The paper addresses the problem of transforming observable, time-reversible and multi-input single-output discrete-time state equations into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the inputs, output, and a finite number of their past values. The intrinsic necessary and sufficient conditions for existence of the extended observer form are provided in terms of a certain vector field, defined by the system output and its past values. The algorithm is presented to find a parametrized state transformation that takes the state equations into the considered extended observer form. Two examples, one of them academic, illustrate the theory.

Physical human-robot collaboration (pHRC) requires both compliance and safety guarantees since robots coordinate with human actions in a shared workspace. This paper presents a novel fixed-time adaptive neural control methodology for handling time-varying workspace constraints that occur in physical human-robot collaboration while also guaranteeing compliance during intended force interactions. The proposed methodology combines the benefits of compliance control, time-varying integral barrier Lyapunov function (TVIBLF) and fixed-time techniques, which not only achieve compliance during physical contact with human operators but also guarantee time-varying workspace constraints and fast tracking error convergence without any restriction on the initial conditions. Furthermore, a neural adaptive control law is designed to compensate for the unknown dynamics and disturbances of the robot manipulator such that the proposed control framework is overall fixed-time converged and capable of online learning without any prior knowledge of robot dynamics and disturbances. The proposed approach is finally validated on a simulated two-link robot manipulator and then extended to the simulated UR10 robot. Simulation results show that the proposed controller is superior in the sense of both tracking error and convergence time compared with the existing barrier Lyapunov functions based controllers, while simultaneously guaranteeing compliance and safety.

This article addresses the optimal formation control for unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) system via a distributed optimal control approach. A user-friendly global cost function is well designed in a linear quadratic regulator (LQR) form. The proper choice of the weighting matrices for optimizing the cost function are given. To deal with the graph coupling of optimal control and distributed control, we propose a distributed optimal formation control protocol, and the protocol is independent of the communication graph. The proposed protocol can guarantee the optimization of the cost function and the achievement of the formation control. Three simulation examples are provided to demonstrate the results.

Real-world dynamical control systems are often subject to input saturation due to the physical constraints of actuators. This causes the response performance of the system to be reduced due to the effect of input saturation. To this end, we propose a finite-time performance enhanced bounded control (FTPE-BC) method based on sliding mode control for finite time tracking of linear systems with input saturation. In this method, an approach rate based on inverse tangent function is proposed to make the system converge in finite time. A bounded controller based on sliding mode control is proposed, in which two control parameters are introduced to reduce steady-state error, settling time and overshoot. Meanwhile, the finite-time stability of the system is proved in a domain of attraction. The parameters selection principle of the controller is given to improve the transient and steady-state performance of the closed-loop system. The simulation results verify the superiority of the proposed method in the transient and steady-state performance enhancement.

The problem of fixed-time formation tracking for multi-spacecraft systems without internal collisions is investigated in this paper. A novel adaptive immersion and invariance (I&I)-based control protocol is designed to solve this technical problem, with the goal of driving formation members to accurately realize and maintain the required configuration within the user-given time. The novelty here lies in two things. First and foremost, unlike the asymptotic convergence of the traditional I&I related works, the proposed protocol guarantees the fixed-time stability by integrating the prescribed performance control. Secondly, the event-triggered mechanism is adopted to alleviate the pressure of communication resources between formation members and reduce unnecessary information interaction. Lyapunov stability analysis shows that the proposed protocol can enable the defined implicit manifold to converge to the origin for most initial conditions. Also, benefiting from the prescribed performance techniques, the convergence time eliminates the dependence of designed controller parameters or initial system conditions, relying only on the actual mission requirements. In addition, we adopt a linear extended state observer to deal with the parameter uncertainties and external disturbances, and use the I&I adaption to estimate the observer errors to further improve the system performance. Moreover, a new exponential-type artificial potential function is designed to avoid close proximity between formation members and prevent internal collisions. Finally, numerical simulations are provided to verify the theoretical results.

The paper deals with the security control stabilization problem of uncertain Markov jump power systems with input dead zone under stochastic denial-of-service (DoS) attack. DoS attack is modeled as a discrete-time Markov process. Dual hidden Markov models are respectively used to detect the modes of the original power systems and the one under DoS attack. Based on the detected modes and neural networks (NNs), adaptive NN-based security asynchronous control strategies are proposed, where both state feedback and output feedback are studied simultaneously. With the developed control laws, all trajectories of the closed-loop systems are bounded stable in the stochastic setting. Simulation results demonstrate the correctness and usefulness of the proposed techniques.

