Sampled-data Output Research Articles

Sampled-data stabilization of a class of nonlinear differential algebraic systems via partial-state and output feedback

In this paper, the problem of sampled-data stabilization for a class of nonlinear differential-algebraic systems is considered by using partial-state and output feedback. First, based on the output feedback domination approach, a systematic design procedure for sampled-data output feedback controller is proposed without using the states of the algebraic subsystem. It is shown that the proposed sampled-data controller can ensure the whole closed-loop nonlinear differential-algebraic system is asymptotically stable by choosing appropriate scaling gains and sampling period. In addition, due to the domination nature of the proposed method, the obtained results can be extended to more general class of nonlinear differential-algebraic systems easily. Finally, simulation examples are provided to illustrate the effectiveness of the proposed control method.

When Is a Nonlinear System Semiglobally Asymptotically Stabilizable by Digital Feedback?

For multi-input–multi-output (MIMO) nonlinear systems, we prove that while global asymptotic stabilizability may not ensure semiglobal asymptotic stabilizability (SGAS) by sampled-data state feedback, global asymptotic plus local exponential stabilizability (GALES) does imply the existence of an SGAS sampled-data state feedback controller. Based on this result, we further prove the main contribution of this article: GALES and uniform observability imply SGAS by sampled-data output feedback, which is indeed a hybrid version of the “separation principle” for nonlinear systems. The development of the “digital separation principle” is made possible by employing a subtle Lyapunov argument that makes the estimation of domains of attraction and semiglobal asymptotic analysis relatively intuitive and simple, without involving intricate Lyapunov functions and the corresponding level sets. Results on SGAS by sampled-data feedback for representative classes of nonlinear systems are also given as illustrations.

Sampled-data output feedback controllers for nonlinear systems with time-varying measurement and control delays

Abstract In this paper, we propose sampled-data output feedback controllers for nonlinear systems with time-varying measurement and input delays. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. The density of these delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. Our sampled-data feedback controllers are obtained as zero-order discretizations of continuous time controllers.

Networked Output Feedback Control for a Class of Uncertain Nonlinear Time-Delay Systems

This paper studies the global stabilization problem for a class of uncertain time-delay nonlinear systems by designing a sampled-data output feedback controller via network. Under a lower triangular linear growth condition, when only the output is measurable, a sampled-data output feedback network controller, whose observer and control law are both linear, is constructed to solve the stabilization problem. Using a feedback domination design approach which substantially differs from the separation principle, we explicitly construct a Lyapunov–Krasovskill functional to prove the global asymptotic stability with the help of inductive proof method. The control law is discrete-time and linear, hence simulation examples be easily implemented with computers to show the effectiveness of our proposed method.

Sampled-data output regulation of unstable well-posed infinite-dimensional systems with constant reference and disturbance signals

We study the sample-data control problem of output tracking and disturbance rejection for unstable well-posed linear infinite-dimensional systems with constant reference and disturbance signals. We obtain a sufficient condition for the existence of finite-dimensional sampled-data controllers that are solutions of this control problem. To this end, we study the problem of output tracking and disturbance rejection for infinite-dimensional discrete-time systems and propose a design method of finite-dimensional controllers by using a solution of the Nevanlinna-Pick interpolation problem with both interior and boundary conditions. We apply our results to systems with state and output delays.

Sampled-data output voltage regulation for a DC–DC buck converter nonlinear system with actuator and sensor failures

This paper considers the regulation problem for a DC–DC buck converter nonlinear system with uncertain components and actuator and sensor failures. We establish a novel reduced-order observer to estimate the unmeasured state. Then, a new fault-tolerant sampled-data controller with an allowable sampling period is constructed to guarantee that the output voltage of the DC–DC buck converter nonlinear system can tend to the desired voltage. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method.

Global sampled-data output feedback stabilization for a class of switched stochastic nonlinear systems with quantized input and unknown output gain

This paper aims at addressing the sampled-data output feedback control problem for a class of uncertain switched stochastic nonlinear systems, whose control input is quantized by a logarithmic quantizer and the output gain cannot be precisely known. We design a compensator with the quantized information. With the help of the feedback domination approach and the backstepping design method, a sampled-data output feedback controller is constructed with appropriate design parameters and a maximum sampling period to guarantee the global exponential stability in mean square of the closed-loop system under arbitrary switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

ABSTRACTIn this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.

