NON‐BLOCKING SUPERVISORY CONTROL FOR INITIALISED RECTANGULAR AUTOMATA

We consider the problem of supervisory control for a class of rectangular automata and more specifically for compact rectangular automata with uniform rectangular activity, i.e. initialised. The supervisory controller is state feedback and disables discrete‐event transitions in order to solve the non‐blocking forbidden state problem. The non‐blocking problem is defined under both strong and weak conditions. For the latter maximally permissive solutions that are computable on a finite quotient space characterised by language equivalence are derived.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

AN LMI APPROACH TO ROBUST H∞ CONTROL FOR UNCERTAIN CONTINUOUS‐TIME SYSTEMS

This paper investigates the problems of robust H∞ control for uncertain continuous‐time systems with time‐varying, norm‐bounded uncertainties in all system matrices. Necessary and sufficient conditions for the above problems are proposed. All conditions are represented in the form of linear matrix inequalities (LMIs). The robust H∞ controller can be easily designed from the solutions of the LMI conditions. Unlike earlier works, the proposed method does not involve any parameter tuning. Thus the robust H∞ optimization control problem, which has not been discussed in earlier reports, can be dealt with using this newly proposed method.     

ROBUST ADAPTIVE CONTROL FOR STRICT‐FEEDBACK NONLINEAR SYSTEMS

In this paper, we propose a robust adaptive tracking control based on the backstepping strategy for strict‐feedback nonlinear systems with nonparametric uncertain nonlinearities. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be decomposed by unknown bounded nonlinear functions and known nonlinear functions. The proposed method can deal with uncertain nonlinearities that appear at the control input term too. It is also shown that suitable choice of design parameters guarantees the convergence of tracking error to any desired bound.     

VOLTAGE REGULATION OF A BUCK BOOST CONVERTER—A HYBRID CONTROL APPROACH

In this paper, the output voltage regulation problem in a buck boost converter is defined as a hybrid control problem. For control design, the mutually interacting continuous and discrete dynamics are modeled as a hybrid automaton. Thus, the control problem is defined as a guard selection problem of the hybrid automaton. The system trajectory is switched between different modes based on the guards to achieve the required voltage regulation. The guards defined are fixed surfaces represented in terms of the state variables for a given operating condition. The logic‐based switching in the state plane is stable in terms of the chaotic and bifurcation behavior. The effectiveness of the control scheme for buck and boost operation under line and load disturbances is demonstrated by simulation in the MATLAB‐SIMULINK environment and the results are presented.     

SENSITIVITY APPROACH TO OPTIMAL CONTROL FOR AFFINE NONLINEAR DISCRETE‐TIME SYSTEMS

This paper deals with the optimal control problem for a class of affine nonlinear discrete‐time systems. By introducing a sensitivity parameter and expanding the system variables into a Maclaurin series around it, we transform the original optimal control problem for affine nonlinear discrete‐time systems into the optimal control problem for a sequence of linear discrete‐time systems. The optimal control law consists of an accurate linear term and a nonlinear compensating term, which is an infinite sequence of adjoint vectors. In the present approach, iteration is required only for the nonlinear compensation series. By intercepting a finite sum of the series, we obtain a suboptimal control law that reduces the complexity of the calculations. A numerical simulation shows that the algorithm can be easily implemented and has a fast convergence rate.     

ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

This paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of a bounded tracking‐error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.     

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

In many mechanical devices with chaotic behavior, stabilizing unstable periodic orbits (UPOs) of the system has positive effects in the lifetime and effectiveness of these devices. In this study, a new non‐parallel distributed compensation (non‐PDC) observer‐based tracking controller is presented for Takagi–Sugeno fuzzy systems to control the chaotic behavior of such systems. Asymptotic stability synthesis of the closed‐loop system is investigated using a fuzzy Lyapunov function to derive less conservative conditions than common quadratic Lyapunov function‐based approaches. To tackle the main drawback of the fuzzy Lyapunov‐based approaches, which assume some upper bounds on the derivatives of the fuzzy grade functions, we propose a new procedure by considering a constraint on the control signal. The new design conditions are given in the form of linear matrix inequalities (LMIs). The proposed control structure is applied to spinning disks in which chaos phenomena appear in lateral vibration. Simulation results are given to show the applicability of the proposed tracker to the UPO problem.     

LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.     

A NEW APPROACH TO TERMINAL SLIDING MODE CONTROL DESIGN

In this paper, terminal sliding mode control design is considered. A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite‐time control ideas. Then terminal sliding mode control laws are constructed for some classes of nonlinear systems.     

