Control Of Uncertain Discrete-time Systems Research Articles

Dynamic event-triggered sliding mode control for the uncertain discrete-time system using the reaching law

Based on the reaching law, this paper investigates the issue of dynamic event-triggered sliding mode control for uncertain discrete-time systems with disturbances. A dynamic event-triggered mechanism is proposed to enhance the data utilization rate, and an observer is introduced accordingly. An observer-based linear sliding surface is then designed. Furthermore, a sliding mode controller based on a chattering-free reaching law is designed to ensure the reachability of the sliding region. The stability of the closed-loop system, including quasi-sliding mode and error dynamics, is analyzed. Finally, two illustrative examples are presented to compare and validate this method.

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

This paper investigates the optimal guaranteed cost (GC) control problem for uncertain discrete-time (DT) systems with state saturation nonlinearities via static-state feedback. The parameter uncertainties in the system state and input matrix are considered to be norm bounded. Utilizing Lyapunov theory and sector-based characterization of saturation nonlinearities, a novel criterion for the existence of GC controllers is proposed. The criterion is expressed in the framework of linear matrix inequalities (LMIs) and is thus computationally tractable. The proposed GC controllers make the closed-loop (CL) system asymptotically stable and ensure an adequate level of performance for all admissible parameter uncertainties. To design an optimum GC controller, a convex optimization problem with LMI constraints is formulated. The effectiveness of the proposed approach is illustrated by examples.

A systematic review of uncertainty theory with the use of scientometrical method

Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

Necessary optimality conditions of fractional-order discrete uncertain optimal control problems

This paper is primarily dedicated to the necessary conditions of optimal control for uncertain discrete-time systems of fractional-order governed by left Riemann-Liouville-like fractional-order nabla difference equations. First, an existence result of solutions for backward right Riemann-Liouville-like fractional-order nabla difference equations is derived from the Banach contraction mapping theorem. Besides, necessary optimality conditions of these fractional-order uncertain optimal control problems are proposed by the variational method and Lagrange multiplier technique. Finally, a special LQ optimal control problem for uncertain discrete-time systems of fractional-order is solved by necessary conditions of optimality derived.

Robust induced [formula omitted] optimal control of discrete-time systems having magnitude and rate-bounded actuators

The design of robust state- and output-feedback control for uncertain discrete-time systems with physical magnitude and rate constraints on their actuator dynamics was addressed. Unlike the traditional methods such as anti-windup (AW) methods, nested ellipsoids, model predictive controllers (MPCs) and integral quadratic constraints(IQCs) formulated by sector bounded inequalities, this paper uses a transformation of the system dynamics to a form which considers control signal and its rate as controlled outputs and using discrete-time ℓ∞ induced (peak-to-peak) norm from disturbance inputs to these outputs. To cope with the magnitude and rate bound non-linearities together, the induced ℓ∞ norm from disturbance input to the outputs involving control signal and its rate is utilised. On the other hand, discrete-time(DT) induced ℓ2 norm from disturbance input to the main controlled output is used to mitigate the effects of disturbances. We can tackle this ambitious non-linear control problem in the domain of linear convex multi-objective optimal control problem, which can be solved by effective semi-definite optimisation methods by using the proposed transformation and handling the control constraints in terms of worst case peak-to-peak gain of the system. Extended Linear Matrix Inequalities (LMIs) and full block S-procedure based design conditions developed over Linear Fractional Representation(LFR) framework allow the user to obtain robust state- and output-feedback control solutions with reduced conservatism. For the first time, this paper introduces an extended LMI based robust output-feedback control design for magnitude and rate bounded (MRB) systems, using full block S-procedure. We demonstrate the performance of the proposed controller through several simulations over benchmark examples covering systems having multi-variable structures and uncertainties. Our study also involves comparison results with a recently introduced technique based on multi-stage AW technique. The simulation results show that the proposed method of this paper is much effective and less conservative compared to the recent AW method provided in the literature.

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.

Robust guaranteed cost control for uncertain discrete-time systems with state and input quantizations

The robust guaranteed cost control problem for uncertain discrete-time systems with state and input quantizations has been studied in this paper. The polytope type uncertainties are considered in the plants. Different from previous related works, a novel guaranteed cost control strategy has been put forward in this paper. The novelty and challenge lie in that the quantized state and quantized input are included in the guaranteed cost function. Through introducing some auxiliary scalars and combining with the S-procedure, new criteria are developed for the robust stability and guaranteed cost performance for discrete-time systems with state and input quantizations. Based on a new two-step design strategy, the controller and dynamic quantizers can be easily obtained by means of linear matrix inequalities. In the end, two examples are given to demonstrate the effectiveness and applicability of the proposed method.

