Trajectories Of Closed-loop System Research Articles

Stabilization of Semi-Markovian Jumping Uncertain Complex-Valued Networks with Time-Varying Delay: A Sliding-Mode Control Approach

This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.

Performance-Driven Fault Detection for Uncertain Takagi–Sugeno Fuzzy Feedback Control Systems

This paper mainly studies the performance-driven fault detection for general uncertain Takagi-Sugeno fuzzy feedback control systems, where the infinite-horizon quadratic index is introduced to describe the concerned system performance. Different from the existing output-driven fault detection methods, the proposed approach aims to detect the performance degradations induced by faults. For this purpose, the performance index embedded with the information of system dynamics is reformulated for linear feedback control systems with reference inputs. The performance residual, which is adopted as the evaluation function, is derived based on the Bellman equation and further represented into an explainable form. Then, for uncertain linear feedback control systems, the boundaries of the performance residual are analyzed via the linear matrix inequality technique and an advantaged threshold setting scheme is proposed with the aid of randomized algorithm. Concerning the main objective, a novel approximation method which combines the fuzzy blend of local performance indices and the radial basis function neural network is developed to approximate the global performance index for Takagi-Sugeno fuzzy systems. Based on the result in linear case, the performance residual is constructed along the closed-loop system trajectory and the threshold is determined for the fuzzy control systems with reference inputs and model uncertainties. Finally, simulation studies are provided to show the effectiveness of the proposed theoretical results.

Distributed adaptive control architectures for uncertain multiagent system in the presence of coupled dynamics

This paper studies the analysis and synthesis of distributed adaptive control architectures for uncertain multiagent systems with coupled dynamics in a leader-follower setting, where overall closed-loop system stability is established, and sufficient stability conditions are defined. Specifically, we first analyse a standard distributed adaptive control law and reveal local stability conditions that guarantee the boundedness of the closed-loop system trajectories. We next synthesise fixed and adaptive robustifying terms to show relaxed local stability conditions. We also show that the fixed robustifying term can yield high-gain parameters in the resulting control signals, where the adaptive robustifying term removes this high-gain requirement. Finally, an illustrative numerical example is further presented to compare the proposed methods and demonstrate our theoretical contributions.

Nonlinear controller design for hydraulic turbine regulating systems via immersion and invariance

This paper proposes a nonlinear controller strategy for the frequency regulation of a hydraulic turbine regulating system (HTRS). An immersion and invariance (I&I) technique is utilised to develop the desired control law. The derived control method is used to guarantee that the equilibrium point is asymptotically stable. Furthermore, it can ensure that all overall closed-loop system trajectories are bounded. The feasibility and effectiveness of the technique are demonstrated using a nonlinear dynamical system of an HTRS connected to a single-machine infinite bus (SMIB) power system. The simulation results demonstrate that the technique is capable of regulating the frequency and improving dynamic performance despite large disturbances. It is capable of rapidly reducing oscillations and surpasses two known nonlinear controllers, namely the synergetic control and the backstepping control techniques. Additionally, despite the fact that the HTRS's parameters vary, the proposed technique is capable of providing consistent control performance. As a result, the presented controller is insensitive to variations in the system's parameters.

Instant distributed MPC with reference governor

Model predictive control is a popular choice for systems that must satisfy prescribed constraints on states and control inputs. Although much progress has been made in distributed model predictive control, existing algorithms tend to be computationally expensive. This limits their use in systems with fast dynamics. In this paper, we propose a new distributed model predictive control algorithm that we term as instant distributed model predictive control (iDMPC). The proposed algorithm employs a realisation of the primal-dual algorithm in the controller dynamics for fast computation. We show that the closed-loop system trajectories with the proposed iDMPC algorithm converge asymptotically to a desired reference. To ensure the satisfaction of the state constraints during the transient, we also include an explicit reference governor in the feedback loop.

