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In this paper, the constrained control of systems evolving on matrix Lie groups with uncertainties is considered. The proposed methodology is composed of a nominal Model Predictive Control (MPC), and a feedback controller. The previous work on the control of systems on manifolds is applied to design the nominal MPC, which generates the nominal trajectory. In the nominal MPC, the state and input constraints on the Lie group are transformed into the constraints on the Euclidean space. While to deal with uncertainties, the feedback control used to track the nominal trajectory is designed directly on the Lie group. The tracking error in the feedback control is proved to be bounded in invariant sets, which are further used to revise the constraints in nominal MPC. We prove that the input‐to‐state stability of the entire system under the proposed control methodology with respect to the disturbances can be achieved. The proposed methodology is applied to the constrained attitude control of rigid bodies with uncertainties. In the application example, the detailed mathematical proof and the comparative numerical simulation are presented to demonstrate the feasibility of the proposed methodology. [ABSTRACT FROM AUTHOR]

Since the complexity nonlinearities generated by discontinuous control and event‐triggered scheme, fixed‐time formation in event‐based framework is a more challenging issue compared with the continuous‐time control. This paper focuses on fixed‐time leaderless formation problem for multi‐agent systems with undirected topology. We propose a distributed robust event‐triggered control strategy for the fixed‐time formation where predictor‐based state transformation is employed to deal with input delay and sliding mode technology is implemented to solve bounded disturbances. We also obtain that the upper bound of the formation settling time is only determined by delay time, control design parameters, network connectivity, and independent of the initial conditions. In addition, the lower bound for the interexecution time is calculated to ensure that there is no Zeno behavior occurs. Finally, some numerical simulations are presented to show the effectiveness of the strategies. [ABSTRACT FROM AUTHOR]

In this article, distributed tracking control is studied for multiple Euler–Lagrange systems in the presence of external disturbances and input saturation. Specifically, full‐state constraints, input saturation, communication delays, and unmeasured velocities are all considered simultaneously. First, a novel event‐triggered scheme is developed to save the communication source and reduce computational load. Second, the anti‐saturation compensation algorithm is exploited to compensate for system saturation. Third, an adaptive law is designed to offset external disturbances. Moreover, a high‐gain observer is employed to estimate unmeasured velocities. Theorem analysis shows the stability of the closed‐loop system, and numerical simulations are provided to verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this article, a novel robust finite‐time tracking control scheme is proposed for a class of uncertain nonlinear systems subject to the model uncertainty, external disturbance, and input saturation. A barrier function based disturbance observer (BFDO) with finite‐time convergence performance is developed to estimate the non‐smooth nonlinear compound disturbance, which includes the uncertainty, disturbance of system and input saturation. In addition, an adaptive continuous nonsingular terminal sliding mode controller, based on the barrier function and the estimate of the BFDO is developed. The Lyapunov stability and finite‐time convergence of the proposed control scheme are proved. The effectiveness and performance advantage of the proposed control scheme is demonstrated by numerical simulations and comparison with existing works. [ABSTRACT FROM AUTHOR]

This article studies the event‐triggered control problem for nonlinear systems that are merely integral input‐to‐state stable (iISS) with respect to measurement errors and external inputs. By using the iISS Lyapunov function, which comes from a necessary and sufficient condition on iISS, an integral‐based event‐triggering mechanism is introduced to compensate the effects of measurement errors. Under some assumptions on the gains of the iISS Lyapunov function, both the closed‐loop iISS and Zeno‐freeness are proved when the external inputs are measurable. In the presence of unknown disturbances, a novel switching event‐triggering mechanism is designed based on the relationship between the transmitted state and some threshold constant. Subsequently, the corresponding lower bound of inter‐event times is given explicitly to ensure Zeno‐freeness. It is shown that the proposed switching mechanism can be applicable to the nonlinear systems where some existing event‐triggering mechanisms are invalid in avoiding Zeno behavior. Finally, numerical simulations are provided to illustrate the efficiency and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we propose a networked control architecture to ensure the plant's safety in the presence of cyber‐attacks on the communication channels. In particular, we consider systems subject to both state and input constraints that must be preserved for safety reasons despite any admissible attack scenario. To this end, first, two different detectors are proposed to detect attacks on the setpoint signal as well as on the control inputs and sensor measurements. Then, an emergency controller (EC), local to the plant, is designed to replace the networked controller whenever an attack is detected. Finally, the concept of robust N‐step attack‐safe region is introduced to ensure that the EC is activated, regardless of the detector performance, at least one‐step before the safety constraints are violated. It is formally proved that the plant trajectory is uniformly ultimately bounded in an admissible region regardless of the attacker's actions and duration. Finally, by considering a continuous‐stirred tank reactor system, numerical simulations are presented to show the proposed solution's capabilities. