In recent years the use of delayed controllers has increased considerably, since they can attenuate noise, replace derivative actions, avoid the construction of observers, and reduce the use of extra sensors. Also, delayed controllers have been shown to be more insensitive to high-frequency noise. However, currently, there are few criteria for tuning this type of controllers. This manuscript presents a rigorous study of performance, fragility, and robustness for a first-order system in closed-loop with a delayed controller, which leads to consider a quasi-polynomial q( a, k, s), where a ∈ R m denotes the system parameters, k ∈ R n are the controller gains, and s∈C. The best performance gains k ∗ , p are obtained for a fixed a. These gains provide the maximum exponential decay achievable in the system response to guarantee exponential convergence to a desired trajectory. Also, for a fixed a, criteria are given to obtain the least fragile gains k ∗ , f that ensure the desired trajectory tracking in the presence of controller’s gains variations. Meanwhile, for a fixed gains k, the greatest robustness parameters a ∗ , r are obtained. Thus, the desired trajectory tracking of the systems is ensured in the event of parametric variations. Finally, to illustrate and corroborate the proposed theoretical results, a real-time implementation is presented on a mobile prototype, known as omnidirectional mobile robot, studying a quasi-polynomial of degree 9 with three commensurable delays. These results offer convincing reasons to implement controllers with delayed-action and take into account an analysis of performance, fragility, and robustness to tune this type of controllers.

The event-triggered group consistency problem of a class of second-order multi-agent systems (MASs) under denial of service attacks (DoS) is studied. The main contribution lies in the proposed group generation partition algorithm for multi-agents with directed network topology, which successfully solves the problem of multi-task assignment in complex networks. Then, the algorithm transforms the adjacency matrix into a standard diagonal type to reduce the algorithm complexity. A new adaptive event triggering mechanism (ETM) is designed using a fuzzy logic system for the directed network. The trigger threshold is adjusted by the relative motion trajectory between adjacent agents, the output feedback error of the agents, and the adaptive parameters of the fuzzy logic system, which can reduce the communication burden. Finally, the Lyapunov stability theory is used to prove the asymptotic stability and consistency of the closed-loop system, and the effectiveness of the proposed algorithm is verified by two simulation examples.

This paper introduces a novel approach for designing optimal control using data-driven Stochastic Game Theoretic Differential Dynamic Programming (SGT-DDP). The proposed method addresses unknown stochastic systems by approximating both drift and diffusion dynamics. The drift dynamics is estimated via Gaussian Process Regression (GPR) using input-output data. The diffusion dynamics is approximated from the noise data, which is extracted through subtracting the noisy output from the smoothed output. Subsequently, the binning method is combined with GPR to obtain the approximate model of the diffusion dynamics. These approximations are integrated into the SGT-DDP framework to compute optimal control policies. Simulations on benchmark nonlinear systems under unknown dynamics demonstrate the effectiveness of the method.

For absolute value terms related to yaw velocity generated by cross-flow effect and the unmodeled factors, a nonlinear parameter-varying (NPV) model is established with absolute value disturbances to regulate the heading of unmanned surface vehicle (USV) by state feedback (SF) control with a NPV disturbance observer (NPVDO). Firstly, the model of NPVDO is designed with gains to estimate the non-differentiable absolute disturbance. Secondly, a Lyapunov function is constructed with full states and varying parameter to solve the gains with NPVDO stability conditions by Euler homogeneity. Thirdly, since the NPVDO stability conditions contain the coupling term between the observer gain and the Lyapunov matrix, it is decoupled into NPVDO-sum of squares (SOS) conditions by the projection theorem and matrix transformation to solve NPVDO gains. Finally, a robust SF with NPVDO is designed for heading regulation with NPV model. Simulations and experiments indicate that NPVDO has a superior performance on parameter variation suppression and nonlinear non-differentiable disturbance estimation by comparing with other methods to reduce heading errors.