Quasi-sliding mode control for discrete-time uncertain systems with time-varying delay and stochastic disturbance

This paper investigates an effective controller design method for discrete-time linear system with parameter uncertainty, time-varying delay, input nonlinearity and process disturbance. A novel discrete-time quasi-sliding mode control (DQSMC) scheme is mainly proposed. Since the sliding mode bound is directly involved in the DQSMC law, the chattering bound can be accurately specified. By the proposed method, the dynamic of the sliding mode is unable to escape from the pre-given neighbourhood once it is attracted into the neighbourhood, in addition, the closed-loop system achieves the almost surely stable in mean square sense. Moreover, the proposed DQSMC provides a convenient method to simultaneously regulate the convergence rates of the sliding mode and the closed-loop system. Numerical example is provided to demonstrate the effectiveness of the proposed method.

Sliding Mode Control for Uncertain Discrete-Time Systems Using an Adaptive Reaching Law

This brief presents the design, analysis, and validation of a new adaptive reaching law and the corresponding sliding mode controller, which are dedicated to robust control of disturbed discrete-time systems with parameter uncertainties. In state-of-the-art discrete-time reaching law schemes, a priori boundedness assumption on the generalized uncertainty, consisting of the parameter uncertainties and the external disturbances, is required to guarantee the boundedness of the controlled system. However, a priori bounded generalized uncertainty imposes a priori boundedness assumption on the system state before designing the controller. Different from existing similar works, an adaptive law is integrated into the proposed reaching law to estimate the unknown system parameters and external disturbances in Lyapunov sense, which ensures robust control of uncertain discrete-time systems without requiring a priori bounded system state. The controlled system stability in the presence of parameter uncertainties and external disturbances is analyzed in theory. The feasibility of the reported method is verified and compared by conducting simulation studies.

Indefinite LQ optimal control for discrete-time uncertain systems

This paper is concerned with a linear quadratic (LQ) optimal control for discrete-time uncertain systems, with indefinite state and control weighting matrices in the cost function. Firstly, a recurrence equation of general optimal control problem for discrete-time uncertain systems is obtained by applying Bellman’s principle of optimality. Then, the optimal state feedback control is obtained based on the recurrence equation. Moreover, a sufficient condition of well-posedness for the LQ problem is proposed and a general expression for the optimal control set is given. Furthermore, a numerical example is presented by using the obtained results. Finally, as an application of the indefinite LQ optimal control, an optimal production inventory problem of uncertain environment is solved.

Sliding-mode-disturbance-observer-based adaptive neural control of uncertain discrete-time systems

Sliding-mode-disturbance-observer-based adaptive neural control of uncertain discrete-time systems

A Novel Reaching Law for Sliding Mode Control of Uncertain Discrete-Time Systems

This paper proposed a new sliding mode control algorithm for discrete-time systems with matched uncertainty. The new control algorithm is characterized by a new discrete switching surface. Although the exponential reaching law can reduce oscillation, the control effectiveness will be suppressed when the rate of change of disturbance is high. The exponential reaching law cannot force the system states to approach sliding surface sk=0. In order to solve the contradiction between guaranteeing the basic property of quasi-sliding mode and reducing oscillation, a new discrete reaching law is proposed to improve the reaching process of discrete exponent reaching laws. The proposed method not only can force system state to approach the sliding surface sk=0 in less width of the switching manifold than existing studies, but also can alleviate chattering when the system representative points are near zero point. Simulation results are provided to validate the feasibility and reasonability of the method.

Robust preview control for a class of uncertain discrete-time systems with time-varying delay

This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

Adaptive control for uncertain discrete-time systems with unknown disturbance based on RNN

A new robust adaptive control algorithm is developed for a class of uncertain discrete-time SISO systems. Different from the existing investigated systems, the concerned discrete system here is with both uncertain smooth nonlinear functions and unknown disturbance. On the basis of the idea of neural network (NN) approximation, a novel recurrent neural network (RNN) is first proposed and used to approximate a backstepping control law following the transformation of the original system into a predictor form. According to Lyapunov stability theorem, a new on-line tuning law for parameters of RNN is obtained. Meanwhile, in order to achieve satisfying robust tracking performance, a novel controller is constructed by virtue of the approximation error of RNN. It has been proved that all the concerned signals are uniformly ultimately bounded. In addition, a very small tracking error can be obtained through appropriate selection of control parameters. Finally, we give a simulation example to demonstrate the validness of the newly proposed control algorithm for the investigated systems.