In this paper, we consider the matrix-weighted consensus problems with disturbances. To this end, we firstly propose a new disturbance observer design for systems with unknown matched or mismatched disturbances representable as a linear combination of time-varying basis functions. Under some assumptions on the boundedness and persistent excitation of the regression matrix, the disturbances can be precisely estimated at an exponential rate and thus, can be compensated by a suitable compensation input. Next, disturbance-observer based consensus algorithms are proposed for matrix-weighted networks of single- and double-integrators with matched or mismatched disturbances. We show that both matched and mismatched disturbances can be estimated and actively compensated, and the system globally asymptotically converges to a fixed point in the kernel of the matrix-weighted Laplacian. Depending on the network connectivity, the system can asymptotically achieve a consensus or a cluster configuration. The disturbance-observer based consensus design is further extended for higher-order integrators with disturbances. Finally, simulation results are provided to support the mathematical analysis.

This paper investigates the distributed mean square output tracking problem of heterogeneous multi-agent systems with Markovian switching topologies and infinite transmission delays. The main challenge of the concerned problem arises from how to deal with Markovian switching topologies and infinite transmission delays simultaneously. A novel distributed observer is developed based on a newly proposed Lyapunov functional method. Then, a distributed controller based on the distributed observer is developed. It is shown that the stochastic distributed tracking problem is solved in the sense of mean square if the union graph of the underlying Markovian switching topology contains a spanning tree. A distinctive feature of the proposed controller is that the infinite delays are not required to be known. Finally, the effectiveness of the proposed controller is illustrated by two numerical examples.

In this paper, the prescribed-time consensus problem of multi-agent systems with finite control gain is investigated. A novel control Lyapunov function (CLF) framework for prescribed-time stability is developed by using the time space deformation approach. For both leaderless and leader-following prescribed-time consensus, new switching time-varying gain-based protocols are proposed, in which, the infinite time-varying control gain is turned off before the prescribed time and the global finiteness of control gain is thus guaranteed. It is mathematically proved that the agents equipped with the proposed protocols can achieve less conservative prescribed-time consensus in both leaderless cases and leader-following cases, on the basis of the developed CLF framework. The superiority of the proposed prescribed-time protocols in terms of consensus accuracy, control energy consumption, and control peak value is demonstrated through comparison simulations using illustrative examples.

Monte Carlo simulations have long been a widely used method in the industry for control system validation. They provide an accurate probability measure for sufficiently frequent phenomena, but are often time-consuming and may fail to detect very rare events. Conversely, deterministic techniques such as µ or IQC-based analysis allow fast calculation of worst-case stability margins and performance levels, but in the absence of a probabilistic framework, a control system may be invalidated on the basis of extremely rare events. Probabilistic µ-analysis has therefore been studied since the 1990s to bridge this analysis gap by focusing on rare but nonetheless possible situations that may threaten system integrity. The solution adopted in this paper implements a branch-and-bound algorithm to explore the whole uncertainty domain by dividing it into smaller and smaller subsets. At each step, sufficient conditions involving µ upper bound computations are used to check whether a given requirement – related to the delay margin in the present case – is satisfied or violated on the whole considered subset. Guaranteed bounds on the exact probability of delay margin satisfaction or violation are then obtained, based on the probability distributions of the uncertain parameters. The difficulty here arises from the exponential term classically used to represent a delay, which must be replaced by a rational expression to fit into the Linear Fractional Representation (LFR) framework imposed by µ-analysis. Two different approaches are proposed and compared in this paper. First, an equivalent representation using a rational function of degree 2 with the same gain and phase as the real delay, which results into an LFR with frequency-dependent uncertainty bounds. Then, a Padé approximation, whose order should be chosen carefully to handle the trade-off between conservatism and complexity. A constructive way to derive minimal LFR from Padé approximations of any order is also provided as an additional contribution. The whole method is first assessed on a simple satellite benchmark, and its applicability to realistic problems involving a larger number of states and uncertainties is then demonstrated.

This paper proposes an adaptive neural network (NN) optimal control approach for autonomous relative motion control of non-cooperative spacecraft in proximity. The proposed method aims to minimize fuel consumption under various challenges including model uncertainty, state constraints, external disturbances, and input saturation. To account for uncertain parameters of non-cooperative target and external disturbances, we start by designing a NN disturbance observer. Subsequently, a novel optimal control index function is presented. An adaptive NN based on the actor-critic (A-C) framework and backstepping theory is then utilized to approximate the solution of Hamilton-Jacobi–Bellman (HJB) equation and obtain an optimal control law. The Lyapunov framework is leveraged to establish the stability of the closed-loop control system. Finally, numerical simulations are conducted to assess the feasibility and effectiveness of the proposed control scheme in comparison with an existing approach.

This paper is concerned with parameter estimate and adaptive control problems of deterministic autoregressive moving average (DARMA) systems on the basis of quantized data of system output signals which are generated by a kind of uniform quantizer. By designing system input signals, the extended least-squares (ELS) algorithm with uniform output observations is proved to yield bounded estimation errors under some mild assumptions. Moreover, the adaptive tracking controller under inaccuracy observations are also designed. To analyse the properties of tracking error, I use the expanded form of ELS and research the properties of quantization noise. In addition, I give the expression of tracking error and show how it depends on the size of quantization step when the quantization step satisfies some conditions. A numerical example is supplied to demonstrate the theoretical results.

