Observer-based Control Law Research Articles

Exponential stabilizability and observability at the target imply semiglobal exponential stabilizability by templated output feedback

For nonlinear analytic control systems, we introduce a new paradigm for dynamic output feedback stabilization. We propose to periodically sample the usual observer based control law, and to reshape it so that it coincides with a “control template” on each time period. By choosing a control template making the system observable, we prove that this method allows to bypass the uniform observability assumption that is used in most nonlinear separation principles. We prove the genericity of control templates by adapting a universality theorem of Sussmann.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.

Prescribed-time and output feedback stabilization of heat equation with an intermediate-point heat source and boundary control

This paper addresses the problem of prescribed-time stabilization for the heat equation with an interior point heat source under output feedback. The study employs a two-step backstepping approach along with time-varying feedback techniques. A prescribed-time state observer and an observer-based boundary control law are developed. The proposed method extends the applicability of the prescribed time-stabilizing algorithm to heat equations with non-strict feedback terms. Numerical simulations validate its effectiveness.

Predefined-Time Platoon Control of Unmanned Aerial Vehicle with Range-Limited Communication

In this paper, the predefined-time platoon control for multiple uncertain unmanned aerial vehicles (UAVs) under range-limited communication and external disturbance constraints is considered. A novel control scheme, which can guarantee communication connectivity, collision avoidance, and the predefined convergence time simultaneously, is proposed. To achieve disturbance robustness, an observer-based distributed control law is firstly proposed with a time-varying gain. Then, a radial basis function neural network (RBFNN) with an adaptive tuning law is applied to approximate uncertainties of the system. Under the time and error transformation techniques, uniformly ultimate boundedness (UUB) stability of the closed-loop system is guaranteed within predefined convergence time. Compared with the existing results, the proposed method allows the system to have UUB within any predefined time without depending on the initial conditions or system parameters. Finally, simulation results are presented to verify the derived theorem.

Fault-Tolerant Control of Stochastic High-Order Fully Actuated Systems.

In recent years, high-order fully actuated (HOFA) systems, founded by Prof. GR Duan, have recorded rapid progress for deterministic systems. However, the control issue of stochastic fully actuated systems is still an open problem. This study develops a novel stochastic HOFA system model that complements the existing HOFA methodology. Notably, stochastic signals can be considered in the proposed model, different from the case in the deterministic model. By adopting a high-order operator, equivalent control and stabilization control laws are realized to guarantee the global asymptotic stability in probability of the closed-loop system. For the system with sensor gain faults, an observer-based fault-tolerant control law is designed. Finally, the simulation results validate the effectiveness of the proposed control schemes.

Observer-based control for large-scale interconnected systems with parameter uncertainty and application to wireless power transfer systems

In the work, the observer-based control is designed and analyzed for a class of large-scale interconnected systems subject to parameter uncertainty. In the beginning, we build a large-scale interconnected system with parameter uncertainty and apply this model to a multi-level wireless power transfer system. By using this modeling method, the order of multi-level wireless power transfer system is greatly deduced. In addition, the multi-level wireless power transfer system include coupling terms and uncertain parameters considered in the observer-based control law design. We earn sufficient conditions of this model stability for multi-level wireless power transfer systems under this control law through the Lyapunov stability theorem and Young’s inequality. The stability analysis method suggested in the work could also be adopted in other practical plants. At last, the correctness and availability of this suggested approach are verified through simulation results.

Time-varying formation for MSVs with input and prescribed performance constraints by fixed-time event-triggered sliding mode control

This work develops a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve the control performance, ensure the navigation safety and reduce the communication burden. At first, a fixed-time adaptive radial basis function neural network (FxRBFNN) observer is designed to provide the estimations for external environmental disturbances and model parameters uncertainties. Then, observer-based fixed-time distributed time-varying formation event-triggered control law is proposed based on the novel fixed-time auxiliary dynamic system (FxADS), the proposed prescribed performance function, the designed fixed-time nonsingular terminal sliding mode (FxNTSM) manifold and the proposed uniform exact differentiator. Finally, the system stability is proved by Lyapunov theory. The salient features as follows. First, to enhance the convergence performance for time-varying formation control method, a novel hyperbolic cosecant prescribed performance function (PPF) is introduced. Second, a novel FxADS is proposed to confront input constraints. Third, the proposed scheme is combined with a relative threshold event-triggered strategy to reduce the unnecessary updates of actuators under the premise of ensuring the control performance. Fourth, to avoid the proposed formation control law including adjacent vessel accelerations, this work proposed an improved uniform exact differentiator to identify them. Numerical simulations confirm that the proposed scheme has superior control performance.