Adaptive Control of Nonlinear Systems with Sinusoidal Uncertainties via Internal Model Principle

In this paper, an adaptive control scheme is established for nonlinear systems with sinusoidal uncertainties from the perspective of internal model principle. We propose to embed the controller with a dynamic compensator which plays the role of an internal model for reproducing the unknown sinusoidal parameter. For linearly parameterized systems, under some full-information stabilizability assumptions, internal-model-based controllers are developed, rendering the closed-loop system trajectories to be bounded and the plant states to be asymptotically convergent to zero. Further, we extend the proposed internal-model-based control scheme to nonlinearly parameterized systems with a (strictly) monotonic assumption. Two simulation examples are given to verify the effectiveness of the proposed schemes.

HOW EVENT-DRIVEN INTERMITTENT CONTROL WITH UNSTABLE OPEN & CLOSED-LOOP DYNAMICS LEAD TO BOUNDED RESPONSE IN HUMAN POSTURAL CONTROL

Event-driven intermittent feedback control is a form of feedback control in which the variables of interest are observed continuously, but corrective control action is only initiated intermittently based on certain threshold criteria. According to the literature, the human central nervous system (CNS) adopts event-driven intermittent control strategy while performing various tasks such as stabilize upright posture, control of saccadic eye movement or while driving. In this paper, we examine whether event-driven intermittent control when applied to a system wherein both open-loop dynamics and continuous closed-loop dynamics are unstable can yield bounded overall response (as has been observed in some situations of human postural control). With the help of both illustrative example simulations and experimental results from a table-top experiment inspired from human postural control, we show that this is indeed possible. We further provide insights using passivity theory and phase space analysis. Our analysis shows that bounded response is possible even if the phase trajectories of unstable open-loop and unstable closed-loop systems do not diverge in opposite directions or when Hurwitz convex combinations are not feasible. This study does not necessitate any assumption regarding the stabilizability or passivity of any of the constituent subsystems.

Fixed-time control under spatiotemporal and input constraints: A Quadratic Programming based approach

This paper presents a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. First, we study the problem of fixed-time convergence in the presence of input constraints. The relation between the domain of attraction for fixed-time stability with respect to input constraints and the required time of convergence is established. It is shown that increasing the control authority or the required time of convergence can expand the domain of attraction for fixed-time stability Then, we consider the problem of finding a control input that confines the closed-loop system trajectories in a safe set and steers them to a goal set within a fixed time. To this end, we present a Quadratic Programming (QP) formulation to compute the corresponding control input. We use slack variables to guarantee the feasibility of the proposed QP under input constraints. Furthermore, when strict complementary slackness holds, we show that the solution of the QP is a continuous function of the system states and establish the uniqueness of closed-loop solutions to guarantee forward invariance using Nagumo’s theorem. To corroborate our proposed methods, we present two case studies, an example of an adaptive cruise control problem and a two-robot motion planning problem.

Learning Contraction Policies From Offline Data

This letter proposes a data-driven method for learning convergent control policies from offline data using Contraction theory. Contraction theory enables constructing a policy that makes the closed-loop system trajectories inherently convergent towards a unique trajectory. At the technical level, identifying the contraction metric, which is the distance metric with respect to which a robot’s trajectories exhibit contraction is often non-trivial. We propose to jointly learn the control policy and its corresponding contraction metric while enforcing contraction. To achieve this, we learn an implicit dynamics model of the robotic system from an offline data set consisting of the robot’s state and input trajectories. We propose a data augmentation algorithm for learning contraction policies using this learned dynamics model. We randomly generate samples in the state space and propagate them forward in time through the learned dynamics model to generate auxiliary sample trajectories. We then learn both the control policy and the contraction metric such that the distance between the trajectories from the offline data set and our generated auxiliary sample trajectories decreases over time. We evaluate the performance of our proposed framework on simulated robotic goal-reaching tasks and demonstrate that enforcing contraction results in faster convergence and greater robustness of the learned policy.

