Robust sampled‐data model predictive control for networked systems with time‐varying delay

In this paper, the problem of sampled‐data model predictive control (MPC) is investigated for linear networked control systems with both input delay and input saturation. The delay‐induced nonlinearity is overapproximatively modeled as a polytopic inclusion. The nonlinear behavior of input saturation is expressed as a convex polytope. The resulting closed‐loop systems are represented as linear systems with polytopic and additive norm‐bounded uncertainties. The aim is to determine a robust MPC controller that asymptotically stabilizes the uncertain system at the origin with a certain level of quadratic performance. The effectiveness of the proposed algorithm is demonstrated by a numerical example.     

Mixed Event‐Triggered Mechanism Modeling and Controlling for Networked Control Systems with Time‐Varying Delays and Uncertainties

This paper is concerned with modeling and controlling under the mixed event‐triggered mechanism (ETM) for networked control systems (NCSs) with time‐varying delays and uncertainties. Firstly, an event‐triggered threshold is set by using both state and state‐independent informations in the mixed ETM. Then the event‐triggered NCSs with network‐induced time‐varying delays which exist in both sensor‐to‐controller and controller‐to‐actuator channels are modeled as a general time‐delay system. Based on the piecewise differentiable characteristic of the time‐varying delay and by using the approach of free weighting matrix and reciprocally convex, a less conservative criterion to be globally uniformly ultimately bounded (GUUB) stability and a controller design method are derived. Furthermore, an algorithm is proposed to obtain the desired mixed ETM and state‐feedback controller which can render the network load and control performance to reach an expected level. Compared with the relative and absolute ETMs, the proposed mechanism can effectively improve the transmission efficiency during the whole working time. Finally, a numerical example is given to show the effectiveness of the proposed approach.     

Fault Diagnosis and Sliding Mode Fault Tolerant Control for Non‐Gaussian Stochastic Distribution Control Systems Using T‐s Fuzzy Model

For the non‐Gaussian stochastic distribution control system using Takagi‐Sugeno fuzzy model, a new fault diagnosis and sliding mode fault tolerant control algorithm is presented. First, a new adaptive fault diagnosis algorithm is adopted to diagnose the fault that occurred in the system, and the observation error system is proven to be uniformly bounded. Second, the sliding mode control algorithm is used to reconfigure the controller, based on the fault estimation information. The post‐fault probability density function can still track the given distribution, leading to fault tolerant control of non‐Gaussian stochastic distribution control systems using Takagi‐Sugeno fuzzy model. Finally, simulation results show the effectiveness of the proposed method.     

Local input‐to‐state stabilization and ℓ ∞ ‐induced norm control of discrete‐time quadratic systems

This paper addresses the problems of local stabilization and control of open‐loop unstable discrete‐time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state‐space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input‐to‐state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the ? _∞ ‐induced norm of the closed‐loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and ? _∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state‐dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive Dual Control of Discrete‐Time Lqg Problems with Unknown‐But‐Bounded Parameter

The dual control for a class of discrete‐time linear‐quadratic Gaussian (LQG) problems is studied in this paper, where there exist unknown‐but‐bounded parameter uncertainties both in the state equation and the observation equation. It is assumed that the unknown parameter belongs to a known bounded interval. To achieve the adaptive dual control, a subdivision for the continuous bounded interval is used, thus, the computational tractability is ensured. Based on such subdivision, the adaptive dual controller developed can learn a more accurate interval that contains the true value of the unknown parameter with a learning error given in advance. The performance of the controller is illustrated with two examples.     

Robust Model Predictive Control for Linear Discrete‐Time System With Saturated Inputs and Randomly Occurring Uncertainties

This paper investigates the robust model predictive control (RMPC) problem for a class of linear discrete‐time systems subject to saturated inputs and randomly occurring uncertainties (ROUs). Due to limited bandwidth of the network channels, the networked transmission would inevitably lead to incomplete measurements and subsequently unavoidable network‐induced phenomenon that include saturated inputs as a special case. The saturated inputs are assumed to be sector‐bounded in the underlying system. In addition, the ROUs are taken into account to reflect the difficulties in precise system modelling, where the norm‐bounded uncertainties are governed by certain uncorrelated Bernoulli‐distributed white noise sequences with known conditional probabilities. Based on the invariant set theory, a sufficient condition is derived to guarantee the robust stability in the mean‐square sense of the closed‐loop system. By employing the convex optimization technique, the controller gain is obtained by solving an optimization problem with some inequality constraints. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed RMPC scheme.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

Robust Adaptive Fuzzy Control of Nonlinear Systems with Unknown and Time‐Varying Saturation

In this paper, a robust adaptive fuzzy control approach is proposed for a class of nonlinear systems in strict‐feedback form with the unknown time‐varying saturation input. To deal with the time‐varying saturation problem, a novel controller separation approach is proposed in the literature to separate the desired control signal from the practical constrained control input. Furthermore, an optimized adaptation method is applied to the dynamic surface control design to reduce the number of adaptive parameters. By utilizing the Lyapunov synthesis, the fuzzy logic system technique and the Nussbaum function technique, an adaptive fuzzy control algorithm is constructed to guarantee that all the signals in the closed‐loop control system remain semiglobally uniformly ultimately bounded, and the tracking error is driven to an adjustable neighborhood of the origin. Finally, some numerical examples are provided to validate the effectiveness of the proposed control scheme in the literature.     

