In this paper, a bias-Lyapunov iteration method is proposed to solve the optimal control problem of unknown Markovian jump linear systems. By incorporating a bias parameter into the conventional Lyapunov iteration method, the proposed method eliminates initial admissible control requirements. A model-based theoretical framework is subsequently established, accompanied by a rigorous convergence proof for the modified iteration process. Subsequently, a data-driven version of bias-Lyapunov iteration is developed to learn an optimal control for Markovian jump linear systems with completely unknown dynamics. Simulation examples validate the efficacy and advantage of the proposed bias-Lyapunov iteration method.

This study investigates the problem of achieving consensus within a prescribed time for general linear multiagent systems (MASs) operating over directed communication graphs, particularly when agents can only access relative output data via their onboard sensors. Under the assumption of strong observability, we design a periodic delayed output measurements-based distributed observer to recover the relative state information. Leveraging the reconstructed states, a linear time-varying control protocol is developed to ensure consensus is attained within the desired time. In contrast to conventional approaches, our method brings several key benefits. Most importantly, it removes the requirement for direct data exchange over the network, making the system inherently robust against cyber-attacks. Furthermore, the protocol is entirely distributed, which enhances adaptability to dynamic communication structures. At last, since the proposed method utilizes linear state feedback, it avoids the need for real-time solutions of system-related differential equations, thus reducing computational overhead. Numerical simulations demonstrate the efficacy of the proposed strategy.

This paper presents the bias-policy iteration, a modified adaptive dynamic programming method, to achieve optimal control design of discrete-time nonlinear systems. Firstly, the formulation of the bias-policy iteration method and the thorough convergence analysis are provided. By leveraging the bias parameter, the constraint of admissible control is relaxed while the fast convergence of traditional policy iteration is inherited. The actor-critic framework is utilized to realize the implementation of the proposed method accordingly. Finally, the proposed method is applied to optimal control problem of the inverted pendulum system. The simulation is conducted to verify the effectiveness of the bias-policy iteration approach.

This paper studies the stochastic cooperative output regulation problem for linear discrete-time multi-agent systems (MASs) with Markov switching topologies and communication/input delays. First, a moment stability criterion for an interconnected time-homogeneous Markov jump linear systems is builded. Then, based on the moment stability criterion, a fully distributed output regulation protocol is designed to solve the stochastic cooperative output regulation problem successively. Finally, a numerical simulation is provided to validate the efficiency of the designed protocol.

In this paper, we focus on the proximate orbital pursuit-evasion game of two spacecraft with magnitude-bounded continuous controls. Two scenarios are considered depending on whether the pursuer can access the control magnitude of the evader initially. When the pursuer accesses such information, we propose a fast numerical method for computing a sub-optimal control of the pursuer that guarantees the capture of the evader. The key to accelerating the solving is using a polynomial to approximate an important integration in the control computation, whose direct computing involves repeated calculations of matrices’ singular values. When the control magnitude of the evader is unavailable, we first propose a simple estimator for the evader’s control magnitude, by which the pursuer can estimate the maximal control effort of the evader disclosed over the history based on measured states. Based on the estimate, another fast method for computing the sub-optimal pursuing control is proposed based again on polynomial approximation. Then, considering practical measurements, we analyze how measurement noises influence the estimation of the control magnitude and the pursuing control computation. Finally, we present numerical examples to test the proposed computing methods and discuss the influence of noises.

The prescribed-time semi-global control for a class of time-varying uncertain systems under a nonlinear growth condition is achieved via linear time-varying feedback. The involved nonlinear uncertainties are categorized as unmatched uncertainties (depending on states and time) and matched uncertainties (depending on time only). Both state feedback and observer-based output feedback are constructed relying on the properties of parametric Lyapunov equations and the time-varying gains acquired by solving scalar differential equations. The proposed output feedback approach features a separation principle, that is, the construction of prescribed-time observer and prescribed-time state feedback is conducted separately. The proposed control scheme is validated by simulations carried out on a standard mechatronics system with complicated loads.