Two-dimensional event-triggered sliding mode control for Roesser model with time delays

This paper is concerned with the event-triggered sliding mode control (SMC) strategy for the discrete-time two-dimensional (2-D) systems represented by Roesser model with time delays. Firstly, the linear sliding surface functions combined with the event-triggered scheme are constructed for the 2-D Roesser model. Then sufficient conditions are established for the asymptotic stability of the reduced-order sliding mode dynamics and the existence of linear sliding surface functions in terms of linear matrix inequality. Subsequently, the event-triggered sliding mode control law is designed by the Lyapunov function approach to drive the state trajectories of the resultant closed-loop system into a bounded region and maintain there for subsequent time. Finally, a numerical example is given to illustrate the effectiveness of the proposed SMC design method.

Discrete-Time Angle Constraint Interception with Model-Assisted Target Maneuver Estimator

This paper investigates the problem of designing angle constraint guidance law against unknown maneuvering targets based on discrete-time sliding mode control theory. Invoking the fact that the future course of action of the target, an independent entity, cannot be predicted beforehand due to its complexity and unpredictability, a model-assisted discrete-time disturbance observer in cooperation with a singularity-free strategy is proposed first to estimate the target maneuver. Based on the reconstructed signal and a fast convergence time-varying sliding surface, a new chattering-mitigated super-twisting-like discrete-time impact angle constraint guidance law is then synthesized. Stability analysis shows that the closed-loop system trajectory can be forced to enter into a small region around the sliding surface. Simulations and comparisons with classical discrete-time sliding mode guidance law validate the effectiveness of the proposed guidance law.

Robust Trajectory Tracking in Satellite Time-Varying Formation Flying.

The robust time-varying formation control problem for a group of satellites is addressed. By the static state feedback control strategy and the disturbance estimation theory, a formation flying controller is proposed for the satellite group to form desired time-varying formation patterns and trajectories, and achieve the satellite attitude consensus. The dynamics of each satellite is subject to nonlinearities, parametric perturbations, and external disturbances. Robustness analysis shows that the trajectory and attitude tracking errors of the global closed-loop control system can converge into a given neighborhood of the origin in a finite time. The numerical simulation results validate the effectiveness and advantages of the proposed formation flying controller.

Robust stabilisation of linear time‐invariant time‐delay systems via first order and super‐twisting sliding mode controllers

This study presents a novel scheme for the synthesis of first-order and super-twisting sliding mode controllers for the robust stabilisation of a class of linear time-invariant time-delay systems subject to matched disturbances. Starting from a stability analysis of the system to guarantee that the resulting sliding mode dynamics is asymptotically stable, linear matrix inequality conditions of reduced conservatism are derived by using the Lyapunov-Krasovskii approach. Based on the stability analysis, the sliding mode controllers are synthesised to force the evolution of the closed-loop system trajectories to converge onto a prescribed sliding surface and to ensure that they remain there for all subsequent time. Unlike existing results, the implementation of the proposed approach does not involve strong requirements on the system structure. A numerical and a practical example along with a comparative analysis prove the effectiveness of the proposal and highlight its benefits.

Confidence Regions for Predictions of Online Learning-Based Control

Although machine learning techniques are increasingly employed in control tasks, few methods exist to predict the behavior of closed-loop learning-based systems. In this paper, we introduce a method for computing confidence regions of closed-loop system trajectories under an online learning-based control law. We employ a sampling-based approximation and exploit system properties to prove that the computed confidence regions are correct with high probability. In a numerical simulation, we show that the proposed approach accurately predicts correct confidence regions.

Lyapunov-based Triggering Mechanisms for Event-triggered Control

In this paper, a new event-triggering scheme is proposed for a class of event-triggered control systems directly based on input-to-state stable Lyapunov functions. This class is characterized by a constructed decreasing function which is the upper bound of the suitably chosen ISS Lyapunov funtion. It is proven that, compared with the dynamic event-triggering mechanism reported in the literature, this new scheme can ensure a larger minimum interevent time with the same decay rate of the trajectory of the resultant closed-loop system, which is demonstrated through a numerical example.