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the nonsingular prescribed‐time stabilization problem for p‐normal form systems. Two significant progresses are made for the first time as follows: First, a novel concept named coordinate mapping of time domain, is proposed to transform the nonsingular prescribed‐time convergence problem into the ordinary finite‐time convergence problem of transformed time‐varying system. Second, a set of new parameters are introduced to extend the existing adding a power integrator technique, such that the power restriction is removed. Based on above design procedure, a periodic controller is constructed to stabilize the state of the p‐normal form system into a small neighborhood of the equilibrium in prescribed time. Theoretical result is supported by numerical simulation. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: For the high precise tracking control purpose of a cable‐driven manipulator under lumped uncertainties, a novel adaptive fractional‐order nonsingular terminal sliding mode control scheme based on time delay estimation (TDE) is proposed and investigated in this paper. The proposed control scheme mainly has three elements, ie, a TDE element applied to properly compensate the lumped unknown dynamics of the system resulting in a fascinating model‐free feature; a fractional‐order nonsingular terminal sliding mode (FONTSM) surface element used to ensure high precision in the steady phase; and a combined reaching law with adaptive technique adopted to obtain fast convergence and high precision and chatter reduction under complex lumped disturbance. Stability of the closed‐loop control system is analyzed with the Lyapunov stability theory. Comparative simulations and experiments were performed to demonstrate the effectiveness of our proposed control scheme using 2‐DOF (degree of freedom) of a cable‐driven manipulator named Polaris‐I. Corresponding results show that our proposed method can ensure faster convergence, higher precision, and better robustness against complex lumped disturbance than the existing TDE‐based FONTSM and continuous FONTSM control schemes. [ABSTRACT FROM AUTHOR]

Summary: Novel robust finite‐time stabilizing algorithms are developed side by side for the state and output feedback designs. Being initially developed for a nonlinear cascade second‐order system, these algorithms are straightforwardly extendible to electromechanical systems of relative degree two. The proposed synthesis is based on the disturbance compensation, relying on the dirty differentiation and sliding mode approach, and it is applicable to a wider class of disturbances than that addressed in the literature. Simulation results illustrate the efficiency of the resulting synthesis procedure and support analytical results. [ABSTRACT FROM AUTHOR]

Summary: The purpose of this paper is to present an extension of the generalised supertwisting algorithm (STA) to the multivariable framework. We begin by introducing an algorithm that may be deemed as a linear, quasicontinuous, or discontinuous multivariable system, depending on the functions that define them. For the class represented by such an algorithm we prove the robust, Lyapunov stability of the origin and characterise the perturbations that preserve its stability. In particular, when its vector field is discontinuous or quasicontinuous our algorithm is endowed with finite‐time stability. Due to its resemblance to the scalar case, we denote such finite‐time stable systems as generalised multivariable STA. Furthermore, the class of finite‐time stable systems comprise the currently available versions of STAs. To finalise, by means of simulation examples, we show that our proposed finite‐time stable algorithms are well suited for signals online differentiation and highlight their dynamical traits. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of formation control is considered for a class of unknown nonaffine nonlinear multiagent systems under a repeatable operation environment. To achieve the formation objective, the unknown nonlinear agent's dynamic is first transformed into a compact form dynamic linearization model along the iteration axis. Then, a distributed model‐free adaptive iterative learning control scheme is designed to ensure that all agents can keep their desired deviations from the reference trajectory over the whole time interval. The main results are given for the multiagent systems with fixed communication topologies and the extension to the switching topologies case is also discussed. The feature of this design is that formation control can be solved only depending on the input/output data of each agent. An example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper describes a new robust model predictive control (MPC) scheme to control the discrete‐time linear parameter‐varying input‐output models subject to input and output constraints. Closed‐loop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal set, which are solved offline, for the underlying online MPC optimization problem. The main attractive feature of the proposed scheme in comparison with previously published results is that all offline computations are now based on the convex optimization problem, which significantly reduces conservatism and computational complexity. Moreover, the proposed scheme can handle a wider class of linear parameter‐varying input‐output models than those considered by previous schemes without increasing the complexity. For an illustration, the predictive control of a continuously stirred tank reactor is provided with the proposed method. [ABSTRACT FROM AUTHOR]

