A delay‐independent output feedback for linear systems with time‐varying input delay

It is well known that a delay‐dependent or delay‐independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time‐varying or unknown delay, delay‐independent feedback laws are preferable over delay‐dependent feedback laws as the former provide robustness to the uncertainties in the delay. In the light of few results on the construction of delay‐independent output feedback laws for general linear systems with input delay, we present in this paper a delay‐independent observer–based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin‐type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open‐loop poles at the origin or in the open left‐half plane. Compared with that of the delay‐dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay.     

Time‐ and State‐Dependent Input Delay‐Compensated Bang‐Bang Control of a Screw Extruder for 3D Printing

In this paper, a delay‐compensated bang‐bang control design methodology for the control of the nozzle output flow rate of screw extruder‐based three‐dimensional printing processes is developed. A geometrical decomposition of the screw extruder in a partially and a fully filled regions allows to describe the material convection in the extruder chamber by a one‐dimensional hyperbolic partial differential equation (PDE) coupled with an ordinary differential equation. After solving the hyperbolic PDE by the method of characteristics, the coupled PDE–ordinary differential equation's system is transformed into a nonlinear state‐dependent input delay system. The aforementioned delay system is extended to the non‐isothermal case with the consideration of periodic fluctuations acting on the material's convection speed, which represent the process variabilities due to temperature changes in the extruder chamber, resulting to a nonlinear system with an input delay that simultaneously depends on the state and the time variable. Global exponential stability of the nonlinear delay‐free plant is established under a piecewise exponential feedback controller that is designed. By combining the nominal, piecewise exponential feedback controller with nonlinear predictor feedback, the compensation of the time‐dependent and state‐dependent input delay of the extruder model is achieved. Global asymptotic stability of the closed‐loop system under the bang‐bang predictor feedback control law is established when certain conditions related to the extruder design and the material properties, as well as to the magnitude and frequency of the materials transport speed variations, are satisfied. Simulations results are presented to illustrate the effectiveness of the proposed control design. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Stabilization of linear systems with time‐varying input delay by event‐triggered delay independent truncated predictor feedback

This article deals with the problem of stabilization of linear systems with time‐varying input delay by an event‐triggered delay independent truncated predictor feedback law, either of the state feedback type or the output feedback type. Only the information of a delay bound rather than the delay itself is required in the design of both control laws and event‐triggering strategies. For both the state feedback case and the output feedback case, an admissible delay bound that guarantees the stabilizability of a general linear system is established, and the Zeno behavior is shown to be excluded. For linear systems with all open‐loop poles at the origin or in the open left‐half plane, stabilization can be achieved for a delay under an arbitrarily large bound.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Stabilization of strict‐feedback nonlinear systems with input delay using closed‐loop predictors

In this paper, we consider the control problem of strict‐feedback nonlinear systems with time‐varying input and output delays. The approach is based on the usual observer/predictor/feedback approach, but the novelty is the use of the closed‐loop dynamics in the predictor. This approach allows to develop two designs, an instantaneous predictor and a delay differential equation‐based predictor, that both attain the same performance in terms of system trajectories and input signal as in the case with no delays. The design based on delay differential equations allows to build a cascade of predictors to deal with arbitrarily large delay bounds. The resulting controller is much simpler to implement than classical infinite‐dimensional predictors, and it is robust with respect to actuation and measurement disturbances. We illustrate the approach with an application to the control of a chaotic system with input delay. Copyright © 2016 John Wiley & Sons, Ltd.     

Simultaneous compensation of input and state delays for nonlinear systems

The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.     

Feedback passivity‐based control of discrete nonlinear systems with time‐delay for variable geometry truss manipulator

In this paper, the feedback passivity‐based control of nonlinear discrete time‐delay systems for variable geometry truss manipulators is investigated. To determine an appropriate communication channel in the sense of feedback passivation, we first model the dynamics of the variable geometry truss manipulator as a generalized discrete nonlinear system with time‐delay. Then we further prove that when the infinite norm of estimated error is bounded, as long as there is a controller enables the closed‐loop system to be input‐strictly passive, there must be a deterministic equivalent controller to ensure that the system is stochastically quasi passive. After that, on the basis of the conclusion obtained, a more conclusive corollary is addressed for linear plants. Though passivity is a stricter condition than stability, feedback passivation does not impose more restrictions on estimate errors, and therefore does not require more communication channel information than mean square stability. Finally, we simplify the variable geometry truss dynamics to a linear plant to simulate to verify the validity of our method, and also compared the experimental results with the methods in the existing literature.     

