Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite‐time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion‐based nonlinear proportional‐derivative controller using full‐state feedback is designed first, yielding uniformly almost globally finite‐time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional‐derivative controller ensures finite‐time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high‐gain injection, as opposed to the semi‐global results, but also overcome the unwinding problem associated with some quaternion‐based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Signal reconstruction in the presence of finite‐rate measurements: finite‐horizon control applications

In this paper, we study finite‐length signal reconstruction over a finite‐rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worst‐case reconstruction error. We then compute upper bounds on the error that arise from different coding schemes and under different causality assumptions. When the encoder and decoder are noncausal, we derive an upper bound that either achieves the universal lower bound or is comparable to it. When the decoder and encoder are both causal operators, we show that within a very broad class of causal coding schemes, memoryless coding prevails as optimal, imposing a hard limitation on reconstruction. Finally, we map our general reconstruction problem into two important control problems in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a finite‐rate noiseless channel. The first problem is to minimize a finite‐horizon weighted tracking error between the remote system output and a reference command. The second problem is to navigate the state of the remote system from a nonzero initial condition to as close to the origin as possible in finite‐time. Our analysis enables us to quantify the tradeoff between time horizon and performance accuracy, which is not well studied in the area of control with limited information as most works address infinite‐horizon control objectives (e.g. stability, disturbance rejection). Copyright © 2009 John Wiley & Sons, Ltd.     

Sliding mode output‐feedback causal output tracking for a class of discrete‐time nonlinear systems

The output tracking (OT) of arbitrary references in discrete‐time (DT) nonlinear systems is addressed by designing an output‐feedback control. A set of difference‐algebraic equations is proposed as an exact solution of the problem. Using a novel technique of approximating DT functions, the system disturbance and steady states, characterized by tracking error identically zero, for both the system state and the control input, are represented as signals generated by a disturbed dynamic system. Using the mentioned dynamics, the control system is extended. Then, a state observer is proposed to estimate the resulting extended system state. Finally, a DT sliding mode controller is designed to achieve the approximate OT. Simulations show the effectiveness of the proposed control scheme.     

Fixed‐time output‐feedback consensus tracking control for second‐order multiagent systems

This paper is concerned with the problem of fixed‐time consensus tracking control for a class of second‐order multiagent systems under an undirected communication graph. A distributed output‐feedback fixed‐time consensus tracking control scheme is proposed to make the states of all individual agents simultaneously track a time‐varying reference state even when the reference state is available only to a subset of the group members and only output measurements are available for feedback. Homogeneous Lyapunov function and homogeneity property are employed to show that the control scheme can guarantee the consensus tracking errors converging the origin in finite time which is bounded by a fixed constant independent of initial conditions. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control law.     

Real‐time nonlinear moving horizon observer with pre‐estimation for aircraft sensor fault detection and estimation

This paper presents a real‐time nonlinear moving horizon observer (MHO) with pre‐estimation and its application to aircraft sensor fault detection and estimation. An MHO determines the state estimates by minimizing the output estimation errors online, considering a finite sequence of current and past measured data and the available system model. To achieve the real‐time implementability of such an online optimization–based observer, 2 particular strategies are adopted. First, a pre‐estimating observer is embedded to compensate for model uncertainties so that the calculation of disturbance estimates in a standard MHO can be avoided without losing much estimation performance. This strategy significantly reduces the online computational complexity. Second, a real‐time iteration scheme is proposed by performing only 1 iteration of sequential quadratic programming with local Gauss‐Newton approximation to the nonlinear optimization problem. Since existing stability analyses of real‐time moving horizon observers cannot address the incorporation of the pre‐estimating observer, a new stability analysis is performed in the presence of bounded disturbances and noises. Using a nonlinear passenger aircraft benchmark simulator, the simulation results show that the proposed approach achieves a good compromise between estimation performance and computational complexity compared with the extended Kalman filtering and 2 other moving horizon observers.     

