Set stabilization of boolean networks via sampled‐data control

The paper investigates the sampled‐data state feedback control (SDSFC) for set stabilization of Boolean control networks (BCNs). Set stabilization means that a system converges to a subset of the state space under certain controllers. Assume that the given subset is , where and sampling period is τ. We consider two conditions q ≤ τ;q > τ and for any given subset , calculate the corresponding largest control invariant subset (LCIS). Moreover, a design procedure to calculate all possible SDSFCs for set stabilization of BCNs is obtained. Ultimately, we provide an example to demonstrate the efficiency of the results.     

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.     

Sliding Mode Control for Markovian Jump Systems with Generalized Switching

In this paper, the sliding mode control (SMC) problem for continuous‐time Markovian jump systems (MJSs) is considered, in which the transition rate matrix (TRM) is partially unknown and uncertain. Firstly, the sliding mode surface S(t) = 0 is designed, which is mode‐dependent. Therefore, is used instead of in the SMC algorithm. Via adopting a linear matrix inequality (LMI) approach, sufficient conditions are proposed to ensure that the reduced order system is exponentially stable in mean square. Furthermore, the reduced order system is completely insensitive to the external disturbance. Secondly, SMC law is designed correspondingly which dominated by a Markov process. It could drive the state trajectories onto the specified sliding mode surface in finite time quickly and maintain them on the surface in subsequently time. Thirdly, a new term in will be introduced in the designed SMC and should be handled by a new approach. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

Adaptive Fault‐Tolerant Attitude Tracking Control of Rigid Spacecraft on Lie Group with Fixed‐Time Convergence

This paper investigates the fixed‐time attitude tracking problem for rigid spacecraft in the presence of inertial uncertainties, external disturbances, actuator faults, and input saturation constraints. The logarithm map is first utilized to transform the tracking problem on SO(3) into the stabilization one on its associated Lie algebra ( ). A novel nonsingular fixed‐time‐based sliding mode is designed, which not only avoids the singularity but also guarantees that the convergence time of tracking errors along the sliding surface is independent of the state value. Then, an adaptive fault‐tolerant control law is constructed, in which an online adaptive law is incorporated to estimate the upper boundary of the lumped uncertainties. The combined control scheme enforces the system state to reach a neighborhood of the sliding surface in the sense of the fixed‐time concept. The key feature of the resulting control scheme is that it can accommodate actuator failures under limited control torque without the knowledge of fault information. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed fixed‐time controllers.     

On the regional control problem of the bilinear wave equation

The present research deals with regional optimal control problem of the bilinear wave equation evolving on a spatial domain $\mathrm{\Omega }\subset {\mathrm{ℝ}}^n,n\ge 1$. Such an equation is excited by bounded controls that act on the velocity term. It addresses the tracking of a desired state all over the time interval $[0,T]$ only on a subregion $\omega$ of $\mathrm{\Omega }$ with minimum energy. Then, we prove that an optimal control exists and is characterized as a solution to an optimality system. Algorithm for the computation of such a control is given and successfully illustrated through simulations.     

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 .     

Hybrid-triggered scheme asynchronous control for hidden Markov jump systems with partially unknown probabilities and cyber attacks

This paper is concerned with the issue of hybrid-triggered scheme $H_{\infty }$ asynchronous control for networked Markov jump systems (MJSs) with probabilistic cyber attacks. First, in view of the subsistent phenomenon that the controller cannot capture the system modes synchronously, the hidden Markov model (HMM) with partly unknown probabilities is introduced in this article to describe such asynchronous phenomenon. In addition, the hybrid-triggered scheme includes time-triggered scheme and event-triggered scheme, in which the switching signal between two schemes obeys random Bernoulli distribution. By utilizing Lyapunov stability theory and matrix inequality technique, some sufficient conditions are developed, which can guarantee the networked MJSs mean-square asymptotically stable (MSAS) and $H_{\infty }$ performance; also, the desired controller gains are obtained by singular value decomposition (SVD) methods. Moreover, as the special cases of the results above, three corollaries are given. Finally, a numerical example and a pulse width-modulation-driven boost converter (PWMDBC) model are provided to demonstrate the usefulness and reliability of our developed approaches.     

Linear Diophantine equation (LDE) decoder: A training-free decoding algorithm for multifrequency SSVEP with reduced computation cost

Multifrequency steady-state visual evoked potentials (SSVEPs) have been developed to extend the capability of SSVEP-based brain-machine interfaces (BMIs) to complex applications that have large numbers of targets. Even though various multifrequency stimulation methods have been introduced, the decoding algorithms for multifrequency SSVEP are still in early development. The recently developed multifrequency canonical correlation analysis (MFCCA) was shown to be a feasible training-free option to use in decoding multifrequency SSVEPs. However, the time complexity of MFCCA is shown to be $O(n^3)$, which will lead to long computation time as $n$ grows, where $n$ represents the input size in decoding. In this paper, a novel decoding algorithm is proposed with the aim to reduce the time complexity. This algorithm is based on linear Diophantine equation solvers and has a reduced computation cost $O(nlogn)$ while remaining training-free. Our simulation results demonstrated that linear Diophantine equation (LDE) decoder run time is only one fifth of MFCCA run time under respective optimal settings on 5-s single-channel data. This reduced computation cost makes it easier to implement multifrequency SSVEP in real-time systems. The effectiveness of this new decoding algorithm is validated with nine healthy participants when using dry electrode scalp electroencephalography (EEG).     