On LMI-based sliding mode control for uncertain discrete-time systems

In this paper, a new approach to design a robust discrete-time sliding mode control (DSMC) is proposed for uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the sliding function which is linear to the state. Our proposed robust DSMC can be applied to unstable systems, and also there is no need to stabilize the underlying system first. It has been argued in the literature that for the systems involving balanced external disturbances, using switching component is not needed. In this paper, it is shown that with the assumption of smoothness of the external disturbances, a different form of switching element in the controller can outperform the so-called linear controller in terms of the thickness of the boundary layer around the sliding function and the ultimate bound on the system state. Also, this paper extends the idea of disturbance estimation to the uncertain discrete-time systems. The disturbance estimator is exploited in the controller design and the boundedness of the obtained closed-loop system is analyzed. Also, two novel forms of variable structure DSMC are suggested in this paper.

Guaranteed cost control of discrete-time uncertain systems with both state and input delays

ABSTRACTThe paper proposes a guaranteed cost feedback control for discrete-time uncertain systems with both state and input delays. The delays are assumed to be time-varying and bounded. In addition to norm-bounded parametric uncertainties, the class of admissible uncertainties and nonlinearities of the system comprehend several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions for the existence of the guaranteed cost control are given by bilinear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed method.

Quantized Output Feedback Control of Uncertain Discrete-Time Systems with Input Saturation

This paper deals with the problem of quantized output feedback control for uncertain discrete-time systems with input saturation. Input quantization case and output quantization case are studied, respectively. The purpose of the study was to design of dynamic output feedback controllers such that all the trajectories of the closed-loop system converge to a small ellipsoid for every initial condition starting from large admissible domain. By solving the optimization problem, the corresponding domains can be obtained. Finally, two simulation examples are provided to demonstrate the applicability of the proposed approach.

Robust Reliable Control for a Class of Uncertain Discrete-Time Systems with Multiple Time-Varying Delays

The robust reliable control design problem of uncertain discrete-time control systems with multiple time-varying delays is addressed in this article. Uncertainty in system is assumed to satisfy the norm-bounded condition and the time-delay parameter is time-varying unstructured. Under the proposed concepts of exponentially robust stability and exponentially robust stabilization, the delay-dependent exponential stability condition for the robust reliable control system is derived and a new delay-dependent state feedback controller design method is provided. The relationship between system stability and time-delays is also studied. Simulation study shows the effectiveness and feasibility of the proposed controller design method.

Sliding mode control for uncertain discrete-time systems with Markovian jumping parameters and mixed delays

This paper is concerned with the robust sliding mode control (SMC) problem for a class of uncertain discrete-time Markovian jump systems with mixed delays. The mixed delays consist of both the discrete time-varying delays and the infinite distributed delays. The purpose of the addressed problem is to design a sliding mode controller such that, in the simultaneous presence of parameter uncertainties, Markovian jumping parameters and mixed time-delays, the state trajectories are driven onto the pre-defined sliding surface and the resulting sliding mode dynamics is stochastically stable in the mean-square sense. A discrete-time sliding surface is firstly constructed and an SMC law is synthesized to ensure the reaching condition. Moreover, by constructing a new Lyapunov–Krasovskii functional and employing the delay-fractioning approach, a sufficient condition is established to guarantee the stochastic stability of the sliding mode dynamics. Such a condition is characterized in terms of a set of matrix inequalities that can be easily solved by using the semi-definite programming method. A simulation example is given to illustrate the effectiveness and feasibility of the proposed design scheme.

A novel reaching law approach of quasi-sliding-mode control for uncertain discrete-time systems

A novel discrete-time reaching law was proposed for uncertain discrete-time system, which contained process noise and measurement noise. The proposed method reserves all the advantages of discrete-time reaching law, which not only decreases the band width of sliding mode and strengthens the system robustness, but also improves the dynamic performance and stability capability of the system. Moreover, a discrete-time sliding mode control strategy based on Kalman filter method was designed, and Kalman filter was employed to eliminate the influence of system noise. Simulation results show that there is no chattering phenomenon in the output of controller and the state variables of controlled system, and the proposed algorithm is also feasible and has strong robustness to external disturbances.