Robust Output Feedback Control of Single-Link Flexible-Joint Robot Manipulator with Matched Disturbances Using High Gain Observer.

This article focuses on the output feedback control of single-link flexible-joint robot manipulators (SFJRMs) with matched disturbances and parametric uncertainties. Formally, four sensing elements are required to design the controller for single-link manipulators. We have designed a robust control technique for the semiglobal stabilization problem of the angular position of the link in the SFJRM system, with the availability of only a position sensing device. The sliding mode control (SMC) based output feedback controller is devised for SFJRM dynamics. The nonlinear model of SFJRM is considered to estimate the unknown states utilizing the high-gain observer (HGO). It is shown that the output under SMC using HGO-based estimated states coincides with that using original states when the gains of HGO are sufficiently high. Finally, the results are presented showing that the designed control technique works well when the SFJRM model is uncertain and matched perturbations are expected.

Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty.

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller-which was jointly optimized with a linear derivative estimator-with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

Event-Driven Observer-Based Smart-Sensors for Output Feedback Control of Linear Systems.

This paper deals with a recent design of event-driven observer-based smart sensors for output feedback control of linear systems. We re-design the triggering mechanism proposed in a previously reported system with the implementation of self-sampling data smart sensors; as a result, we improve its performance. Our approach is theoretically supported by using Lyapunov theory and numerically evidenced by controlling the inverted pendulum on the cart mechanism.

Observer-based event-triggered recursive optimal tracking control for a class of strict-feedback nonlinear systems.

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness.

Non-fragile output-feedback control for time-delay neural networks with persistent dwell time switching: A system mode and time scheduler dual-dependent design.

This paper is concerned with non-fragile output-feedback control for time-delay neural networks with persistent dwell time (PDT) switching in a continuous-time setting. The main purpose is to design an output-feedback controller subject to gain fluctuations, guaranteeing both asymptotic stability and L2-gain of the closed-loop control system. To achieve reduced conservatism, the controller is formulated to depend not only on the system mode but also on a time scheduler constructed based on the PDT switching rule and minimum time span. A criterion for the asymptotic stability and L2-gain analysis is established through the application of the Gronwall-Bellman inequality and mathematical induction. Then, a numerically tractable design approach for the desired controller is proposed, utilizing a four-section piecewise time-dependent Lyapunov-Krasovskii functional and several nonlinearity decoupling techniques. For comparative purposes, a simple case, independent of the time scheduler, is also investigated, and the corresponding controller design approach is presented. Finally, a simulation example is given to illustrate the effectiveness and superiority of the proposed system mode and time scheduler dual-dependent controller design approach.

A novel output feedback consensus control approach for generic linear multi-agent systems under input saturation over a directed graph topology.

This paper considers an output feedback consensus control approach for the generic linear multi-agent systems (MASs) under input saturation over a directed graph. A region of stability-based approach has been established for dealing with the input saturation. A conventional Luenberger observer for estimating the states of followers by themselves and an advanced cooperative observer for estimating the state of leader by followers have been applied for an estimated state feedback control. The stability conditions have been derived by considering a three-term-based combined Lyapunov function. Moreover, computationally simple controller and estimator design conditions have been obtained by resorting to a decoupling approach A set of initial conditions has been investigated to achieve the leader-following consensus of MASs under the input saturation constraint. To the best of our knowledge, an output feedback consensus approach, providing a consensus region, for generic linear MASs under input saturation over directed graphs without requiring the exact state of the leader has been explored for the first time. In contrast to the existing methods, the proposed approach considers an output feedback approach (rather than the state feedback), accounts for both linear and nonlinear saturation regions, applies an estimate of the state of the leader through cooperative observer, and is based on a generalized sector condition for the saturation nonlinearity. In addition, it offers a computationally simple design solution owing to the proposed decoupling method. Simulation results are provided to validate the efficacy of the designed protocol for F-18 aircraft and unmanned ground vehicles.

Nonfragile output-feedback control for switched singular positive systems with time-varying delay under the Round-Robin protocol.

