Predictor feedback control of discrete-time systems with multiple state delays and distinct input delays is investigated in this paper. At first, a prediction scheme for the considered system is developed step by step. Then, a predictor-based state feedback law is designed based on this prediction scheme. In addition, the property of the closed-loop system under the designed control law is analyzed. When the system state is unavailable for feedback, a full-order state observer is designed such that the current state can be estimated. With this estimated state, the stabilization for this class of time delay systems can also be achieved under the designed observer-based predictor feedback control law.

In this article, the attitude maneuver control with the arbitrary convergence time is investigated for rigid spacecraft. First, a time-varying sliding mode function expressed by a piecewise function is designed by using an exponential function. This designed sliding mode function contains two equilibria of the attitude control systems. Furthermore, an attitude control law is designed with the aid of this new sliding mode function such that the states of the closed-loop attitude system remain on the sliding mode surface from the initial time instant, and converge to the origin at an arbitrarily preset time. In addition, the unwinding phenomenon can also be avoided when the proposed control law is used.

In this paper, observer-based output feedback control is developed for discrete-time systems with multiple state delays and input delays. In order to estimate the system state, two types of state observers are designed, including a full-order observer and a reduced-order state observer. With the estimated state generated by the designed observers, predictor-based control laws are implemented. Further, the separation property of the closed-loop system under the designed control laws is revealed.

In this article, the data-driven optimal control problem is addressed for discrete-time linear periodic systems with unknown system dynamics. To reduce the number of iterations required by existing data-driven control algorithms, two novel value iteration (VI)-based adaptive dynamic programming (ADP) algorithms are presented. In these two VI algorithms, the latest updated estimates are utilized to approximate the unique positive definite solution of the algebraic Riccati matrix equation (ARE), and the suboptimal controller is obtained. Since the latest estimation is generally closer to the optimal value than that of the last iteration step, the number of iterations is significantly reduced in the two proposed algorithms. Moreover, the backward VI algorithm requires fewer iteration steps compared to the forward VI algorithm. In addition, the proposed methods do not require an initial stabilizing controller. Finally, two examples are provided to demonstrate the effectiveness of the two proposed iterative algorithms.

In this paper, the stabilization problem of discrete-time systems with both input delays and multiple state delays is concerned. For this end, two interesting properties are derived for the bivariant fundamental matrix related to a discrete-time linear system with multiple state delays. A prediction scheme of the considered system is presented via the corresponding bivariant fundamental matrix, and then a predictor-based feedback control law is proposed for the considered systems with both input delays and multiple state delays. Furthermore, the characteristic equation of the closed-loop system of the considered system under the designed predictor feedback law is analyzed. Finally, the effectiveness of the proposed method is illustrated by numerical examples.

In this article, the stabilization problem is investigated for input-delayed systems with unknown system dynamics. To solve this problem, a value iteration (VI)-based adaptive dynamic programming (ADP) algorithm is established to learn the state feedback controller from the data along the trajectory of the system. In order to design this control algorithm, the input-delayed system is transformed into a delay-free system at first. Thus, the algebraic Riccati matrix equation (ARE) of the delay-free system is iteratively solved in the absence of system model, and then the controller is designed by using the approximation to the solution of the ARE. In particular, the rank condition of the data-constructed matrices is satisfied by utilizing basis functions, and an initial stabilizing controller is not required in the proposed algorithm. Finally, the effectiveness of the proposed algorithm is illustrated by two practical examples.

The stabilization problem for discrete-time time-variant linear state-delayed systems with distinct input delays is investigated in this article. A predictor is constructed for this class of delayed systems in a concise and explicit form by using the state transition matrices as tools. With the aid of the proposed prediction scheme, a predictor-based feedback law is designed to stabilize the considered system. It is shown that the characteristic equation of the closed-loop system under the proposed predictor-based feedback law for the case of time-invariant systems is the same as that of the closed-loop system without distinct input delays. Finally, two numerical examples are employed to verify the effectiveness of the proposed method.

The attitude tracking control with unwinding-free performance for rigid spacecraft is studied in this article. A full-state feedback control law based on a hyperbolic sine function is developed such that the resulted closed-loop system can achieve two stable equilibria. By Lyapunov stability theory and Barbalat’s Lemma, it is proven that the obtained closed-loop system is almost globally asymptotically stable, and achieves unwinding-free performance. Further, by constructing a strict Lyapunov function, it is demonstrated that the two stable equilibria are exponentially stable. Moreover, subsets of attraction regions corresponding to each stable equilibrium are characterized. The simulation results illustrate that the proposed attitude control scheme can effectively avoid the unwinding problem during attitude tracking.

Motivated by the fact that there exists the operation of conjugation in quantum systems, the concept of bicon-numbers is proposed in this article. The bicon-numbers are defined by introducing two symbolic parameters into the set of complex numbers. The basic functions of these two symbolic parameters are specified by an axiom which abstracts the operation of complex conjugation. Basic properties are developed for the operations of addition and multiplication in the bicon-number set. In addition, several different forms are given for bicon-numbers, and the corresponding operation rules are established. By exploring the relations of the vensors in the bicon-number set, the structure of the bicon-number set is depicted, and real matrix representations of bicon-numbers are also presented. Besides, bicomplex matrix representations for bicon-numbers are also investigated in view that the operation of multiplication for bicomplex numbers possesses commutativity property. In addition, the matrices with bicon-numbers as entries are investigated, and state responses of some quantum systems are given within the framework of bicon-numbers.