Sliding Mode ∑‐Δ Modulation Control of the Boost Converter

A switched implementation of average dynamic output feedback laws trough a ∑‐Δ‐modulator, widely known in the classic communications and analog signal encoding literature, not only frees the sliding mode control approach from state measurements and the corresponding synthesis of sliding surfaces in the plant's state space, but it also allows to effectively transfer all desired closed loop features of an uniformly bounded, continuous, average output feedback controller design into the more restrictive discrete‐valued (ON‐OFF) control framework of a switched system. The proposed approach is here used for the input‐output sliding mode stabilization of the “boost” DC‐to‐DC converter. This is achieved by means of a well known passivity based controller but any other output feedback design would have served our purposes. This emphasizes the flexibility of the proposed sliding mode control design implementation through ∑‐Δ‐modulators.     

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Bounded‐Input Control of the Quadrotor Unmanned Aerial Vehicle: A Vision‐Based Approach

In this paper, a bounded‐input controller is designed for the quadrotor vertical take‐off and landing unmanned aerial vehicle (UAV). Visual information is used to localize the aircraft with respect to its environment and an image‐based visual servo scheme is developed to navigate the motion of it. The visual features are selected from perspective image moments and projected on a rotated image plane, which simplifies the controller design. The flow of the features is used as the linear velocity information, and the controller assumes angular velocity and attitude information available for feedback. To design the controller, the dynamics of the quadrotor are decoupled into two parts: translational dynamics and rotational dynamics. First visual data are used to design a bounded‐input controller for the translational dynamics, and then a saturated controller is designed for the rotational dynamics. The boundedness of the controller increases the chance of keeping the visual features in the field of view of the camera. Furthermore, the controllers also cope with the unknown depth of the image, and the external disturbances. The complete stability analysis of the overall system is presented to show that all states are bounded and the error signals converge to zero asymptotically. Simulation examples are provided in both nominal and perturbed conditions which show the effectiveness of the proposed theoretical results.     

Adaptive Non‐Backstepping Fuzzy Control for a Class of Uncertain Nonlinear Systems with Unknown Dead‐Zone Input

Based on the approximation property of fuzzy logic systems, we propose a novel non‐backstepping adaptive tracking control algorithm for a class of single input single output (SISO) strict‐feedback nonlinear systems with unknown dead‐zone input. In this algorithm, we introduce some novel state variables and coordinate transforms to convert the strict‐feedback form into a normal one, and it is not necessary to consider the traditional approximation‐based the backstepping scheme. Due to new states variables being unavailable, the tracking control is changed from a state‐feedback one to an output‐feedback one. So, observers need to be designed to estimate the indirect nonmeasurable states. According to Lyapunov stability analysis method, the developed controller can guarantee that all of the signals in the closed‐loop system will be ultimately uniformly bounded (UUB), and the output can track the reference signal very well. Simulation results are presented to show the effectiveness of the proposed approach.     

On input‐to‐state stability of rigid‐body attitude control with quaternion representation

The concept of input‐to‐state stability (ISS) is important in robust control, as the state of an ISS system subject to disturbances can be stably regulated to a small region around the origin. In this study, the ISS property of the rigid‐body attitude system with quaternion representation is thoroughly investigated. It has been known that the closed loop with continuous controllers is not ISS with respect to arbitrarily small external disturbances. To deal with this problem, hybrid proportional‐derivative controllers with hysteresis are proposed to render the attitude system ISS. The controller is far from new, but it is investigated in a new aspect. To illustrate the applications of the results about ISS, 2 new robust hybrid controllers are designed. In the case of large bounded time‐varying disturbances, the hybrid proportional‐derivative controller is designed to incorporate a saturated high‐gain feedback term, and arbitrarily small ultimate bounds of the state can be obtained; in the case of constant disturbances, a hybrid adaptive controller is proposed, which is robust against small estimate error of inertia matrix. Finally, simulations are conducted to illustrate the effectiveness of the proposed control strategies.     

Event‐triggered PCS Based Trajectory Tracking Control of Systems with Perturbation

This paper is aimed at reducing network load for saving bandwidth by designing appropriate trigger signals that decide when the transmission should be done. An event‐triggered piecewise continuous systems (PCS) based control for time‐varying trajectory tracking is proposed. By designing the sensor system and controller system, the communication between them is reduced while still retaining a satisfactory closed‐loop behavior of the whole system. The major idea behind a designed sensor system is the use of a Luenberger observer and planning of event‐triggered mechanism (ETM). The main principle behind the designed controller system is the proposal of a new event‐triggered PCS based controller. The development is motivated by consideration of variable network induced time delays. Tracking error is proved to be norm‐bounded in both the original and developed case. Finally, to show the proposed method's performance, we present the simulation results for a mobile cart.     