This paper investigates a class of switched singular positive systems with time-varying delay, where the system parameters are uncertain. In order to decrease the consumption of the communication resources and avoid the phenomenon of data congestion, Round-Robin protocol is employed here. This is the first few attempts to introduce the Round-Robin protocol for such kind of positive systems. Moreover, the nonfragile controller is designed to suppress the undesired dynamical behaviors, which may occur if no control is implemented. By means of the matrix decomposition technique and the mode-dependent average dwell time method, sufficient conditions are established to ensure that the obtained closed-loop system has a prescribed l1 disturbance attenuation performance. Finally, three examples are presented to illustrate feasibility and effectiveness of the proposed control scheme.

Funnel function-based adaptive prescribed performance output feedback control of hydraulic systems with disturbance observers.

This study structures an adaptive prescribed performance output feedback controller for hydraulic systems with large uncertainties including disturbances and parametric uncertainties. Adaptive control is structured to approximate real system parameters. Based on estimated parameters, a nonlinear disturbance observer for largely mismatched disturbance and an extended state observer for matched disturbance and unmeasurable system states are integrated. Then, to guarantee prescribed tracking performance, an output feedback controller is proposed with uncertainty compensation based on the funnel function using the backstepping method. In addition, to avoid the occurrence of complex analytical calculations and "complexity explosion" in the backstepping method, a differentiator is adopted. Then, the Lyapunov method is utilized to prove the stability of the closed-loop system with estimation errors. Finally, experimental results were obtained to demonstrate that the proposed controller is valid.

Non-fragile output-feedback synchronization for delayed discrete-time complex-valued neural networks with randomly occurring uncertainties.

This paper is step forward to establish an exponential synchronization criterion for discrete-time complex-valued neural networks (CVNNs) having time-varying delays subject to randomly occurring uncertain weighting parameters, in order to overcome the fluctuation when the output-feedback controller imposes on its dynamics. To achieve this, Jensen's weighted summation inequalities (WSIs) and an extended reciprocal convex matrix inequality (ERCMI) are extended into the domain of complex field. By introducing some augmented vectors, a Lyapunov-Krasovskii functional (LKF) is constructed to attain an improved delay-dependent linear matrix inequalities (LMIs) constraint for the exponential synchronization phenomenon of the desired master-slave neuronal system model. For instance, the upper bound of the quadratic summation terms occurred in the finite difference of the LKF have been obtained from its linearization that has been made by the developed complex-valued WSIs and complex-valued ERCMI. The proposed results are less restrictive with the minimum number of decision variables than those obtained using existing inequalities. The designed output-feedback control gain has been determined by solving a set of complex-valued LMIs and it has been enforced with a prescribed exponential decay rate. Finally, in sight of MATLAB software, the established results have been examined via a numerical example supported by the simulation results.

Output feedback H∞ control for singular hybrid systems with partly unknown transition rates and input saturation.

This paper investigates dynamic output feedback H∞ control for singular Markovian jump systems with partly unknown transition rates and input saturation. Necessary and sufficient conditions that singular Markovian jump system satisfies stochastic admissibility and H∞ performance index are successfully deduced in terms of linear matrix inequalities under the two different conditions of completely known transition rates and partly unknown transition rates. Mode-dependent dynamic output feedback controller is designed to ensure that the closed-loop singular Markovian jump system satisfies stochastic admissibility and H∞ performance index. Novel set invariant condition is proposed, and it not only provides an estimate of the attractive domain of the closed-loop system but also allows the analysis of performance outside the stability region within this invariant set. Furthermore, the estimation of the attraction domain comes down to the determination of the largest contractively invariant ellipsoid satisfying the necessary and sufficient conditions and the novel set invariant condition, and it is solved as an optimization problem with linear matrix inequality constraints. Finally, the effectiveness and utility of the proposed method are verified by a numerical example and an oil catalytic cracking process.

Reliable fuzzy control of uncertain nonlinear networked systems under actuator faults.

