Model Predictive Control for Discrete‐Time Systems with Random Delay and Randomly Occurring Nonlinearity

In this paper, the model predictive control problem is investigated for a class of discrete‐time systems with random delay and randomly occurring nonlinearity. The randomly occurring nonlinearity, which describes the phenomena of a class of nonlinear disturbances occurring in a random way, is modeled according to a Bernoulli distributed white sequence with a known conditional probability. Moreover, the random delay is governed by a discrete‐time finite‐state Markov chain. The approach of delay fractioning is applied to the controller synthesis. It is shown that the proposed model predictive controller guarantees the stochastic stability of the closed‐loop system. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed 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.     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust delay‐dependent ℋ︁∞ control of time‐delay systems with state and input delays

This paper studies the design problem of robust delay‐dependent ??_∞ controller for a class of time‐delay control systems with time‐varying state and input delays, which are assumed to be noncoincident. The system is subject to norm‐bounded uncertainties and ??₂ disturbances. Based on the selection of an augmented form of Lyapunov–Krasovskii (L‐K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time‐delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay‐dependent criteria are developed for a stabilizing ??_∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm‐bounded uncertainties, both the BRL and ??_∞ stabilization criteria are easily extended by employing a well‐known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

Feedback passification of switched stochastic time‐delay systems with multiple disturbances via DOBC

This paper is concerned with the problem of feedback passification for switched stochastic time‐delay systems with multiple disturbances subject to mode‐dependent average dwell‐time switching. The multiple disturbances are composed of two parts: one is given through an exogenous system and the other is described in the form of norm‐bounded vector. A disturbance observer is constructed to estimate an exogenous disturbance. Then, a state feedback controller that includes the estimation value is designed to guarantee the passivity of the closed‐loop system. The observer and controller gains are developed via linear matrix inequalities. The effectiveness of the proposed method is verified through a numerical example and an application example to PWM‐driven boost converter.     

Robust State Feedback Formulation for High Order Repetitive Controllers

This paper presents a robust state feedback formulation for high order repetitive controllers (HORC) able to track references and/or reject disturbances with uncertain period. We propose a modified structure of the HORC with low‐pass filter in series with the delay element, allowing us to work in the state‐space framework. The filter cut‐off frequency effects and the controller sensitiveness to harmonic and intermediary components are analyzed. A methodology based on the solution of an optimization problem subject to linear matrix inequality constraints is presented for robust synthesis of feedback gains. The advantages regarding the proposed control scheme are discussed with a simulated example of a DC motor driving an eccentric mass.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

Input‐to‐state stability of switched nonlinear systems with delay in the active mode detection

A switched nonlinear system subject to disturbances is considered in this paper. The switching signal admits an average dwell time and a state feedback control depending on the system operating modes, detected with a maximum time delay, is applied to the system. In this framework, the input‐to‐state stability problem of the closed‐loop system is addressed. Based on some established existence conditions of mode‐dependent Lyapunov‐like functions, the values of the maximum time delay and the average dwell time that allow to achieve the input‐to‐state stability of the closed‐loop system are determined. In order to obtain more tractable results, the existence conditions of the mode‐dependent Lyapunov‐like functions are given in terms of sum‐of‐squares programming in the case of polynomial nonlinearities. In the linear case, they are expressed in terms of linear matrix inequalities and a procedure for the synthesis of the mode‐dependent controller is provided in this situation. The established theoretical results are illustrated through a control problem of a building ventilation system and a switched control problem of a vehicle suspension system.     

Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator

In this article, one linear and one nonlinear robust control strategies are proposed for uncertain nonlinear continuous‐time systems with disturbances and state delays. The approaches are based on the uncertainty and disturbance estimator (UDE) introduced in 2004. In the case of a linear controller, the terms containing the nonlinear functions and time delays are treated as additional disturbances to the system. In the case of a nonlinear controller, both known and unknown delay scenarios are considered. In the case of an unknown time delay, the terms containing the delay are treated as additional disturbances to the system. The algorithms provide excellent tracking and disturbance rejection performance. Simulations are given to show the effectiveness of the strategies, first via a simple example and second via an application to a continuous stirred tank reactor system. Copyright © 2010 John Wiley & Sons, Ltd.     