An Lmi Approach To Non‐Fragile Guaranteed Cost Control Of Uncertain Discrete Time‐Delay Systems

This paper studies the non‐fragile Guaranteed Cost Control (GCC) problem via memoryless state‐feedback controllers for a class of uncertain discrete time‐delay linear systems. The systems are assumed to have norm‐bounded, time‐varying parameter uncertainties in the state, delay‐state, input, delay‐input and state‐feedback gain matrices. Existence of the guaranteed cost controllers are related to solutions of some linear matrix inequalities (LMIs). The non‐fragile GCC state‐feedback controllers are designed based on a convex optimization problem with LMI constraints to minimize the guaranteed cost of the resultant closed‐loop systems. Numerical examples are given to illustrate the design methods.     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.     

Continuous‐ and discrete‐time fixed‐gain controller designs for the control of vehicle lateral dynamics

In this paper, fixed‐gain feedback linearization controls are presented to stabilize the vehicle lateral dynamics at bifurcation points for both continuous‐time and discrete‐time cases. Based on the assumption of constant driving speed, a second‐order nonlinear lateral dynamics model is adopted for controller design. Via the feedback linearization scheme and the first‐order Taylor series expansion, a time‐invariant feedback linearization control is proposed as a fixed‐gain linear version of the previously proposed nonlinear one. Furthermore, the conventional linear quadratic regulator (LQR) design is applied to facilitate the choice of the fixed‐gain matrix. Refined controls to compensate the model uncertainty and their local stability analysis are provided. Extension of the continuous‐time design results to discrete‐time cases is also addressed. Numerical simulations for an example model demonstrate the effectiveness of the proposed continuous‐time and discrete‐time design results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Containment control of multi‐agent systems by exploiting the control inputs of neighbors

This paper studies the containment control problem for multi‐agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous‐time and discrete‐time systems are considered. For continuous‐time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete‐time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Prediction‐based Adaptive Robust Tracking Control of an Uncertain First‐Order Time‐Delay System

This paper considers the tracking problem of a delayed uncertain first‐order system which is simultaneously subject to (possibly large) known input delay, unknown but bounded time‐varying disturbance, and unknown plant parameter. The proposed predictor adaptive robust controller (PARC) involves prediction‐based projection type adaptation laws with model compensation and prediction‐based continuous robust feedback such that the closed loop system has global exponential convergence with an ultimate bound proportional to delay, disturbance bound, and switching gain. Further, if there are only delay and parameter uncertainties after some finite time, then semi‐global asymptotic tracking is guaranteed. The proposed design is shown to have significant closed loop performance improvement over the baseline controller.     

Robust stability,stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters

In this paper, the problems of stochastic stability and stabilization for a class of uncertain time‐delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process. The parametric uncertainties are assumed to be real, time‐varying and norm‐bounded that appear in the state, input and delayed‐state matrices. The time‐delay factor is constant and unknown with a known bound. Complete results for both delay‐independent and delay‐dependent stochastic stability criteria for the nominal and uncertain time‐delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed ?_∞‐performance are guaranteed. We establish that the control problem for the time‐delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability analysis and output‐feedback stabilization of discrete‐time systems with a time‐varying state delay and nonlinear perturbation

This paper aims to derive stability conditions and an output‐feedback stabilization method for discrete‐time systems with a time‐varying state delay and nonlinear perturbation. With a new way of handling the Lyapunov stability criterion, linear matrix inequality conditions are obtained for estimating bounds on delay to ensure the asymptotic stability. Based on the conditions, a synthesis procedure is developed for finding stabilizing output‐feedback gains, which are formulated as direct design variables. Three numerical examples are employed to demonstrate the effectiveness and advantages of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay

This paper addresses the problem of output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous‐discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled‐data stabilization for lower‐triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

On Designing Time‐delay Feedback Controller for Master‐Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing a time‐delay output feedback controller for master‐slave synchronization of Lur'e systems. The time delay is divided into two intervals and different energy functions are defined in each interval, which together provide a new Lyapunov–Krasovskii functional and derive a new delay‐dependent synchronization criterion. A sufficient condition for the existence of such a feedback controller is given, and an explicit expression of such a controller is also achieved. These algorithms are formulated in terms of linear matrix inequalities that can be solved easily. Chua's circuit is used to illustrate the effectiveness of the design method.     

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.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.