This article examines the normal form of a multiple-input-multiple-output (MIMO) linear time-varying (LTV) system. It explores the transformation of such a system into its normal form using an LTV transformation, if it possesses a general relative degree that may not be uniform (strict). Based on the obtained normal form, the internal and external dynamics as well as the inverse system of the LTV system are investigated. Additionally, the zero dynamics can be effectively parameterized. Moreover, by employing the derived LTV normal form, the proportional-derivative output-feedback stabilization and output tracking problems are resolved. Finally, an illustrative example is presented to showcase the effectiveness of the proposed controllers.

This paper studies the differential flatness of time-delay systems (TDSs). Based on factorizations in the pseudo-polynomials ring, a flat output for the single-input linear commensurate TDS (namely, the delays in the system are multiplies of a certain unit delay) is constructed explicitly. Then the TDS can be converted into a high-order fully actuated system (HOFAS) model with the generalized state as the flat output, and the finite spectrum assignment (FSA) problem can be solved immediately by using the HOFAS approach, which provides some new insight into the study of the FSA problem. By parameterizing the considered TDS via the constructed flat output and applying the interpolation theory, the state trajectory planning problem and state tracking problem are solved, resulting a two-degree-of-freedom (2DOF) controller. Numerical examples demonstrates the effectiveness of the presented approach.

This paper delves into the adaptive prescribed-time leader-following consensus control within a class of nonlinear networked multi-agent systems. Firstly, the nonlinear multi-agent network subjected to matched disturbances employs parameterization of the non-identical unknown nonlinear dynamics. Distributed bounded protocols leveraging parametric Lyapunov equation and adaptive laws are introduced, incorporating local consensus errors and relative state feedback. The proposed solution attains prescribed-time consensus, ensuring the boundedness of estimated parameters. Subsequently, building upon these findings, fully distributed adaptive bounded protocols for the nonlinear multi-agent networks in the lower triangular structure are presented. These fully distributed protocols rely solely on the relative states between the neighboring agents and do not necessitate information about the underlying communication topology to attain a prescribed-time consensus. Finally, the established results are substantiated through numerical examples, illustrating their effectiveness.

This article focuses on the dual-observer-based stabilization of linear systems with delays in both the inputs and outputs. By a model reduction approach the system can be converted to an equivalent linear system without delays, for which a dual-observer-based stabilizing controller can be designed. However, such a controller is infinite dimensional or memory-based. To solve such a problem, a modified memoryless dual-observer-based stabilizing controller is designed, and the closed-loop stability is proven under some additional conditions. Compared with the reduced-order observer-based controller, the dimension of the dual-observer-based controller is smaller if the system has more inputs than outputs. At the same time, the design approach is more challenging in proving closed-loop stability, as for example a more intricate Lyapunov-Krasovskii functional has to be constructed associated with the proposed approach. The proposed approach is applicable to both continuous-time and discrete-time systems. Numerical simulations validate the effectiveness of the proposed method.

In this article, the λ -policy iteration ( λ -PI) method for the optimal control problem of discrete-time linear systems is reconsidered and restated from a novel aspect. First, the traditional λ -PI method is recalled, and some new properties of the traditional λ -PI are proposed. Based on these new properties, a modified λ -PI algorithm is introduced with its convergence proven. Compared with the existing results, the initial condition is further relaxed. The data-driven implementation is then constructed with a new matrix rank condition for verifying the feasibility of the proposed data-driven implementation. A simulation example verifies the effectiveness of the proposed method.

This article studies the design of prescribed-time full- and reduced-order unknown input observers (UIOs) for linear singular systems with input delay, satisfying the acrlong OMC, and the strong observability condition. To this end, a condition in terms of a matrix equation is first used to transform the considered linear singular system into a regular one with unknown input. Then, prescribed-time full- and reduced-order UIOs are established by employing a periodic delayed output approach such that the estimation error converges to zero in prescribed time. Finally, comparative simulations are shown to demonstrate the effectiveness and superiority of the proposed approaches.