In this article, a parametric predictor is constructed to predict the future state of a discrete-time linear system with a known constant input delay and external disturbances by introducing a tuning parameter. Then, a predictor-based feedback controller is given to attenuate the unknown disturbance signal. The ultimate bound of the state of the resulted closed-loop system is obtained when the state feedback control law based on this novel predictor is utilized. Based on the expression of the ultimate bounds, the capacity to attenuate the unknown disturbance is analyzed for the parametric predictor within a certain range of parameters. An easily calculated interval is provided for the range of the tuning parameter such that the proposed predictor achieves a better disturbance attenuation capacity. Moreover, for the unknown constant disturbance, the estimation error between the proposed predictor with an arbitrary parameter and the future state can be eliminated. Finally, two numerical examples are utilized to illustrate the effectiveness of the proposed parametric predictor for bounded time-varying disturbances.

State responses for several classes of linear systems are investigated in this article. The involved systems include state-delayed linear systems, and high-order linear systems. At first, the single-fundamental-matrix-based approach is extended to these systems, and their state responses are expressed by their fundamental matrices (FMs). In addition, the multiple-FMs-based approach is presented for these systems. Based on a group of FMs, the state responses for the considered time-invariant systems are derived. For the considered time-variant systems, their state responses are explicitly expressed by their transition matrices. As an application of the fundamental-matrix-based approach, a stabilizing control law is designed for a class of high-order fully actuated continuous-time linear systems with a single input-delay.

Although the literature on control of overhead crane systems is extensive and relatively mature, there is still a need to develop strategies that can simultaneously handle factors such as the double pendulum effect, variable cable length, input saturation, input dead zones, and external disturbances. This article is concerned with adaptive tracking control for underactuated overhead cranes in the presence of the above-mentioned challenging effects. The proposed controller is composed of the following two components. First, a tracking signal vector that effectively reduces system swing magnitudes is constructed to improve the transient performance and guarantee smooth operation of the system. Second, an adaptive law is designed to estimate and compensate for the overall effects of the friction, the external disturbances, and certain nonlinearities. The system stability has been proved rigorously via the Lyapunov method and Barbalat's lemma. Extensions to the cases with input saturation and dead zones have also been discussed. Extensive numerical simulations have been conducted to verify the performance and robustness of the proposed controller, in comparison to some existing methods.

This article studies the consensus problem of a class of multi-input–multi-output (MIMO) multiagent systems (MASs) subject to parametric uncertainties and external disturbances via a fully distributed model reference adaptive event-triggered control (MRA-ETC) protocol. Incorporate both the MRA and ETC, a reference model using the predicted relative state information initialized by intermittently collected state information of neighbors as input and a self-contained adaptive estimator of uncertainties are constructed, where the transmitted information is asynchronous and intermittent. We consider both the cases of matched and unmatched external disturbances, where each agent is assigned a reference model to track. Asymptotic consensus is achieved for the case of matched disturbances by using the sliding-mode control, while for the case of unmatched disturbances, the uniformly ultimately bound consensus is obtained via the adaptive$\sigma$-modification technique. The communication resources have been significantly saved via the proposed event-triggered mechanism (ETM) with strictly excluding the Zeno behavior. Moreover, with the help of the designed adaptive control gains for the reference models, the consensus algorithm can be implemented in a fully distributed fashion without employing any global information of the MASs. Finally, the simulation examples are illustrated to show the correctness of the proposed control schemes.

The bias compensation technique combined with the least‐squares estimation algorithm with forgetting factors is applied to the parameter estimation of output error models with moving average noise. It is shown that the bias term induced by the noise is determined by the weighted average variance of the white noise and the parameters of the unknown noise model. Therefore, in order to give a recursive estimation of the bias term, an interactive estimation of the weighted average variance and noise parameters is constructed by using the principle of hierarchical identification. In addition, a recursive form is also established to estimate the so‐called weighted average variance of the white noise. The estimation algorithm is finally established by combining the interactive estimation and the recursive estimation of weighted average variance. A simulation example is employed to show the effectiveness of the proposed bias compensation based least‐squares estimation algorithm with two forgetting factors.

A type of generalized proportional-integral-derivative observers is proposed for descriptor linear systems. Based on a general parametric solution to a type of generalized Sylvester matrix equations, a parametric design approach for such observers is established. The proposed approach provides parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes the elimination of impulsive behaviors, and guarantees the regularity of the observer system. The design method can offer all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances. In addition, a numerical example is employed to show the design procedure and illustrate the effect of the presented approach.

A parametric design approach for proportional-integral (PI) observers for continuous-time descriptor linear systems is proposed based on a complete general parametric solution to the generalized Sylvester matrix equation. The proposed approach provides complete parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding finite left eigenvector matrix of the observer system matrix, realizes elimination of impulsive responses, and guarantees the regularity of the observer system. The design method offers all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances and, thus, has great potentials in applications. A numerical example is employed to show the design procedure and illustrate the effect of the proposed approach. Simulation results show a satisfactory tracking performance for descriptor linear systems.