Linear-Quadratic (LQ) problems that arise in systems and controls include the classical optimal control problems of the Linear Quadratic Regulator (LQR) in both its deterministic and stochastic forms, as well as H ∞ -analysis (the Bounded Real Lemma), the Positive Real Lemma, and general Integral Quadratic Constraints (IQCs) tests. We present a unified treatment of all of these problems using an approach which converts linear-quadratic problems to matrix-valued linear-linear problems with a positivity constraint. This is done through a system representation where the joint state/input covariance (the outer product in the deterministic case) matrix is the fundamental object. LQ problems then become infinite-dimensional semidefinite programs, and the key tool used is that of linear-conic duality. Linear Matrix Inequalities (LMIs) emerge naturally as conal constraints on dual problems. Riccati equations characterize extrema of these special LMIs, and therefore provide solutions to the dual problems. The state-feedback structure of all optimal signals in these problems emerge out of alignment (complementary slackness) conditions between primal and dual problems. Perhaps the new insight gained from this approach is that first LMIs, and then second, Riccati equations arise naturally in dual, rather than primal problems. Furthermore, while traditional LQ problems are set up in L 2 spaces of signals, their equivalent covariance-representation problems are most naturally set up in L 1 spaces of matrix-valued signals.

When a parameterized dynamical system is not (structurally locally) identifiable, it is crucial to reparameterize the system to ensure that the new parameters can be uniquely determined, at least locally. In the article [1], Theorem 2 (also presented in [2] as Theorem 1) claims the existence of an identifiable reparameterization for a parameterized analytic function. We first give a counter-example to show that its conditions are indeed incomplete. Consequently, to address its incompleteness, we will propose a modified version of the theorem.

Unmanned Aerial Vehicles (UAVs) are expected to fully exploit their maneuvering capabilities to conduct aggressive maneuvers to complete tasks such as racing and aerobatics even in harsh environments. However, most of related works often focus on slow movements only suitable for regular tasks in well-structured environments. This motivates us to propose a highly robust control scheme designed specifically for UAV aggressive maneuvers, encoded by rapid and large changes in either position or attitude. The core of our approach is the data informed incremental dynamics and the quaternion facilitated control scheme. The former facilitates the model-free control that eliminates the requirement to model the complex dynamics at high velocities and accelerations accurately; While the latter avoids potential singularities during large angular changes. In particular, we first utilize one-step-backward data to construct incremental dynamics, a model-free representation of the UAV dynamics. Then, the constructed incremental dynamics serves as the basis for the development of both position-priority and attitude-priority control schemes, wherein the novel quaternion based aggressive maneuver tracking controllers are designed with complete theoretical analysis. The aggressive maneuvers such as roulette, barrel roll, multiple-flip and cobra maneuvers are chosen for tri/quad/hexa/octocopter platforms to evaluate the performance of our proposed position-priority and attitude-priority control schemes, during which the linear velocity up to 20 m/s, the angular changes up to 360 ◦.

This paper studies the practical fixed-time consensus (Fd-TC) for uncertain multi-agent systems (MASs) under strongly connected directed graphs utilizing adaptive event/self-triggered controllers, respectively. Considering the uncertainty in the agent’s nonlinear dynamic parameters, the adaptive event-triggered controller is designed by incorporating an event-triggered strategy with an adaptive control scheme, which achieves the practical Fd-TC for uncertain nonlinear MASs and the settling time remains constant irrespective of the initial conditions. Moreover, the designed controller is independent of any global information, including communication topology and network size. It also employs the hyperbolic tangent function to tackle Zeno and nondifferential issue. Following this, the adaptive event-triggered controller serves as the foundation for introducing a self-triggered controller, which eliminates the necessity for continuous monitoring and guarantees practical Fd-TC. Furthermore, the results are extended to a more generalized case with uncertain disturbances, highlighting the adaptability of the designed controller. Finally, two numerical simulation examples are conducted to validate the efficacy of the developed controllers.

