function) of a linear difference equation (DE). The novelty is to explicitly exploit the precise knowledge of the function describing the time‐varying parameter by incorporating the associated DE in the conditions, providing less conservative results when compared with conventional approaches based on bounded or arbitrary rates of variation. The advantage of the method comes from the fact that, differently from the available methods, the pointwise stability for the whole domain of the time‐varying parameters is not a necessary condition to obtain feasible solutions. The applicability and benefits of the proposed technique are investigated in terms of numerical examples concerning robust stability analysis,  filtering, and  state‐feedback control. As a final contribution, the problem of time‐varying sampling periods in the context of networked control systems is investigated using the proposed strategy. A numerical example based on a practical application is presented to illustrate the superiority of the approach when compared to methods from the literature based on matrix exponential computation.     

Asynchronous control for two‐dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities

This study focuses on the asynchronous control problem for two‐dimensional discrete‐time hidden Markovian jump systems where the mode observation conditional probability matrix is partly known. Considering the original system modes are invisible, the observed modes emitted from an observer serve as an alternative for stability analysis and controller design where a mode observation conditional probability matrix is constructed to characterize the emission between system modes and observed modes. Specially, only partly known information of the mode observation conditional probability matrix is accessible. With the introduction of the free‐connection weighting matrices, the asymptotic mean square stability criterion is firstly derived based on Lyapunov method. This introduction provides a further degree of relaxation and less conservatism is therefore achieved. Secondly, we present synthesis conditions for asynchronous state feedback controller design given in terms of a set of interconnected linear matrix inequalities. Moreover, cluster concept based on the partitions of observed modes is adopted which helps to decrease the number of controllers and simplify the design complexity. A numerical example, regarding the cases with and without clustering of the observed modes, is presented to illustrate the effectiveness of the proposed method.     

Stability and stabilization for stochastic Cohen‐Grossberg neural networks with impulse control and noise‐induced control

By applying the It formula, the Gronwall inequality, and the law of large numbers technique, a new simple sufficient inequality condition is presented for the almost surely exponential stability of the stochastic Cohen‐Grossberg neural networks with impulse control and time‐varying delays. Moreover, a new result is also given for the existence of unique states of the systems. An impulsive controller and a suitable noise controller are also given at the same time. The condition contains and improves some of the previous results in the earlier references.     

Iterative ‐conic controller synthesis

This paper proposes a method to synthesize controllers that minimize an upper bound on the closed‐loop ‐norm while imposing desired controller conic bounds. An initial conic controller is synthesized and iteratively improved. Conic sectors can be used to characterize a variety of input‐output properties, such as gain, phase, and minimum gain. If such plant properties hold robustly to uncertainty present, then closed‐loop stability can be ensured robustly via the Conic Sector Theorem by imposing desired controller conic bounds. Consequently, this paper provides a versatile optimal and robust controller synthesis method. Moreover, it relies only on the solution of convex optimization problems subject to linear matrix inequality constraints, making it readily implementable.     

Direct synthesis of reduced order H controllers for a class of multivariable plants

Given an nth order, -control input, p-measured output generalized plant, this article proposes a simple, direct approach to design an output feedback H controller with order satisfying for , or for . For this purpose, the output feedback H control problem is transformed into an H state feedback problem for an augmented generalized system. A class of plants for which this transformation always exists and the ensuing controller has order as above, is identified. As a result, for such plants, the reduced order H controller gains are found just by solving a simple linear matrix inequality problem used in state feedback based H control. The efficacy of the proposed approach is studied on some benchmark examples.     

Data‐based optimal Denial‐of‐Service attack scheduling against robust control based on Q‐learning

Attack optimization is an important issue in securing cyber‐physical systems. This paper investigates how an attacker should schedule its denial‐of‐service attacks to degrade the robust performance of a closed‐loop system. The measurements of system states are transmitted to a remote controller over a multichannel network. With limited resources, the attacker only has the capacity to jam sparse channels and to decide which channels should be attacked. Under an framework, a data‐based optimal attack strategy that uses Q‐learning is proposed to maximize the effect on the closed‐loop system. The Q‐learning algorithm can adaptively learn the optimal attack using data sniffed over the wireless network without requiring a priori knowledge of system parameters. Simulation results sustain the performance of the proposed attack scenario.     

A discrete‐time nonlinear state observer for the anaerobic digestion process

This paper is concerned with the design of an LMI‐based discrete‐time nonlinear state observer for an anaerobic digestion model. In presence of disturbances in both the dynamics of the model and the output measurement signals, the proposed observer robustly estimates all state variables including bacteria concentrations, which are costly and difficult to measure. In the goal to increase applicability of the proposed observer for other systems, we present the theoretical results in a general way. First, due to the use of Young's inequality in a convenient way, we get new sufficient conditions, expressed in terms of bilinear matrix inequalities (BMIs), ensuring the criterion. Then, to render the BMIs convex, two alternative solutions are proposed, where both lead to linear matrix inequality (LMI) conditions. It is shown analytically and numerically that these two solutions provide less conservative LMI conditions compared to the existing methods in the literature. To validate the proposed methodology on a real‐world model, an application to an anaerobic digestion model is given.     

An interval observer for uncertain continuous‐time linear systems

To design robust interval observers for uncertain continuous‐time linear systems, a new set‐integration approach is proposed to compute trajectory tubes for the estimation error. Because this approach, the order‐preserving condition on the dynamics of the estimation error is no longer required. Therefore, synthesis methods can be used to compute observer gains that reduce the impact of the system uncertainties on the accuracy of the estimated state enclosures. The performance of the proposed approach is showcased through illustrative numerical examples.