Formation Control of Networked Mobile Robots With Unknown Reference Orientation

In this article, the distributed leader-following formation control problem of networked mobile robots is investigated. The desired formation is specified by a reference trajectory generated by the leader and the followers' desired relative positions with respect to the leader. On the one hand, for any security-aware multirobot systems, the values of the leader's position and orientation are generally not allowed to be transmitted via the inter-robot communication in the case of the information leakage of formation caused by the possible eavesdropping. On the other hand, relative orientations, different from relative positions, are typically difficult for mobile robots to measure directly, which makes the reference orientation unknown to all followers. In order to track the reference trajectory and form a desired formation in the absence of the reference orientation, followers are divided into two groups according to whether they are able to directly measure the relative positions with respect to the leader. The topology of the sensing/communication network among multirobot systems is described by a directed graph containing a directed spanning tree. Then, two observer-based control laws are proposed for two groups of followers, respectively, in both of which the unknown tracking errors are properly estimated. It is rigorously proven that the resulting closed-loop multirobot system is globally uniformly asymptotically stable. Finally, the effectiveness of our approach is illustrated by an experiment conducted on networked TurtleBot3 Burger mobile robots.

Observer-based event-triggered sliding mode control for delayed systems with unknown disturbances

This paper develops the observer-based event-triggered sliding mode control strategy for delayed systems involving unknown disturbances. This strategy comprises a triggering rule which can effectively save resources and an observer-based control law which can drive the states of delayed systems into the practical sliding mode band in some finite time. Some sufficient conditions coupled with this control strategy are proposed to guarantee the robust performance of the delayed systems. Significant outcome of this strategy is that it can be applied to the case in which the disturbances are unmeasured or unknown. Finally, two numerical examples and its simulations are presented to show the performance of the systems and effectiveness of this control strategy.

Self-triggered resilient stabilization of linear systems with quantized outputs

This paper studies the problem of stabilizing a self-triggered control system with quantized output. Employing a standard observer-based state feedback control law, a self-triggering mechanism that dictates the next sampling time based on quantized output is co-developed with an output encoding scheme. If, in addition, the transmission protocols at the controller-to-actuator (C–A) and sensor-to-controller (S–C) channels can be adapted, the self-triggered control architecture can be considerably simplified, leveraging a delicate observer-based deadbeat controller to eliminate the need for running the controller in parallel at the encoder side. To account for denial-of-service (DoS) in the S–C channel, the proposed output encoding and self-triggered control schemes are further made resilient. It is shown that a linear time-invariant system can be exponentially stabilized if some conditions on the average DoS duration time are met. There is a trade-off between the maximum inter-sampling time and the resilience against DoS attacks. Finally, a numerical example is presented to demonstrate the practical merits of the proposed self-triggered control schemes and associated theory.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

Distributed-Observer-Based Distributed Control Law for Affine Nonlinear Systems and Its Application on Interconnected Cruise Control of Intelligent Vehicles

Distributed-observer-based distributed control law for interconnected systems has become the research focus in recent years. This paper extends this study from linear systems to a class of affine nonlinear systems. Before this, distributed observer for nonlinear systems with control inputs has not been studied, as well as the distributed-observer-based distributed control law. To fill this gap, we overcome the difficulty of proving joint observability for distributed nonlinear observer by an original analysis method based on maximum invariant distribution. In addition, the influence of model mismatch on distributed observer and distributed controller is also investigated and analyzed in detail. By analyzing the complex coupling relationship between observer dynamics, control input, and model mismatch, we successfully deal with the dissatisfaction of separation principle and prove the stability of observer error systems and closed-loop systems. The results show both the error dynamics of distributed observer and the system states of closed-loop system formed by the observer-based distributed control law can converge to an arbitrarily small invariant set around the origin. In addition to the original work in distributed-observer-based distributed control law, this paper also contributes to the design of distributed observer. Firstly, the proposed design method is also applicable to distributed observer of autonomous systems. Compared to the existing results, our method admits weaker assumptions. Specifically, one could find an approximate system to meet the assumptions required by designing distributed observer when the underlying system fails to meet the requirements. At last, the automated highway system is employed to verify the results.