This study investigates a reliable fuzzy static-output feedback control (SOFC) scheme for uncertain Takagi-Sugeno fuzzy model (TSFM)-based nonlinear systems under the networked induced delays, information package losses and actuator faults, simultaneously. For this purpose, firstly, a comprehensive model for the actuator fault is suggested to enhance the performance of the actuator in the networked control systems (NCSs). More precisely, the suggested model contains an additive stochastic perturbation term in the actuator to further realize the control scheme. Besides, the Markov chain (MC) is employed to model the networked induced arbitrary delays and the information package losses. Hence, the corresponding closed-loop system lies in the Markovian jump systems (MJS). Then, based on the Lyapunov theory, the stochastic robust stability of the obtained system is studied and necessary conditions are extracted in new offline linear matrix inequalities (LMIs). Since the accurate value of the transition probabilities (TP) of the MC is not definite and even the identification is difficult, in view of practical applications in our control strategy, partly unknown TPs are assumed. Finally, to validate the superiorities of the suggested control approach, a truck-trailer system is adopted and simulated. The simulation results confirm the superiorities of the suggested control approach.

Leader-following output-feedback consensus for second order multiagent systems with arbitrary convergence time and prescribed performance.

This paper investigates the prescribed-time leader-following output-feedback consensus problem for second order multiagent systems without velocity measurement. Firstly, by introducing a time-scaling function, novel prescribed-time state observers are designed to estimate the second-order states of the agents. Then, a distributed output-feedback scheme is proposed to achieve leader-following consensus, where the transient performance, including the convergence rate and the overshoot, can be offline pre-assigned. It should be noted that the singularity-like problem is solved for the system under measurement errors by adopting a form of piecewise functions. Moreover, the control strategy is modified by introducing an auxiliary system when taking the common saturation problem into account. Finally, the efficiency of the proposed schemes is illustrated by numerical simulation examples.

Membership-function-dependent dynamic output feedback H∞ controller design of continuous-time T-S fuzzy systems via non-quadratic Lyapunov function.

The dynamic output feedback H∞ (DOFH) control under imperfect premise matching (IPM) is studied in this paper for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from the existing results, the DOFH switching controller, which enjoys membership functions (MFs) distinct from the fuzzy systems, is designed. First, the non-quadratic Lyapunov function (NQLF) based on MFs is utilized to design the controller. The time derivatives of MFs are addressed by the switching strategy. Second, a method based on linear matrix inequality (LMI) is given to make the controller gains solvable. Third, an improved method is developed to incorporate the more boundary information of MFs into the stability conditions to reduce conservatism. Finally, three examples are used to certify the advantage of the approach.

Tracking control of state constrained fractional order nonlinear systems.

This article investigates adaptive output-feedback control problems for full-state constrained fractional order uncertain strict-feedback systems with unmeasured states and input saturation. By considering the structure of the systems, a fractional order observer is framed to estimate unmeasurable states. By using the backstepping procedure and barrier Lyapunov function, the adaptive controller with adaptation laws are proposed in each step. With the Lyapunov stability theory for fractional order systems, it proves all the states remain in their constraint bounds and the error system converges to a bounded set containing the origin. In the end, Two examples are presented to show the effectiveness of the designed control scheme.

Practical fixed-time trajectory tracking control of constrained wheeled mobile robots with kinematic disturbances.

This paper addresses the problem of practical fixed-time trajectory tracking for wheeled mobile robots (WMRs) subject to kinematic disturbances and input saturation. Firstly, considering the under-actuated characteristics of the WMR systems, the WMR model under kinematic disturbances is transformed into a two-input two-output interference system by using a set of output equations. Then, the tracking error state equation with lumped disturbances in the acceleration-level pseudo-dynamic control (ALPDC) structure is established. The lumped disturbances are estimated by a designed fixed-time extended state observer (FESO) without requiring the differentiability of the first-time derivatives of the kinematic disturbances. Meanwhile, a practical fixed-time output feedback control law is developed for trajectory tracking. By resorting to the Lyapunov stability theorem, the fixed-time stability analysis of the closed-loop WMR system in the presence of input saturation is conducted. Finally, simulation results are presented to show the effectiveness of the proposed approach.