A fault diagnosis and compensation problem for two-dimensional discrete time systems with time-varying state delays is studied in this paper. The concerned two-dimensional systems are described by the Fornasisi-Marchesini second model and are subject to unknown disturbances. First, a fault detection and diagnosis module is designed to obtain the information on sensor faults; a new fault detection and diagnosis integrated design, using the observer based on descriptor system approach, is proposed to detect and estimate the sensor faults. The integrated design can maximize the fault detection rate for a given false alarm rate. Sufficient conditions for the existence of the integrated fault detection and diagnosis design are derived in the context of norm evaluation and provided in terms of matrix inequalities. Second, a fault-tolerant control module is proposed upon an existing output feedback controller. When the sensor fault occurs, the faulty measurement can be identified and corrected by the proposed fault detection and diagnosis module. In this case, the feedback controller can guarantee the performance of the closed-loop system even when encountering sensor faults. Finally, the proposed method is applied to a thermal process to illustrate its effectiveness. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we apply the active disturbance rejection control approach to output-feedback stabilization for uncertain lower triangular nonlinear systems with stochastic inverse dynamics and stochastic disturbance. We first design an extended state observer (ESO) to estimate both unmeasured states and stochastic total disturbance that includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance, and uncertainty caused by the deviation of control parameter from its nominal value. The stochastic total disturbance is then compensated in the feedback loop. The constant gain and the time-varying gain are used in ESO design separately. The mean square practical stability for the closed-loop system with constant gain ESO and the mean square asymptotic stability with time-varying gain ESO are developed, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A generalized homogeneous exact set-point tracking control methodology for a class of disturbed higher-order nonlinear systems is investigated in this paper. By virtue of utilizing the disturbance estimation and active elimination approach, a homogeneous domination feedback technique is then integrated such that a generalized composite active anti-disturbance control framework is proposed with a delicate handling procedure of the non-vanishing nonlinearities. The proposed methodology has several new features. First, a genuine nonlinear composite controller employing the system nonlinearities will bring an improvement of the control performances. Second, the flexility of the design methodology renders its suitability for random output tracking with mismatched disturbances in every channel. Moreover, the control function is constructed in a neat nested form and hence easier to be implemented. Numerical simulation results affirm the output tracking control performances. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a robust sliding mode-based extremum-seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input-output linearizing method with variable-structure feedback, such that the closed-loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum-seeking control algorithms, the control scheme includes a dynamic modelling-error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient-based optimization algorithm. Practical stabilizability for the closed-loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with the robust finite time tracking of desired trajectories for a wide group of robotic manipulators in spite of unknown disturbances, uncertainties, and saturations of actuators while only manipulator's positions are available and its velocities are not measurable physically. A new form of chattering-free second order fast nonsingular terminal sliding mode control scheme is introduced to design input torques for fulfilling the determined tracking objective in the adjustable total finite settling time. The proposed control algorithm is incorporated with two nonlinear observers to estimate disturbances and velocities of joints within finite settling times. The global finite time stability of the closed-loop manipulator is analytically proved. Finally, a numerical simulation is carried out to verify the effectiveness of the designed input torques. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to address the reduction of online computational complexity and infeasibility problem of explicit model predictive control for constrained systems under external disturbance. In feasible state space, in order to avoid the expensive database searching procedure, support vector machine-based approximation is proposed to yield a novel unified explicit optimal control law rather than a piecewise affine one developed by explicit model predictive control. In infeasible state space, through constructing finite maximum control invariant sets around fictitious equilibrium points, a reachable controller is devised to steer the infeasible state asymptotically to the feasible state space without violating the hard constraint. Consequently, global robustness is guaranteed by introducing a minimum robust positively invariant set by means of the tube-based technique, despite the coexistence of external disturbance and training error. Finally, the performance of the presently proposed control law is evaluated through three groups of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new event-switched control method is presented for controlling discrete-time linear systems subject to bounded disturbances. The main advantage of the proposed method is that the nominal performance of the controlled system with periodic control updates is kept in a framework that do not require to periodically update the control law. The feedback control loop can be opened as long a state-dependent event condition is satisfied. This condition is obtained using set theory approaches. In particular, the concept of robustly positively invariant sets is used to calculate the nominal performance and the event condition. The simulation presented in this paper confirms the efficiency of the present approach. A reduction of the numerical complexity of the approach is also proposed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A robust consensus controller is proposed for heterogeneous higher-order nonlinear multi-agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time-varying nonhomogeneous finite-time disturbance observer and sliding mode control is designed to realize the network consensus of higher-order multi-agent systems. The time-varying finite-time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite-time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, robust containment problem is investigated for a class of multi-leader multi-agent linear systems in the presence of time-varying uncertainties. To achieve containment, a new kind of adaptive containment protocols are proposed for the multi-agent systems. Specifically, the designed protocols consist of a continuous linear term and a discontinuous term. The linear term of the designed protocol is employed to achieve containment while the discontinuous term is utilized to eliminate the effect of uncertain dynamics on the achievement of containment. By using tools from non-smooth analysis and algebraic graph theory, some efficient criteria for achieving robust containment in the closed-loop multi-agent systems are obtained and analyzed. One favorable property of the designed protocol is that containment in the closed-loop multi-agent systems can be achieved in a fully distributed fashion over any given connected and detail-balanced communication graph without using any global information about the communication graph. The effectiveness of the analytical results is finally verified by performing numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we study the robust consensus tracking problem for a class of high-order multi-agent systems with unmodelled dynamics and unknown disturbances. A continuous robust state feedback control algorithm is proposed to enable the agents to achieve robust consensus tracking of a desired trajectory. By utilizing Lyapunov analysis methods and an invariance-like theorem, sufficient conditions for semi-global asymptotic consensus tracking are established. A robust output feedback control algorithm is designed to obtain a uniformly ultimately bounded consensus tracking result. Numerical simulations are provided to show the effectiveness of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Integrated guidance and control of an elastic flight vehicle based on constrained robust model predictive control is proposed. The design is based on a partial state feedback control law that minimizes a cost function within the framework of linear matrix inequalities. It is shown that the solution of the defined optimization problem stabilizes the nonlinear plant. Nonlinear kinematics and dynamics are taken into account, and internal stability of the closed-loop nonlinear system is guaranteed. The performance and effectiveness of the proposed integrated guidance and control against non-maneuvering and weaving targets are evaluated using computer simulations. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed robust finite-time attitude containment control for multiple rigid bodies with uncertainties including parametric uncertainties, external disturbances, and actuator failures. Two novel types of distributed control laws are designed corresponding to two different cases, respectively, and both of them can drive the orientations of the followers into the convex hull formed by the orientations of leaders in a finite time. Simulation results show the effectiveness of the proposed design. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we develop a nonlinear controller to achieve output tracking for a nonminimum phase vertical take-off and landing aircraft without velocity measurements. To attenuate the effects of input disturbances and unmatched uncertainties, auxiliary control inputs are introduced in the state observer. Then by taking the aircraft lateral movement into consideration, a control law is proposed to force the vertical take-off and landing aircraft to asymptotically track the desired trajectories even in the presence of unexpected changes of the trajectories, while driving the unstable internal dynamics to follow the bounded and causal ideal internal dynamics via the stable system center method. Numerical simulation results illustrate the effectiveness and robustness of the proposed controller. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]