Event-triggered sliding mode control of nonlinear dynamic systems

In this work, the problem of sliding mode observer design is investigated for a class of repeated scalar nonlinear systems via dynamic event-triggered approach. By constructing an event-triggered observer and a sliding mode surface, the system dynamics is obtained and an event-triggered controller is designed to ensure that the closed-loop system trajectories are restricted to the pre-specified sliding region. Sufficient conditions are provided to guarantee that the system dynamics is asymptotically stable with a desired H∞ performance level. Two illustrative examples are provided to demonstrate the effectiveness and potential of the proposed design method.

Quaternion-based adaptive attitude control of asteroid-orbiting spacecraft via immersion and invariance

The design of an attitude control system for an asteroid-orbiting satellite via immersion and invariance is the subject of this paper. It is assumed that the asteroid is rotating with a constant rate, and that the inertia parameters of the satellite and the coefficients in the spherical harmonic gravitational potential of the asteroid are not known. The objective is to regulate the quaternion trajectory of the satellite orbiting in an equatorial orbit. Based on the immersion and invariance (I&I) theory, a noncertainty-equivalence adaptive (NCEA) attitude control law is derived. For the design, a backstepping design process involving two steps is used, and filtered signals are constructed to overcome the difficulty in solving certain matrix inequalities of the I&I methodology. The control law includes a stabilizer and an identifier - designed separately. Unlike the classical certainty-equivalence adaptive (CEA) systems, here the estimated parameters include not only the signals obtained from an integral type update law, but also judiciously chosen nonlinear algebraic signals that yield stronger stability properties. By the Lyapunov stability analysis, it is shown that the quaternion trajectories of the disturbance input-free closed-loop system asymptotically converge to the equilibrium point. The control law is effective in regulating the attitude to the equilibrium point with minimal rotation of spacecraft. Also, for the model with disturbance input, uniform ultimate boundedness of system trajectories is established. Simulation results for the attitude control of spacecraft in orbit around asteroid 433 Eros are presented for illustration. These results show that the spacecraft achieves nadir pointing attitude despite uncertainties in the system dynamics.

Adaptive fault-tolerant control for active suspension systems based on the terminal sliding mode approach

In this paper, a control system is designed for a vehicle active suspension system. In particular, a novel terminal sliding-mode-based fault-tolerant control strategy is presented for the control problem of a nonlinear quarter-car suspension model in the presence of model uncertainties, unknown external disturbances, and actuator failures. The adaptation algorithms are introduced to obviate the need for prior information of the bounds of faults in actuators and uncertainties in the model of the active suspension system. The finite-time convergence of the closed-loop system trajectories is proved by Lyapunov's stability theorem under the suggested control method. Finally, detailed simulations are presented to demonstrate the efficacy and implementation of the developed control strategy.

Robust formation flying control for a team of satellites subject to nonlinearities and uncertainties

This paper addresses the problem of robust formation controller design for a group of satellites the dynamics of which involve nonlinearities and uncertainties. A formation flying controller is proposed for the satellite group, which includes a position controller to form the desired accurate formation and an attitude controller to align the satellite attitudes. It is shown that the trajectory and attitude tracking errors of the overall closed-loop control system can converge into a given neighborhood of the origin in a finite time. Numerical simulation studies are provided to demonstrate the advantages of the proposed formation control scheme.

Adaptive Control by Regulation-Triggered Batch Least Squares

The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of nonobservable parameters. The extension is achieved by using a novel batch least-squares identifier (BaLSI), which is activated at the time of the events. BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system (nominal in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well known control problem—the state regulation of the wing-rock model. Comparisons with other adaptive schemes are also provided for this particular problem.