Fault‐Tolerant Finite Frequency H∞ Control for Uncertain Mechanical System with Input Delay and Constraint

In this paper, a novel fault‐tolerant finite frequency H_∞ controller (FFHC) is developed for uncertain mechanical system with input delay and constraint. First, the mathematical model of uncertain mechanical system is derived, where the uncertainties occur in mass, damping and stiffness matrices, respectively. Then, in view of the fact that the dominant resonance energies are caused by low‐order vibration modes of mechanical system, the finite frequency control algorithm is investigated to suppress these low‐order resonances peaks. By virtue of Lyapunov‐Krasovskii functional (LKF) and generalized Kalman‐Yakubovich‐Popov (GKYP) lemma, the desirable fault‐tolerant controller can be obtained by convex optimization. Numerical simulations verify the improvements and advantages of proposed cotroller in disturbance rejection when compared with the classic entire frequency H_∞ controller (EFHC).     

Two‐stage stability control for strict‐feedback systems with input delays and input nonlinear uncertainties

In this paper, a two‐stage control procedure is proposed for stabilization of a class of strict‐feedback systems with unknown constant time delays and nonlinear uncertainties in the input. A nominal controller is first designed to compensate input time delays without considering input nonlinear uncertainties. Extended from backstepping algorithm, input delay compensation is realized by means of predicted states that are computed through integration of cascaded system dynamics, making the nominal closed‐loop system asymptotically stable. Based on the nominal controller presented for the input delay system, a multi‐timescale system is subsequently developed to estimate the unknown input nonlinearity and make the estimate approach the nominal control input as fast as possible. It is proved that the proposed control scheme can make states of the strict‐feedback systems converge to zero and all the signals of the closed‐loop systems are guaranteed to be bounded in the presence of input time delays and nonlinear uncertainties. Simulation verification is carried out to illuminate the effectiveness of the proposed control approach.     

Control for Time‐Varying Delay Systems by Integrating Semi‐Discretization and Hysteresis‐Based Switching

In this paper, we develop an innovative control method for linear systems with time‐varying delay by integrating the semi‐discretization method and the hysteresis‐based switching algorithm. The semi‐discretization method is adopted to design an optimal controller for each fixed time‐delay and form a candidate controller family. The switching algorithm acts as the principal law for switching among various controllers according to the instantaneous value of the time‐delay. A theoretical proof is presented regarding the stability of the switching time‐delay system. It is shown that the most significant factors that affect the system stability are the size of the candidate controller family, the value of the switching coefficient, and the changing rate of the time‐delay. Two case studies are presented to show the effectiveness of the proposed method.     

Fuzzy Sliding‐mode Strategy for Air–fuel Ratio Control of Lean‐burn Spark Ignition Engines

Minimization of emissions of carbon dioxide and harmful pollutants and maximization of fuel economy for lean‐burn spark ignition (SI) engines relies to a large extent on precise air–fuel ratio (AFR) control. However, the main challenge of AFR control is the large time‐varying delay in lean‐burn engines. Since the system is usually subject to external disturbances and uncertainties, a high level of robustness in AFR control design must be considered. We propose a fuzzy sliding‐mode control (FSMC) to track the desired AFR in the presence of periodic disturbances. The proposed method is model free and does not need any system characteristics. Based on the fuzzy system input–output data, two scaling factors are first employed to normalize the sliding surface and its derivative. According to the concept of the if‐then rule, an appropriate rule table for the logic system is designed. Then, based on Lyapunov stability criteria, the output scaling factor is determined such that the closed‐loop stability of the internal dynamics with uniformly ultimately bounded (UUB) performance is guaranteed. Finally, the feasibility and effectiveness of the proposed control scheme are evaluated under various operating conditions. The baseline controllers, namely, a PI controller with Smith predictor and sliding‐mode controller, are also used to compare with the proposed FSMC. It is shown that the proposed FSMC has superior regulation performance compared to the baseline controllers.     

Model Based Robust Control Law for Linear Event‐Triggered System

This paper proposes a framework to design an event‐triggered based robust control law for linear uncertain system. The robust control law is realized through both static and dynamic event‐triggering approach to reduce the computation and communication usages. Proposed control strategies ensure stability in the presence of bounded matched and mismatched system uncertainties. Derivation of event‐triggering rule with a non‐zero positive inter‐event time and corresponding stability criteria for uncertain event‐triggered system are the key contributions of this paper. The efficacy of proposed algorithm is carried out through a comparative study of simulation results.     

H∞ output feedback control for stochastic systems with randomly occurring convex‐bounded uncertainties and channel fadings

In this paper, the H_∞ output feedback control problem for a class of stochastic discrete‐time systems with randomly occurring convex‐bounded uncertainties and channel fadings is investigated. A sequence of mutually independent random variables with known probabilistic distributions are utilized to describe the randomness that convex‐bounded uncertainties appear in practical systems. The measurements with channel fadings are given by a stochastic Rice fading model which is regulated by a set of random variables with certain probability density functions. The purpose of this paper is to design an output feedback controller such that the closed‐loop control system is asymptotically stable with a prescribed H_∞ performance level. The less conservative results are obtained by employing the stochastic Lyapunov technique. Numerical examples are presented to illustrate effectiveness of the proposed approach.