This paper proposes a fault-tolerant control strategy for the air path system of a turbocharged diesel engine, considering the simultaneous presence of matched and mismatched external disturbances, additive and loss of effectiveness fault modes in the EGR and VGT subsystems. Firstly, a disturbance observer based on H ∞ theory is designed for estimating additive faults and external disturbances, and the upper bound of observation error is obtained. Based on the observation information, an integral sliding mode surface is designed, and the effectiveness of the sliding mode surface is analyzed. For the loss of effectiveness faults in the actuators, a novel adaptive update sliding mode controller is designed. The proposed control algorithm can get the fault information of the system and achieve fault-tolerant control of through controller reconstruction. Ultimately, the effectiveness of the proposed method is validated through simulations and comparative analysis.

This paper develops a neuro-adaptive observer for state and nonlinear function estimation in systems with partially modeled process dynamics. The developed adaptive observer is shown to provide exponentially stable estimation errors in which both states and neural parameters converge to their true values. When the neural approximator has an approximation error with respect to the true nonlinear function, the observer can be used to provide an H ∞ bound on the estimation error. The paper does not require assumptions on the process dynamics or output equation being linear functions of neural network weights and instead assumes a reasonable affine parameter dependence in the process dynamics. A convex problem is formulated and an equivalent polytopic observer design method is developed. Finally, a hybrid estimation system that switches between a neuro-adaptive observer for system identification and a regular nonlinear observer for state estimation is proposed. The switched operation enables parameter estimation updates whenever adequate measurements are available. The performance of the developed adaptive observer is shown through simulations for a Van der Pol oscillator and a single link robot. In the application, no manual tuning of adaptation gains is needed and estimates of both the states and the nonlinear functions converge successfully.

This article investigates an event-triggered adaptive estimated inverse control scheme for a class of uncertain nonlinear systems with hysteresis effects, parametric uncertainties and disturbances. An online estimated inverse hysteresis compensation mechanism is developed, where an adaptive technique is employed to obtain the value of unknown hysteresis parameters. Compared with the common approaches, its biggest advantage lies in that it is not necessary to obtain the hysteresis parameters by means of experiment, which relaxes time-consuming off-line identification work.Moreover, an adaptive radial basis functions neural network (RBFNN) is utilized to approximate the unknown disturbances, whose weight coefficients along with parametric uncertainties are all estimated by the adaptive technique. Besides, the communication cost can be largely saved by introducing the relative threshold event-triggered control (ETC). Through Lyapunov analysis, the proposed controller guarantees the boundedness of all the signals and the convergence of the error signals. The results of numerical simulation illustrate the effectiveness and superiority of the developed controller.

In this paper, the cooperative consensus tracking control problem is investigated for hybrid multi-agent systems with slow interference time-varying signals and directed topology. First of all, the dynamical model of hybrid multi-agent system with slow interference time-varying signals is built up, which contains second-order continuous and first-order discrete time agents. Secondly, interference observers of first-order and second-order agents are introduced, which can effectively detect interference signals, and estimate the velocity of second-order agents to realize compensation. Meanwhile a kind of sliding mode controllers based on interference compensation are designed to come true the cooperative consensus tracking of hybrid multi-agent systems. Then, via Lyapunov method, the stability of hybrid multi-agent system is attested. And the sufficient conditions are given for the realization of cooperative consensus tracking. In the end, simulation examples ulteriorly demonstrate the validity of our results.

In this paper, we study consensus robustness and performance problems for continuous-time multi-agent systems. We consider first-order unstable agents interconnected by an undirected graph, coordinated by a delayed output feedback protocol. Our objectives are twofold. First, we seek to determine the largest range of delay permissible so that the agents may achieve robustly consensus despite variation of the delay length, herein referred to as the delay consensus margin. Second, we attempt to determine consensus error performance quantified under an H 2 norm criterion, which measures the disruptive effect of random nodal noises on consensus. For both problems, we obtain analytical solutions. The explicit expressions provide conceptual insights and exhibit how the agents' unstable pole, nonminimum phase zero, as well as the network topology may limit fundamentally the consensus robustness and performance.

The paper starts from the challenge of the critical cases in difference operator stability for neutral functional differential equations (NFDE). Such cases occur in the NFDE associated to 1 D hyperbolic partial differential equations (PDE) dynamics in Mechanical and Hydraulic Engineering. For some of such applications it resulted that the aforementioned critical (non-asymptotic) stability is connected to the character and level of the energy losses. It is shown that suitable choice of the losses to be taken into account can remove the critical stability properties and give the difference operator the asymptotic stability thus ensuring asymptotic stability for the system’s dynamics and also other asymptotic properties.