Continuous-Time and Sampled-Data Stabilizers for Nonlinear Systems With Input and Measurement Delays

In this paper, we propose continuous-time and sampled-data output feedback controllers for nonlinear multi-input multi-output systems with time-varying measurement and input delays, with no restriction on the bound or serious limitations on the growth of the nonlinearities. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. These delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. We also design sampled-data stabilizers as zero-order discretization of a hybrid modification (with continuous-time states and discrete-time control and innovations) of the continuous-time stabilizers.

Global Practical Tracking for a Class of Switched Nonlinear Systems with Quantized Input and Output via Sampled-data Control

In this paper, we study the global practical output tracking problem for a class of switched nonlinear systems via sampled-data output feedback control. Both the input signal and the output signal are quantized for the sake of less communication burden. The Filippov solution and differential inclusion are adopted to analyze the resulting discontinuous system. Accordingly, an observer is designed to estimate the unmeasurable states at the sampling points. Then, a linear sampled-data output feedback controller is designed with a proper choice of the sampling period, the quantization parameter and the design parameters. Finally, a numerical example and a practical example are presented to verify the effectiveness of the proposed scheme.

Mixed [formula omitted] sampled-data output feedback control design for a semi-linear parabolic PDE in the sense of spatial [formula omitted] norm

This paper addresses distributed mixed H2∕H∞ sampled-data output feedback control design for a semi-linear parabolic partial differential equation (PDE) with external disturbances in the sense of spatial L∞ norm. Under the assumption that a finite number of local piecewise measurements in space are available at sampling instants, a static sampled-data output feedback controller is suggested, where the sampling interval in time is bounded. The local piecewise measurements bring additional difficulty for the exponential stability and performance analysis since the existing Poincaré-Wirtinger inequality in 1D spatial domain is not applicable. By constructing an appropriate Lyapunov–Krasovskii functional candidate and employing Wirtinger’s inequalities, a variant of Poincaré-Wirtinger inequality in 1D spatial domain, as well as Agmon’s inequality, it is shown that the suggested static sampled-data output feedback controller not only guarantees the output exponential stability of the resulting closed-loop PDE in the spatial L∞ norm but also ensures the mixed H2∕H∞ performance index defined in the spatial L∞ norm, if the sufficient conditions presented in terms of standard linear matrix inequalities (LMIs) are fulfilled. The satisfactory and better performance of the suggested sampled-data feedback controller is demonstrated by numerical simulation results of an illustrative example.

Uncertain Nonholonomic Systems Control via Sampled-Data Output Feedback of Motor Robot With Two-Dimensional Z-States

Nonholonomic systems with uncertain nonlinearities are sufficiently important to research due to the numerous applications in the real world. It is imperative to find a sampled-data controller for nonholonomic systems due to their implementation within digital computers. It has been proven that under a lower-triangular growth condition, a class of nonholonomic system with a single z-state can be globally stabilized by a sampled-data output feedback controller whose observer and control laws are discrete-time and linear. In this paper, we will further extend the results to the two-dimensional z-states which is more challenging since the boundedness of the change of coordinates is not proved. To solve this problem, we firstly design a controller for the z-system, which can guarantee the boundedness of the change of coordinates after a certain time. From this, we can construct a globally stabilizing output feedback controller for nonholonomic systems. The examples and computer simulations were conducted to show the effectiveness of the proposed controllers for the two-dimensional z-states.

Differential linear matrix inequality in optimal sampled-data control

This paper addresses the design of optimal sampled-data output feedback full order controllers for linear continuous-time invariant systems. First, H2 and H∞ performance indices are determined and expressed through differential linear matrix inequalities (DLMIs). Second, in each scenario, the optimal sampled-data controller of the aforementioned class is determined from a convex programming problem expressed by DLMIs. Theoretical achievements are based on the direct application of the celebrated Bellman’s Principle of Optimality expressed in terms of the dynamic programming equation associated to the time interval corresponding to two successive sampling instants. The design problems to be dealt with are convex and are solved by converting all constraints to LMI and adopting a piecewise linear solution. The possibility of aperiodic sampling is considered and briefly discussed. Finally, academic examples are solved for illustration.