This paper addresses the identification of Nonlinear (NL) systems using a linearization approach, introducing a combined estimator to tackle this challenge. We assume that the unknown NL system operates around a stable, slowly varying operating point. The system trajectory is then perturbed slightly via small, typically fast, input perturbations. We demonstrate that the NL system’s response to these small perturbations can be approximated by a Linear Parameter-Varying (LPV) system model. Furthermore, we show that this LPV model represents the linearized version of the unknown NL system around the operating point. A new parametrization for the LPV model coefficients is introduced, establishing a structural relationship between the LPV coefficients. This structural relationship reduces the number of parameters to be estimated and ensures that the LPV model always corresponds to the linearized form of the NL system. Additionally, we demonstrate that this LPV model structure allows for the unique reconstruction of the NL system model through symbolic integration, resulting in a closed-form nonlinear Ordinary Differential Equation (ODE). This integration introduces a second structural relationship, linking the LPV model to the NL model. By leveraging these two structural relationships, we reformulate the problem of NL system identification via linearization as a combined estimation problem, leading to a unified LPV-NL estimation framework. This approach utilizes all available data, including perturbation data (linear response) and the varying operating point (NL response). We propose a combined estimator that jointly estimates the NL-LPV model, capturing the intrinsic structure of NL system identification through linearization. Finally, we present a numerical example to illustrate the performance of the proposed method.

The stochastic approximation based control law has been proved to be a powerful tool to achieve the robust distributed coordinated control for multi-agent systems (MASs) with uncertain disturbances in fixed or balanced time-varying network. However, its effectiveness proof in unbalanced time-varying networks is not well solved. The main contribution of this paper is solving this problem in two typical coordinated control problems based on a time-varying quadratic Lyapunov function. Firstly, the stochastic approximation for consensus problem of discrete-time single-integrator MASs with additive noises is studied. We build the weak consensus, mean square and almost sure consensus conclusion under the assumption that the time-varying network is uniformly strongly connected (USC) by adopting the stochastic approximation based consensus protocol. The convergence rate of the weak consensus is also quantified. Secondly, the stochastic approximation for formation control problem of MASs with relative-position information in the plane as an application of the built consensus conclusion is studied. We show that the stochastic approximation based formation control law can be used to achieve the desired formation for MASs if the network is USC. We finally give numerical simulations to verify the correctness of the conclusion.

This paper focuses on privacy-preserving distributed convex optimization across directed graphs within a prescribed time. To reduce the communication cost and achieve fast convergence, we propose a novel event-triggered and prescribed-time convergent distributed optimization algorithm built upon an extended Zero-Gradient-Sum method with free initialization. Specifically, we formulate event-triggering conditions for each agent, ensuring that inter-agent communication occurs solely upon meeting these conditions, thus significantly reducing communication costs. By the Lyapunov stability theory, the proposed algorithm is proven to achieve an accurate convergence to the optima within a prescribed time. Moreover, we establish the absence of Zeno behavior throughout any arbitrary period except the specified convergence time. When the environment exists eavesdropping attacks, we further provide a privacy-preserving prescribed-time event-triggered distributed algorithm based on state and objective decomposition. Finally, two comprehensive simulations demonstrate the performance of our proposed algorithm.

With an increasing focus on both performance and efficiency, UAV control systems have made great progress. In this work, we extend a previous LPV-MPC technique by including a more simplified control system for UAVs. The proposed control method removes the requirement for a velocity controller by concentrating on improving MPC performance using Particle Swarm Optimization (PSO) of the weight matrices. This system uses PSO to balance control effort with trajectory ac-curacy and simplifies the control architecture, hence improving UAV control efficiency. It is especially appropriate for situations where simplicity and energy economy are absolutely important.