This article establishes the linear static and dynamic time-varying event-triggered and self-triggered controllers with designable minimal interevent times (MIETs) to stabilize input constrained linear systems. We first design a static event-triggered control (ETC) algorithm, in which the control gain dependent on the solution to a parametric Lyapunov equation is time-varying and is only scheduled at a specified time decided by the static event-triggered mechanism (ETM). This can improve the control performance of the closed-loop system and save communication resources synchronously. Moreover, a dynamic ETC is designed to further increase the interevent times. Furthermore, in order to avoid the continuous monitoring of system status, the static and dynamic self-triggered control (STC) algorithms are also established. The Zeno phenomenon is avoided and the corresponding designable MIET is given in all established algorithms. Specifically, the designed control algorithms are extended to solve the corresponding semi-global stabilization problem. In some cases, the MIETs can be selected as an arbitrarily large bounded constant that has no relationship with system itself. Finally, applications to the spacecraft rendezvous control system verify the effectiveness of the designed algorithms.

Stability analysis is considered in this paper for linear neutral delay systems subject to two different delays in both the state variables and the retarded derivatives of state variables. By choosing a suitable state vector indexed by an integer$k$, a new augmented Lyapunov-Krasovskii functional (LKF) is constructed, and a stability criterion based on linear matrix inequalities is developed accordingly. It is shown that the proposed condition is less conservative than the existing methods due to the introduction of the delay-product-type integral terms in the LKF. The resulting stability criterion is then applied to the robust stability analysis of neutral delay systems with norm-bounded uncertainty. Moreover, a delay-independent stability criterion is developed based on the proposed LKF, and its frequency-domain interpretation is also given. These developed stability criteria indexed by an integer$k$exhibit a hierarchical character: the larger the integer$k$, the less conservatism of the resulting stability criterion. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed method.

This article studies the problem of finite-time, fixed-time, and prescribed-time stability analysis and stabilization. First, a linear time-varying (LTV) inequality-based approach is introduced for prescribed-time stability analysis. Then, it is shown that the existing nonlinear Lyapunov inequalities-based finite- and fixed-time stability criteria can be recast into the unified framework of the LTV inequality-based approach for prescribed-time stability. Finally, the unified LTV inequality-based approach is used to solve the global prescribed-time stabilization problem of the attitude control system of a rigid spacecraft with disturbance, and a bounded nonlinear time-varying controller is proposed via back stepping. Numerical simulations are presented to show the effectiveness of the proposed methods.

Multisource remote sensing data observed from sensors with different resolutions and physical properties will present heterogeneous tensor structures and diverse feature distributions, thus posing a significant challenge for building an effective classifier for cross-source object recognition. The representative support tensor machine classifier can inherently preserve tensor structure information of remote sensing data and obtain effective recognition ability, while it can only handle same-source and same-distributed homogeneous data and fail to deal with cross-source heterogeneous remote sensing data with complex structures and various distributions. Therefore, the domain adaptation support tensor machine (DA-STM) is proposed to learn a uniform model for cross-source object recognition. To process heterogeneous tensor from different sources, multiple factor matrices with different modes are constructed to eliminate the structural differences and reduce distribution discrepancies for multisource heterogeneous data. To excavate shared classification information across sources, the shared core tensor is established to learn the classification hyperplane jointly using multisource data, and the adaptive sample labels are then embedded into the model to recover the class information during model training. To ensure efficient training, the decomposition algorithm is developed to accelerate the solving of dual problem of DA-STM. In addition, to improve classification performance as the acquirement of sequential samples, the proposed DA-STM is further upgraded to an online version to update the classification parameters dynamically. Using multi-resolution and multi-angle optical images as well as multi-angle SAR images, experimental results demonstrate that the proposed DA-STM can obtain better recognition results than typical domain adaptation methods.

This article considers the design of prescribed-time unknown input observers (PTUIOs) for linear systems, i.e., observers that estimate the state of a linear system with unknown inputs at a prescribed finite time. To this end, the generalized inverse is used first to transform a form amenable for observer design. Then, PTUIOs are designed by using the periodic delayed output so that their estimation errors converge to zero at a prescribed time. Both full-order and reduced-order PTUIOs are considered. For the reduced-order observer design, an alternative approach is also adopted, based on a transformation to a generalization of the normal form. In addition, the proposed PTUIOs are applied to estimate faults. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.

