This article investigates the stochastic stability of stochastic differential delay systems (SDDSs) with path information and their applications in consensus control of multi-agent systems (MASs) based on the path information feedback. Here, the integral path information and fragment-integral path information are considered respectively. The mean square (m.s.) and almost sure (a.s.) exponential stability criteria of the SDDSs with path integral information are established respectively according to the two types of path information. It is shown that the fragment-integral term may work positively for stochastic stability. Moreover, the obtained stochastic stability theorems are applied to design a distributed proportional integral/ fragment-integral control protocol and establish consensus conditions for stochastic MASs under proportional-integral (PI) -type controls. Finally, the effectiveness of the results is verified through two simulation examples.

This work is absorbed in the neighboring mode-dependent event-triggered control scheme for Markov jump systems with unknown interconnections. A dynamic event-triggered mechanism composed of neighboring modes parameters is provided to save communication resources and reduce the number of solution parameters. Distinguished from existing version, the global operating modes are required to be unknown for each local subsystem. Resorting to neighboring modes information, an event-triggered state feedback controller is established to assure system stability. The cyclic-small-gain criterion is used to tackle the unknown interconnections so that novel stability criteria are obtained for the closed-loop systems with H ∞ performance. Finally, an illustrative example is employed to confirm the proposed method in the aspect of validity.

This paper focuses on the issue of adaptive event-triggered leader-follower consensus for multi-agents systems with output constraints and dead-zone inputs. By introducing an advanced nonlinear mapping technique to obtain the unconstrained auxiliary variables of constrained system states, a new systems model without output constraints is constructed. Unlike existing schemes, the proposed strategy can be used in both constrained and unconstrained situations without requiring changes to the control structure. Moreover, a state estimator is constructed to observe the unavailable states. To conserve communication resources, an event-triggered rule with a dynamic threshold is designed to decrease superfluous information transmissions from the controller to the actuator. It is proven that all signals in closed-loop systems are ultimately bounded and the system output does not violate the given constraint range. At last, a numerical simulation example is provided to confirm the correctness and efficiency of the proposed method.

This article is focused on the design of an LMI-based observer for the class of disturbance-affected nonlinear systems. Two novel LMI conditions are derived by deploying a more general form of the matrix multiplier compared to the one used in the literature. The first method is based on the use of the H ∞ criterion, while the second one utilises an ISS notion. Both LMIs are developed by employing the reformulated Lipschitz property, a well-known LPV approach and the new variant of Young inequality. The key element of the proposed LMI conditions is the incorporation of the novel matrix multipliers which allow us to include some additional decision variables as compared to the methods proposed in the literature. These additional variables add extra degrees of freedom, thus enhancing the LMI feasibility. Furthermore, the effectiveness of the proposed methodologies is showcased through a numerical example.

Steering a nonlinear system from one state to a desired one is a common task in control. While a nominal trajectory can be obtained rather systematically using a model, for example via numerical optimization, heuristics, or reinforcement learning, the design of a computationally fast and reliable feedback control law that guarantees robust asymptotic stability of the found trajectory can be much more involved. An approach that does not require high online computational power and is well-accepted in the industry is gain-scheduling. The results presented here pertain to the stability guarantees and the region of attraction of gain scheduled control laws, based on subsequent linearizations along the reference trajectory. The approach bounds the uncertainty arising from the linearization process, builds polytopic sets of linear time varying systems covering the nonlinear dynamics along the trajectory, and exploits sufficient conditions for robust stability to attempt the derivation of the desired gain-scheduled controller, via the solution of Linear Matrix Inequalities (LMIs). A result to estimate an ellipsoidal region of attraction is provided too. Moreover, arbitrary scheduling strategies between the control gains are considered in the analysis, and the method can be used also to check/assess the stability properties obtained with an existing gain-scheduled law. The approach is demonstrated experimentally on a small quadcopter as well as in simulation to design a scheduled controller for a chemical reactor model and to validate an existing control law for a gantry crane model.

Microgrids are a development trend and have attracted a lot of attention worldwide. The control system plays a crucial role in implementing these systems and, due to their complexity, artificial intelligence techniques represent some enabling technologies for their future development and success. In this paper, we propose a novel formulation of an economic model predictive control (economic MPC) applied to a microgrid designed for a faculty building with the inclusion of a predictive model to deal with the energy demand disturbance using an artificial neural network (ANN). First, we develop a framework to identify an ANN using historical data registered by a smart three-phase power quality analyzer to provide feedforward power demand predictions. Next, we present an economic MPC formulation that includes the prediction model for the disturbance within the optimization problem to be solved by the MPC strategy. We carried out simulations with different scenarios of energy consumption, available resources and simulation times to highlight the results obtained and analyze the performance of the energy management system. In all cases, we observed the correct operation of the proposed control scheme, complying at all times with the objectives and operational restrictions imposed on the system.

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.

In this article, we study an unified resilient asymmetric bipartite consensus (URABC) problem for nonlinear multi-agent systems with both cooperative and antagonistic interactions under denial-of-service (DoS) attacks. We first prove that the URABC problem is solved by stabilizing the neighborhood asymmetric bipartite consensus error. Then, we develop a distributed compact form dynamic linearization method to linearize the neighborhood asymmetric bipartite consensus error. By using an attack compensation mechanism to eliminate the adverse effects of DoS attacks and an extended discrete state observer to enhance the robustness against unknown dynamics, we finally propose a distributed resilient model-free adaptive control algorithm to solve the URABC problem. A numerical example validates the proposed results.

A document by Gargi Chakraborty. Click on the document to view its contents.

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.

This paper is concerned with the stability analysis of the static output-feedback polynomial fuzzy-model-based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive-definite Lyapunov matrix and nonsingular transformation matrix. We proposed a new approximated membership functions, i.e. Lagrange Membership Functions (LMFs) method, which can be introduced into the stabilization process to relieve the stability conservativeness results. The LMFs are general representations of piecewise-linear membership functions (PLMFs), which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points, so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach including the information of premise variables and LMFs are proposed, which can make the stability conditions more relaxed. Finally, a simulation example is given to show the merits of the developed techniques.

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.

Health monitoring is critical for the maintenance and risk management of reinforced concrete (RC) structures. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of RC structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the RC dynamic, while the unknown measurement noise covariance is adapted based on a fixed-lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modeling mismatch in each time increment by solving a minimax game: one “hostile” player tries to select a worst model far from the proposed ACJM with an exponential decay tolerance, while an optimum filter is designed by minimizing the estimation error according to this worst model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.

For the nonlinear parameter-varying (NPV) model of unmanned surface vehicle (USV) with the consideration of the velocities on yaw and surge as well as wave disturbances, a robust H ∞ control method is proposed based on extended homogeneous polynomial Lyapunov function (EHPLF) to regulate heading for the superior performance on the rapidity, accuracy and robustness. Firstly, a NPV model of heading error is established to design a general form of a state feedback controller with a robust H ∞ performance. Secondly, a Lyapunov matrix with full states and varying parameter is constructed to derive the robust H ∞ global exponential stability conditions by Euler’s homogeneity relation for the NPV system, known as the EHPLF stability conditions. Thirdly, since the EHPLF stability conditions consist of a set of nonlinear coupled inequalities that cannot be directly solved by sum of squares (SOS) toolboxes, they are decoupled with matrix transformations to obtain the EHPLF-SOS stability conditions, which is solved for the parameters of the state feedback controller. Finally, the simulation results indicate that EHPLF method exhibits a superior performance on dynamic, steady-state and robustness.