Locomotion Control of a Hydraulically Actuated Hexapod Robot by Robust Adaptive Fuzzy Control with Self-Tuned Adaptation Gain and Dead Zone Fuzzy Pre-compensation

Hydraulically actuated robotic mechanisms are becoming popular for field robotic applications for their compact design and large output power. However, they exhibit nonlinearity, parameter variation and flattery delay in the response. This flattery delay, which often causes poor trajectory tracking performance of the robot, is possibly caused by the dead zone of the proportional electromagnetic control valves and the delay associated with oil flow. In this investigation, we have proposed a trajectory tracking control system for hydraulically actuated robotic mechanism that diminishes the flattery delay in the output response. The proposed controller consists of a robust adaptive fuzzy controller with self-tuned adaptation gain in the feedback loop to cope with the parameter variation and disturbances and a one-step-ahead fuzzy controller in the feed-forward loop for hydraulic dead zone pre-compensation. The adaptation law of the feedback controller has been designed by Lyapunov synthesis method and its adaptation rate is varied by fuzzy self-tuning. The variable adaptation rate helps to improve the tracking performance without sacrificing the stability. The proposed control technique has been applied for locomotion control of a hydraulically actuated hexapod robot under independent joint control framework. For tracking performance of the proposed controller has also been compared with classical PID controller, LQG state feedback controller and static fuzzy controller. The experimental results exhibit a very accurate foot trajectory tracking with very small tracking error with the proposed controller.     

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.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Integral sliding mode design for robust filtering and control of linear stochastic time‐delay systems

This paper presents an integral sliding mode technique robustifying the optimal controller for linear stochastic systems with input and observation delays, which is based on integral sliding mode compen‐sation of disturbances. The general principles of the integral sliding mode compensator design are modified to yield the basic control algorithm oriented to time‐delay systems, which is then applied to robustify the optimal controller. As a result, two integral sliding mode control compensators are designed to suppress disturbances in state and observation equations, respectively, from the initial time moment. Moreover, it is shown that if certain matching conditions hold, the designed compensator in the state equation can simultaneously suppress observation disturbances, as well as the designed compensator in the observation equation can simultaneously suppress state disturbances. The obtained robust control algorithm is verified by simulations in the illustrative example, where the compensator in the observation equation provides simultaneous suppression of state and observation disturbances. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.     

Robust generalized asymptotic regulation against non‐stationary sinusoidal disturbances with uncertain frequencies

Attenuation of sinusoidal disturbances with uncertain and arbitrarily time‐varying frequencies is considered in the form of a generalized asymptotic regulation problem. The disturbances are modeled as the outputs of a parameter‐dependent, unexcited and neutrally stable exogenous system that evolves from nonzero initial conditions. The problem is considered for a plant that depends partially on the uncertain parameters. Moreover, both the plant and the exogenous system are allowed to have dependence on another parameter vector that is measurable during online operation. The problem is then formulated as the synthesis of a controller that is scheduled on the measurable parameter in a way to guarantee robust internal stability and attenuate the disturbance according to a desired profile in steady state. The main result of the paper is a synthesis procedure based on a convex optimization problem, which is identified by a set of parameter‐dependent linear matrix inequalities and can be rendered tractable through standard relaxation schemes. It is also clarified how the transient behavior of the controller can be improved by some additional constraints. The order of the synthesized controller is equal to the order of the plant plus the order of the exogenous system. Copyright © 2010 John Wiley & Sons, Ltd.     

Aero‐Engine DCS Fault‐Tolerant Control with Markov Time Delay Based On Augmented Adaptive Sliding Mode Observer

With a focus on aero‐engine distributed control systems (DCSs) with Markov time delay, unknown input disturbance, and sensor and actuator simultaneous faults, a combined fault tolerant algorithm based on the adaptive sliding mode observer is studied. First, an uncertain augmented model of distributed control system is established under the condition of simultaneous sensor and actuator faults, which also considers the influence of the output disturbances. Second, an augmented adaptive sliding mode observer is designed and the linear matrix inequality (LMI) form stability condition of the combined closed‐loop system is deduced. Third, a robust sliding mode fault tolerant controller is designed based on fault estimation of the sliding mode observer, where the theory of predictive control is adopted to suppress the influence of random time delay on system stability. Simulation results indicate that the proposed sliding mode fault tolerant controller can be very effective despite the existence of faults and output disturbances, and is suitable for the simultaneous sensor and actuator faults condition.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

A Parameter Dependent Controller Design Approach for Delayed LPV System

This paper investigates the memory state feedback controller synthesis problem for linear parameter‐varying (LPV) systems with time‐varying input delay. A novel state transformation is proposed to reduce the influence of time delay, and two types of Lyapunov‐Krasovskii functional are employed to guarantee the stability of the closed‐loop system and induced L₂ norm performance. The controller gain is formulated to parameter dependent, and design method is then led to a convex optimization problem and solved by parameter gridding technique. A numerical example is provided to validate the effectiveness of the proposed approach.