Velocity-free finite-time relative 6-DOF control for rigid spacecraft

This paper addresses the problem of spacecraft’s finite-time six-degree-of-freedom(6-DOF) tracking control without velocity measurements. To estimate the unavailable incorporating angular and translational velocities (called the dual angular velocity), a novel observer with a simple structure and finite-time stability is presented in the dual quaternion frame. Then, combining with the estimated dual angular velocity, a continuous velocity-free 6-DOF control law based on the terminal sliding mode theory is presented to achieve the relative pose tracking objective within finite time, where the specially designed parameter ensures its non-singularity. In addition, by designing the desired reference frame, the proposed control law can be employed to various missions. With consideration of the observation errors, a rigorous proof is provided to demonstrate the finite-time stability of the observer-alone and the observer-based control law. Two typical numerical simulations, hovering and circumnavigation, are carried out to verify the effectiveness of the proposed method.

Anti-disturbance Trajectory Tracking Control for a Quadrotor UAV with Input Constraints⋆

This paper presents the trajectory tracking control for a quadrotor unmanned aerial vehicle(UAV) with disturbances and input constraints. The UAV's system is decomposed into an outer position loop and an inner attitude loop. The position tracking control is achieved by a class of saturated proportional-derivative(PD) control laws. Assuming that the unknown disturbances mainly effect on the translational dynamics, an adaptive control term is investigated to compensate the effects of the disturbances. The position tracking control force implies a coupled-attitude system that connects the inner attitude loop with the outer position loop. An intrinsic PD control law, which is directly designed on the special orthogonal group SO(3), is proposed to track the desired attitude. In order to reduce the calculational difficulty of the attitude tracking control law, an observer-based control law is further developed while the control law and observer can be designed separately. Simulation results complete this work.

Robustly String Stable Longitudinal Control for Vehicle Platoons Under Communication Failures: A Generalized Extended State Observer-Based Control Approach

This paper investigates the longitudinal control of vehicle platoons with a focus on external disturbances, parameter uncertainties, and communication failures. When vehicle platoons encounter vehicle to vehicle wireless communication failures, the preceding vehicle’s acceleration is unavailable, which degrades the performance of the system. However, the existing achievements can not be directly used to address the aforementioned three issues. To this end, a generalized extended state observer-based control (GESOBC) law is contrived. First, the parameter uncertainties and the external disturbances are together regarded as a lumped disturbance. Then, a generalized extended state observer is designed to estimate the lumped disturbance and the preceding vehicle’s acceleration, separately. Based on the estimation, a composite controller consisting of a state feedback control part and an estimation-based feedforward control part is developed. Furthermore, it is proved that the proposed GESOBC method can guarantee the exponentially bounded stability of the individual vehicle and the input to state string stability of the whole vehicle platoon. Finally, numerical simulations are conducted to demonstrate the effectiveness and feasibility of the proposed method.

Evaluating the Optimal Electric Vehicle Location for a Hybrid Energy System Controlled with Novel Active Disturbance Rejection Controller