This paper studies the prescribed-time input-to-state stabilization problem of normal nonlinear systems. With the help of some key properties of a class of parametric Lyapunov equations, the prescribed-time input-to-state stabilization problem of normal nonlinear systems under matched uncertainties is studied. Some bounded time-varying controllers are proposed. It is shown that the closed-loop systems are prescribed-time input-to-state stable. Finally, the effectiveness of the established methods is illustrated by two physical systems.

This article investigates the global stabilization problem of the circular orbit rendezvous system with actuator saturation and time-delay. By decomposing the linearized relative motion equations into a cascade of neutral stable linear systems, linear state feedback controllers are proposed in the presence of both actuator saturation and/or time-delay. The global stability of the closed-loop system is proved. Optimal feedback gain is also obtained in the delay-free case. Simulation results are given to show the effectiveness of the presented methods.

This article designs the static and dynamic event-triggered control (ETC) and self-triggered control (STC) algorithms to achieve the semiglobal stabilization of discrete-time systems with input constraints. First, a novel static ETC algorithm based on the discrete-time parametric Lyapunov equation (DPLE) is designed. In order to further increase the interevent times (IETs), the corresponding dynamic ETC is designed. Next, both static and dynamic STC, where the next control law updates depend on the previous triggered states, are proposed to avoid monitoring the measurement errors. The proposed algorithms are not only capable of reducing the number of transmissions significantly but also build a very simple and clear relationship between the only design parameter and the nontrivial IET (NIET). This allows us to change regularly IETs by adjusting the design parameter so that the nontriviality of static and dynamic ETC and STC is guaranteed and a tradeoff between the IETs and the control performance can be easily found. Specifically, by exploring the properties of DPLE, the designed algorithms avoid the complex relationship between the nontrivial condition and the system matrices. Finally, the designed static and dynamic ETC and STC algorithms are applied to the design of the spacecraft rendezvous control system and their effectiveness is verified by simulation results.

This article proposes static/dynamic event-triggered and self-triggered discrete gain scheduled control with a designable parametric minimal interevent time (MIET) to achieve semiglobal stabilization of linear systems with input constraints. First, a novel static event-triggered discrete gain scheduled control, which can improve the control performance and simultaneously save the communication resources, is proposed by utilizing the properties of the parametric Lyapunov equation (PLE). Moreover, the static self-triggered mechanism, in which the next control law updates based on the previous triggered states, is also designed to avoid the monitoring of all states. In order to further increase the interevent times (IETs), the corresponding dynamic event-triggered and self-triggered discrete gain scheduled control are designed, respectively. All the proposed algorithms can not only avoid the Zeno phenomenon but also provide a designable parametric MIET. This allows to easily find a tradeoff between the IETs and the control performance by adjusting the only design parameter. In addition, by exploiting the properties of the PLE, the designed algorithms avoid the complicated relationship between the MIET and the system matrices. In some cases, the MIET can totally avoid the relationship with the system itself and be designed as an arbitrarily large bounded constant. Finally, applications to the spacecraft rendezvous system show the effectiveness of the established algorithms.

In this paper, we study the consensus problem for high-order discrete-time multiagent systems with state, input, and communication delays, where the input and communication delays can be arbitrarily large yet exactly known. Moreover, the communication delays are different for different agents. Nested predictor-based state feedback protocols and full-order/reduced-order observer-based output feedback protocols are established to solve the problem. It is shown that both the input and communication delays can be compensated completely. Furthermore, linear matrix inequalities-based approaches are provided to design state feedback gains and observer gains. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.

The consensus problem for multiagent systems (MASs) described by discrete-time linear systems with multiple input delays is investigated. Under two reasonable assumptions, a truncated pseudo-predictor feedback (TPPF) approach is established to solve the consensus problem. The proposed TPPF protocols allow arbitrarily large yet bounded delays and are easy to implement in practice since they are finite dimensional and only use the relative current state information of neighboring agents. Moreover, the proposed protocols can also achieve semi-global consensus of MASs if the actuators are subject to saturations. A numerical example is given to illustrate the effectiveness of the proposed approaches.