DISCRETE‐TIME OBSERVER‐BASED OUTPUT TRACKING CONTROLLER DESIGN FOR NONMINIMUM PHASE SYSTEMS WITH PERTURBATIONS

In this paper, an observer‐based output tracking controller for an SISO nonminimum phase discrete‐time system is proposed. When the disturbances between two consecutive sampling instances do not vary significantly, the observer algorithm can simultaneously estimate the system states and the unknown perturbation, and can render the estimation errors of system states and perturbation constrained in a small bounded region. The control law, including a feedforward term and a feedback input, can make the tracking error constrained in a small bounded region with guaranteed system stability. A numerical example is presented to demonstrate the applicability of the proposed control scheme.     

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method.     

Robust adaptive fault‐tolerant tracking control for a class of high‐order nonlinear system with finite‐time prescribed performance

In this article, an improved prescribed performance adaptive control strategy is developed to handle the output tracking control problem for a class of nonlinear high‐order systems with actuator faults. The actuator faults considered include the bias fault and gain fault models. A technique of adding a power integrator is utilized to deal with the controller design problem of high‐order system. With the help of backstepping technology and the classic adaptive control, an output tracking control scheme is proposed, which can guarantee that all signals of the closed‐loop system are bounded and the tracking error converges to a finite‐time predetermined region. Finally, the feasibility of the presented control method is tested through the simulation results.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

Robust Missile Autopilots With Finite‐Time Convergence

This paper presents a new longitudinal autopilot to address the finite‐time tracking problem for uncertain agile missiles. The proposed autopilot is essentially a composite control scheme, which is obtained through the finite‐time control methodology and the nonlinear disturbance observer (NDOB) approach. The key idea in this scheme is that the NDOB is adopted to estimate the aerodynamic uncertainties and external disturbances in an integrated manner. With the aid of the finite‐time bounded function and the Lyapunov function method, the finite‐time stability of the closed‐loop system is established, which shows that the angle‐of‐attack response will converge to the external command signal in finite time. Numerical simulation results are presented to demonstrate the superiority of the proposed scheme.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Reduced‐order observer‐based output‐feedback tracking control of nonlinear systems with state delay and disturbance

In this paper, we investigate the problem of output‐feedback tracking control for a class of nonlinear SISO systems in the strick‐feedback form, which are subject to both uncertain delay‐related functions and disturbances. A reduced‐order observer is first introduced to provide the estimates of the unmeasured states. Then, an output‐feedback controller is recursively designed based on the backsteppng method. By constructing an appropriate Lyapunov–Krasovskii functional, we prove that all the signals in the closed‐loop system are bounded. The tracking performance is guaranteed by suitably choosing the design parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed control algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Event‐triggered approach for finite‐time state estimation of delayed complex dynamical networks with random parameters

This article emphasizes the finite‐time state estimation problem for delayed complex dynamical networks with random parameters. In order to reduce the amount of transmission process, an aperiodic sampled‐data event‐triggered mechanism is introduced to determine whether the measurement output should be released at certain time points which incorporate an appropriate triggering condition and sampling moments. Furthermore, a concept of finite‐time boundedness in the pth moment is proposed to access the performance of state estimator. The objective of this article is to design an event‐triggered state estimator to estimate the states of nodes such that, in the presence of time delays, uncertainties, and randomly changing coupling weights, the estimation error system is finite‐time bounded in the pth moment related to a given constant. Some sufficient conditions in form of linear matrix inequalities and algebraic inequalities are established to guarantee finite‐time boundedness. Finally, a numerical example is presented to show the effectiveness of the theoretical results.     

Distributed output‐feedback finite‐time tracking control of nonaffine nonlinear leader‐follower multiagent systems

The distributed output‐feedback tracking control for a class of networked multiagents in nonaffine pure‐feedback form is investigated in this article. By introducing a low‐pass filter and some auxiliary variables, we first transform the nonaffine system into the affine form. Then, the finite‐time observer is designed to estimate the states of the newly derived affine system. By applying the fraction dynamic surface control approach and the neural network‐based approximation technique, the distributed output‐feedback control laws are proposed and it is proved that the tracking errors converge to an arbitrarily small bound around zero in finite time. Finally, some simulation examples are provided to confirm the effectiveness of the developed method.