Controlling the multi‐plant networked system with external perturbations via adaptive model‐based event‐triggered strategy

This paper concerns the multi‐plant networked control system with external perturbations by applying the adaptive model‐based event‐triggered control strategy. Compared with existing works, we introduce multiple plants topology in order to smooth the information exchanges among different plants. Gained insight into the adaptive model features in the view of event‐triggered thought, the event‐triggered rules, determining when the control inputs update, are obtained using the Lyapunov technique to reduce the communication cost. By designing some adaptive updating laws combined with the concept of event‐triggered, the unknown parameters in uncertain multi‐plant networked control systems are real‐time online estimated and adjusted with respect to the relevant nominal systems at event‐triggered instants. To avoid Zeno phenomena, a lower bound of event‐triggered execution interval is discussed. Furthermore, given the external perturbations, gain stability theory is introduced to analyze the stability of multi‐plant networked control systems with bounded perturbations, and then the sufficient conditions related to the multiple plants topology structure are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of our theoretic results.     

Distributed dynamic matrix control with constrained optimization for collision and obstacle avoidance of simulated multiple quadcopters

A system of fast moving quadcopters has a high risk of collisions with neighboring quadcopters or obstacles. The objective of this work is to develop a control strategy for collision and obstacle avoidance of multiple quadcopters. In this paper, the problem of distributed dynamic matrix control (DMC) for collision avoidance among a team of multiple quadcopters attempting to reach consensus in the horizontal plane and yaw direction ( $x,y$, and $\psi$) is investigated. Violations of a predetermined safety radius generates output constraints on the DMC optimization function, which has not been dealt with in the literature. Different from past works, the proposed strategy can perform collision avoidance in the $x$, $y$, and $z$-directions. In addition, logarithmic barrier functions are implemented as input rate constraints on the control actions. Extensive simulation studies for a team of quadcopters illustrate promising results of the proposed control strategy and case variations. In addition, DMC parameter effects on the system performance are studied, and a successful study for obstacle avoidance is presented.     

Approximate Controllabilty of Semilinear Dynamic Equations on Time Scale

In this paper we study the approximate controllability of semilinear systems on time scale. In order to do so, we first give a complete characterization for the controllability of linear systems on time scale in terms of surjective linear operators in Hilbert spaces. Then we will prove that, under certain conditions on the nonlinear term, if the corresponding linear system is exactly controllable on , for any , then semilinear system on time scale is approximately controllable on .     

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.     

Design of discrete PID controllers for maximizing stability margins

The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed-loop poles being inside the circle of radius $\rho$ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number $\epsilon$, a minimum value ${\rho }_{\epsilon }^{*}$ and the corresponding ${\rho }_{\epsilon }^{*}-\text{stabilizing}$ discrete PID controller set for achieving at least $1-{\rho }_{\epsilon }^{*}$ of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability-margin discrete PID controller design, two numerical examples are provided.     

Bifurcation and control of disease spreading networks model with two delays

In this paper, the dynamical behaviors are investigated for a complex network with two independent delays. Instead of taking time delays as bifurcation parameters, we choose probability $p$ and parameter $\mu$ as the control parameters to study their effects on local stability and Hopf bifurcation, respectively. Moreover, the conditions for generating Hopf bifurcation are given. Furthermore, we further discuss the effects of two time delays on the critical values of parameters $p$ and $\mu$. Finally, numerical simulations are used to illustrate the validity of the obtained results.     

Active fault detection and isolation in linear time-invariant systems: A geometric approach

In this work, a novel approach on active fault detection and isolation for linear time-invariant systems, named forced diagnosability, is proposed. This approach computes a continuous state feedback law to render a fault diagnosable, even when it cannot be diagnosed by using passive diagnosis methods. To do that, this work derives novel geometric relationships between unobservability and $(A,B)$-invariant subspaces that, under certain conditions, guarantee the existence of such state feedback law. The objective of the state feedback law is to force all the faults, except the one required to be diagnosed, named $L_d$, to reside in an unobservability subspace. This effectively decouples the effect of $L_d$ on the system output, from the effect of the other faults, allowing the design of a residual generator to detect and isolate the desired fault. The proposed state feedback law continuously forces diagnosability, and it can be computed in polynomial time. This avoids testing faults only at fixed time intervals and solving complex optimization problems required in other active diagnosis approaches. A numerical example is presented to illustrate the efficiency of the proposed approach.     

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.     

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.     

Convergence on iterative learning control of Hilfer fractional impulsive evolution equations

In this paper, impulsive fractional differential equations with Hilfer fractional derivatives of order and type $0\le \nu \le 1$ is considered. Convergence analysis of $P$-type and $P{I}^{\mu }$-type open-loop iterative learning scheme is studied in the sense of $\lambda$-norm. Examples are provided to explain the theory developed.     

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.