Output-Based Dynamic Event-Triggered Mechanisms for Disturbance Rejection Control of Networked Nonlinear Systems.

This paper proposes a new output-based dynamic event-triggered mechanism (ETM) for disturbance rejection control of a class of networked nonlinear uncertain systems subject to additive time-varying disturbance. In the proposed control method, a new robust output feedback controller is first designed based on a generalized proportional-integral observer to attenuate/compensate the undesirable influence of nonlinear uncertainties and disturbances. Different from the static ETM, two new dynamic variables are defined, and thereafter, two kinds of different discrete-time dynamic ETMs are developed only using the sampled-data output signal, such that a better tradeoff between the communication properties and the control properties can be obtained. It is shown that under the proposed control methods, the global bounded stability of the closed-loop hybrid system can be guaranteed by choosing some appropriate parameters. Finally, the numerical simulations of a single link robot arm are conducted to demonstrate the feasibility and efficacy of the proposed control approach.

Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems

This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall–Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition.

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.

Active steering wheel shimmy control for electric vehicle by sampled-data output feedback

In this paper, a new two Degree of Freedom (DOF) shimmy dynamic model of an Electric Vehicle (EV) with independent suspension subject to uncertain disturbances is built via Lagrange’s theorem firstly. Secondly, Based on the built model, an active control method is proposed to solve the shimmy problem of the steering system via a sampled-data output feedback controller. The output feedback domination approach is also used to dominate uncertain disturbances by using a scaling gain. With the help of these tools, the sampling period and scaling gain are calculated to guarantee global stability and disturbance attenuation for the closed-loop control system. Finally, simulations and tests are conducted to verify the effectiveness of the sampled-data output feedback controller for the EV’s shimmy problem under different conditions.

Global stabilization via sampled-data output feedback for large-scale systems interconnected by inherent nonlinearities

This paper aims to solve the decentralized sampled-data control problem for a class of large-scale systems interconnected by inherent nonlinearities, which violate the linear growth condition. Under a homogeneous growth condition, a set of decentralized sampled-data output feedback controllers are constructed with scaling gains and a sampling period. By the output feedback domination approach, the scaling gains are firstly correlated and then selected to dominate the nonlinearities. Finally, by developing and applying a useful tool to estimate trajectory growth, global stabilization is achieved for the closed-loop system under an appropriate sampling period.

Master–Slave Synchronization of Heterogeneous Systems Under Scheduling Communication

Under the mild assumption that only the sampled-data output information about the master system is available, synchronization of networked master–salve system consisting of a high-order master system and a low-order slave system is investigated in this paper. Specifically, the dynamics of the master system and those of the slave system are allowed to be characterized by heterogeneous nonlinear systems. The communication between these two systems are transmitted by multiple sensors over a communication network, while at each sampling instant, only one sensor is allowed to transmit its current information to the controller’s side according to some carefully designed scheduling protocols. To achieve master–salve synchronization, the stochastic scheduling and the Round-Robin scheduling protocols are, respectively, proposed and utilized. By appropriately designing observer and controller for the slave system, some sufficient synchronization criteria regarding to the gain matrices, sampling intervals and communication delays are derived for the closed-loop master–salve system under respectively the stochastic scheduling and the Round-Robin scheduling protocols. Last, two numerical examples are simulated to validate the effectiveness of the theoretical results.

Semi-Global Asymptotic Control by Sampled-Data Output Feedback

This paper shows that for a class of nonlinear systems with a lower-triangular structure, the problem of semi-global asymptotic stabilization is solvable by sampled-data output feedback, without requiring restrictive conditions on the nonlinearities and unmeasurable states of the system, such as linear growth, output-dependent growth or homogeneous growth conditions as commonly assumed in the case of global output feedback stabilization. The main contribution is to point out that semi-global asymptotic rather than practical stabilizability of certain classes of nonlinear systems is still possible by sampled-data output feedback if a sampling time is small enough. A design method is also given for the construction of semi-globally stabilizing, sampled-data output feedback controllers.