Adaptive fuzzy output-feedback event-triggered control for fractional-order nonlinear system.

This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.

Output feedback based adaptive composite nonlinear flight control design for a small-scale un-crewed helicopter.

This correspondence deals with the trajectory tracking control of an un-crewed helicopter during hover/low-speed flights. A multi-loop architecture is used in which the inner-loop holds the fast changing dynamics and the outer-loop establishes the trajectory tracking. The inner-loop is closed with a constrained H∞ based controller which is cautiously designed to address actuator saturation, atmospheric wind disturbance, and parametric uncertainty. The outer-loop adaptive composite nonlinear control comprises of a linear part and a nonlinear part. A novel adaptive controller is proposed as the nonlinear part which improves the tracking performance by adaptively adjusting the damping ratio. The linear control element of the outer-loop is framed similar to inner-loop. Utilization of output feedback instead of full state feedback makes the flight control design simple and practically feasible. The closed loop stability and robustness property of the proposed scheme are analyzed. Simulation studies are performed to establish the hovering, station keeping, and trajectory tracking performance of the suggested control structure. Further, the performance of the proposed scheme is compared with a constrained static output feedback controller and a model reference adaptive proportional integral controller to confirm its superiority.

Adaptive sliding-mode trajectory tracking control for state constraint master-slave manipulator systems.

This study aims to propose an adaptive state-dependent gain finite-time convergent controller (using the fundamentals of the sliding mode theory) that solves the trajectory tracking for a class of state constraint master-slave robotic system (M-SRS) formed by two manipulators with the same number of articulations. The control design considers the effect of state constraints by implementing a state dependent adaptive gain. A Lyapunov-stability analysis leads to design the gain variation laws yielding proving the finite-time convergence of the sliding surface as well as the asymptotic convergence of the tracking error. The state constraints of the slave system motivate the characterization of the convergence-time as a function of the bounded uncertainties affecting the M-SRS dynamics. The forward-complete setting of the M-SRS justified the application of a robust and exact differentiator which estimated the articulation velocities for the slave robot. The estimated velocities are used as part of the realization of the output feedback controller. Numerical simulations demonstrate that the proposed control scheme provides a smaller quadratic norm of the tracking error compared with the obtained with other controllers (proportional-derivative and conventional sliding modes). The proposed control approach satisfies the state constraints while the sliding manifold converges to the origin in finite-time as justified by the theoretical stability analysis.

Observer-based output feedback control design for a fractional ODE and a fractional PDE cascaded system.

This paper considers a new bi-directional cascaded system of a fractional ordinary differential equation (FODE) and a fractional partial differential equation (FPDE) which interacts at an intermediate point. The space-dependent coefficients, interaction between the FODE and FPDE at an intermediate point and the presence of fractional calculus makes the FODE-FPDE cascaded system, representative. In this note, we first apply an invertible integral transformation to convert the system into a FODE-FPDE coupled system, as the target system, which is Mittag-Leffler stable. Using the backstepping method and under some assumptions of the space-dependent coefficients, we work out the kernel functions in the transformation and we design a boundary controller. Also, by the invertibility of the transformation, we show the Mittag-Leffler stability of the closed-loop system via the Lyapunov approach. Second, we propose an observer for which we prove that it can well estimate the original cascaded system. Then, we design an output feedback boundary control law and show that the closed-loop system is Mittag-Leffler stable under the designed output feedback control law. Finally, we present some numerical illustrations to show the correctness of the theoretical results.

Universal adaptive control for a class of nonlinear time-varying delay systems with unknown output function.

This paper considers the stabilization problem for a class of nonlinear time-varying delay systems with unknown homogeneous growth rates and unknown output function. By introducing the dynamic gain into the system, an adaptive observer is designed. Then, combined with the Lyapunov-Krasovskii functional, an adaptive controller is proposed to guarantee the global stabilization of the closed-loop system. Two examples are provided to verify the effectiveness of the designed controller.