Power system control is an important issue with regard to power system safety, flexibility, and reliability. Over the years, various new power system control strategies have been explored, but the main disadvantage of these control strategies is their complexity in structures with respect to industrially applied PID controller. The present paper introduces a novel control strategy based on modified disturbance rejection control, which is a modification of the PID controller that not only preserves the simplicity of control design but also offers an effective control based on state observer-based control law. The proposed control strategy addresses some basic limitations of a PID controller and implements modified control law to remove these limitations. In order to prove the effective control of the proposed control strategy, a standard IEEE-39 bus power system integrated with renewable energy generations is developed, and a comparative analysis of the proposed controller is performed with respect to its ancestor controllers. The comparison is validated based on the system dynamic responses like frequency and tie-line power deviations when the power system is subjected to different disturbances. Furthermore, the power system is integrated with electric vehices (EVs) in vehicle-to-grid (V2G) mode in order to ascertain the effect of EVs when used in V2G mode. A novel study is carried out in which the optimal location of EVs in the power system is determined based on the enhancement in stability of the power system by EVs. The analyses are carried out in MATLAB Simulink software. Simulation reports reflect the optimal control action of the proposed controller with respect to already established strategies projected in the literature. Moreover, the results illustrate that EVs when connected in Area 1 and Area 3 of the power system, the system deviations and steady-state errors are much less as compared to the other cases.

A robust predictive observer-based integral control law for uncertain LTI systems under external disturbance

The integral control is an effective way to track non-zero constant reference. In this paper, to utilize a robust predictive integral control strategy in the output-feedback case, the control requirement and the goals are formulated in a suitable form. Then, by introducing a novel matrix transformation, the controller designing issue is translated into an optimization problem subjected to some constraints. Such constraints are represented in terms of linear matrix inequality (LMI). By solving a minimization problem, the gains of the integral controller are determined and updated at some time instants. Finally, several numerical simulations are given to evaluate the advantages of the suggested robust control method over similar ones. The outcomes confirm the superiority of the proposed idea compared to the existing approach.

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.

Robust event-triggered finite-time control of faulty networked flexible manipulator under external disturbance

In this paper, finite-time contractive stability analysis and observer-based H ∞ fault tolerant control problem is discussed for a networked single-link flexible manipulator subject to external disturbance, actuator, and sensor faults. The variable delay is considered in both sensor-to-controller and controller-to-actuator channels. In order to conserve the network resources and avoid Zeno phenomenon, the sampled-data-based event-triggered scheme is employed, which only requires the system states in discrete instants. The nonlinear unknown input observer is first designed to achieve the estimation of the system states and faults simultaneously. To reduce the conservatism of designing procedure, the Lyapunov–Krasovskii functional approach is used, which includes the information of the lower and upper bounds of variable data transmission delay. Then, sufficient delay dependent conditions are derived and an observer-based feedback control law and observer gains are computed by a set of linear matrix inequalities to realize that the augmented system is finite-time contractive stable and the states of the system remain within a specified threshold during a fixed time interval, which is smaller than the initial state bound. Furthermore, the prescribed H ∞ performance is satisfied in the presence of external disturbance. At last, simulation results are given to confirm the validity of the presented approach.

Broad-RBFNN-Based Intelligence Adaptive Antidisturbance Formation Control for a Class of Cluster Aerospace Unmanned Systems with Multiple High-Dynamic Uncertainties

This paper investigates the antidisturbance formation control problem for a class of cluster aerospace unmanned systems (CAUSs) suffering from multisource high-dynamic uncertainties. Firstly, to estimate and compensate the uncertainties existing in CAUS coordinate dynamics, an adaptive antidisturbance formation control law, which is combined by a robust adaptive control law and the second order disturbance observer, has been designed. Secondly, aiming at the adverse influences caused by the nonlinear time-varying nonlinearities existing in the formation flight dynamics, the radial basis function neural network (RBFNN) is introduced. Furthermore, considering the rapidly varying characteristics of the aforementioned formation flight nonlinearities, a novel board RBFNN (B-RBFNN) has been constructed and utilized to improve the approximation and compensation performance. In virtue of the fusing of the B-RBFNN and the second-order disturbance observer-based adaptive formation control law, the rapid response rate and the higher control accuracy of the formation control system can be achieved. As a result, a novel B-RBFNN-based intelligence adaptive antidisturbance formation control algorithm has been established for CAUS trajectory coordination and formation flight. Numerical simulation results are proposed to illustrate the effectiveness and advantages of the proposed B-RBFNN-based intelligent adaptive formation control method for the CAUS.