In this paper, we provide an in-depth discussion of the problem of predefined-time formation control for Multi-Agent Systems (MAS) and consider the presence of non-periodic Denial of Service (DoS) attacks. The suggested approach utilizes the system state to achieve time-varying formation of MAS within predefined-time. It effectively mitigates external disturbance or non-periodic DoS attacks. The algorithm combines the predefined-time Lyapunov stability theory with the Terminal Sliding Mode Control (TSMC) is the strategy of predefined-time sliding mode control. It creates a new distributed sliding mode surface to ensure the speed and stability of multi-agent formation under dynamic change and uncertainty conditions. The range of the system convergence time is specifically linked to the changeable parameters, which simplifies the design of the control algorithm to satisfy the appropriate requirements for convergence time. This study demonstrates the stability of the method through theoretical analysis and validates its effectiveness by conducting simulations on the Matlab experimental platform. The simulation results demonstrate that the anticipated limit of the time required for the algorithm to achieve a stable formation is less cautious and more resilient compared to the current TSMC algorithm.

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The semi-global stabilization of a class of cascade systems (e.g., partially linear composite systems) is investigated via partial state feedback. The system comprises a nonlinear subsystem with a cross-term and a linear subsystem in the Byrnes-Isidori normal form. The cross-term that involves any two consecutive states of chains of integrators is incorporated into the nonlinear subsystem. Based on the established lemma for separate design, the semi-global stabilization problem for the entire composite system is reduced to stabilizing its linear subsystem subject to non-peaking constraints on the consecutive states. To address the later problem, a linear low-and-high gain feedback law is developed in the backstepping manner, which can be recognized as partial state feedback for the composite system as it uses only the states of the linear subsystem.

This paper tackles the challenge of designing a memory-dynamic event-triggered output feedback controller for cyber-physical systems (CPSs) under distributed denial of service (DDoS) attacks. First, we consider the impact of hybrid time delays on communication networks and focus on DDoS attacks that can continuously paralyze network. Second, with limited bandwidth communication resources, a memory-dynamic event-triggered scheme (MDETS) that efficiently utilizes the bandwidth resources as well as mitigates the network-induced phenomena is proposed. In addition, to ensure the safe operation of CPSs, an output feedback controller with memory is designed based on time delay states in the measurement channel. Then, selecting the proper multi-area Lyapunov-Krasovskii functionals (LKFs), criteria for sufficient exponentially mean-square H ∞ stability condition is formulated. Finally, an illustrative example is used to demonstrate the effectiveness and applicability of the designed strategies.

With the vigorous development of the electric vehicle (EV) industry, the demand for charging has surged. However, the relative lag in the construction of charging infrastructure has led to a series of problems for drivers, such as difficulty in finding available charging stations and long waiting times for charging. To address this, this paper proposes an EV charging guidance framework based on an Informer network and Multi-Agent Reinforcement Learning (MARL), aiming at achieving efficient EV charging guidance. Firstly, this paper regards charging stations as independent agents, integrating information from vehicles, charging stations, and traffic, transforming the multi-objective optimization problem of EV charging guidance into a multi-agent reinforcement learning task. Then, an Actor-Critic algorithm combined with the Informer is designed, utilizing the Informer in the Critic network to model the interactions between different charging stations, thereby reducing the complexity of policy learning and enhancing coordination among agents. Subsequently, after calculating the advantage function for the agents, the Actor network is updated to improve learning efficiency. The proposed algorithm was simulated and validated in two different EV charging scenarios. The simulation results show that compared with several state-of-the-art methods, our algorithm achieved the best results in multi-objective optimization, demonstrating its superiority and practicality of our proposed algorithm.

In this paper, the prescribed-time fault-tolerant control for multiple input multiple output (MIMO) linear time-varying (LTV) systems is investigated. Both uncertain lexicographically fixed and non-lexicographically fixed LTV systems with precisely known models have been considered. By leveraging the special structure of controllable canonical form and employing the properties of the parametric Lyapunov equation, a global prescribed-time fault-tolerant controller is designed. By choosing a suitable Lyapunov-like function, it will be demonstrated that the state converges to zero within the designated time. In addition, the designed controller is bounded and maintains a linear, concise and smooth form. Ultimately, the effectiveness of the controller is verified through the simulation of the elliptical orbital rendezvous system.