Design of non‐fragile guaranteed‐cost repetitive‐control system based on two‐dimensional model

This paper concerns a new method of repetitive control based on two‐dimensional (2D) system theory. First, a 2D model is presented that enables the independent adjustment of control, which happens within a repetition period, and learning, which happens between periods. Next, the problem of designing a repetitive‐control law is formulated as a state‐feedback design problem for the 2D model. An existence condition and a method of designing a robust repetitive‐control law for a plant containing time‐invariant structured uncertainties are established by combining 2D system theory with linear matrix inequalities. Then, based on those results, a non‐fragile guaranteed‐cost repetitive‐control law is derived. The controller gain to be designed is assumed to have additive gain variations. It guarantees that the value of a quadratic performance function is less than a specified upper bound for all admissible uncertainties. The main feature of this approach is that it enables the control action and the learning process to be adjusted independently by the direct tuning of the weighting matrices in the quadratic cost function. Finally, a numerical example demonstrates the validity of this approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A NEW DESIGN APPROACH TO DELAY‐DEPENDENT ROBUST H∞ CONTROL FOR UNCERTAIN TIME‐DELAY SYSTEMS

A new design approach to delay‐dependent robust stabilization and robust H∞ control for a class of uncertain time‐delay systems is provided in this paper. The sufficient conditions for delay‐dependent robust stabilization and robust H∞ control are derived based on a new state transformation and given in terms of linear matrix inequalities (LMI). Numerical examples are presented to show that the proposed results can be less conservative and can be used to deal with not only small but also large delay systems.     

Robust and non‐linear control of marine system

Robust and non‐linear control theories useful for real marine system are developed and applied to a variety of marine vehicles and equipments. In the thesis, the basic principle of marine control system development is described and advanced robust control algorithm and non‐linear control algorithm applicable for real system are shown. It's effectiveness is confirmed by numerical simulations, tank tests, and sea trial tests. Copyright © 2001 John Wiley & Sons, Ltd.     

A NEW INTEGRAL INEQUALITY APPROACH TO DELAY‐DEPENDENT ROBUST H∞ CONTROL

A design method for the robust H_∞ control of an uncertain linear system with a time‐varying state delay is proposed. First, an integral inequality that we recently obtained is employed to establish a new delay‐dependent bounded real lemma for a system with a time‐varying delay. The lemma uses neither a model transformation nor a bounding technique for cross terms. Then, the lemma is used in combination with a matrix decomposition method to derive delay‐dependent conditions for the existence of robust H_∞ control based on linear matrix inequalities. Finally, some numerical examples are given to demonstrate the validity of the method.     

ADAPTIVE DYNAMIC MATRIX CONTROL FOR NETWORK‐BASED CONTROL SYSTEMS WITH RANDOM DELAYS

Random transfer delays in network‐based control systems (NCSs) degrade the control performance and can even destabilize the control system. To address this problem, the adaptive dynamic matrix control (DMC) algorithm is proposed. The control algorithm is derived by applying the philosophy behind DMC to a discrete time‐delay model. A method to estimate the network‐induced delays is also presented to facilitate implementation of the control algorithm. Finally, an NCS platform based on the TrueTime simulator is constructed. With it, the adaptive DMC algorithm is compared with the conventional DMC algorithm under different network conditions. Simulation results show that the proposed adaptive DMC algorithm can respond to various network conditions adaptively and achieve better control performance for NCSs with random transfer delays.     

MINIMIZING SERVICE DELAY OF APERIODIC TASKS IN DYNAMIC‐PRIORITY NON‐PREEMPTIVE HARD REAL‐TIME SYSTEMS

A scheduling technique is presented to minimize service delay of aperiodic tasks in hard real‐time systems that employ dynamic‐priority scheduling and do not allow task preemption. In a real‐time scheduling process, the execution of periodic tasks can be deferred as long as this does not cause other tasks to violate their time constraints. However, aperiodic tasks that usually have urgent missions should complete execution as early as possible. In this paper, it is assumed that aperiodic tasks also have time constraints. Thus, the problem of deciding whether an aperiodic task with an unpredictable arrival time can be scheduled successfully or not is difficult to solve because delaying periodic tasks may cause them to fail to meet their time constraints. We present a dynamic scheduling technique to solve this problem which makes use of the symmetric property of a schedule. The maximum possible idle slot is always reserved at every scheduling point so that aperiodic tasks can be serviced immediately if the reserved idle slot is big enough to service them. The proposed technique also maximizes utilization of idle slots by reserving them for the longest possible time span.     

A new non‐linear sliding‐mode torque and flux control method for an induction machine incorporating a sliding‐mode flux observer

In this paper a novel sliding‐mode control algorithm, based on the differential geometry state‐co‐ordinates transformation method, is proposed to control motor torque directly. Non‐linear feedback linearization theory is employed to decouple the control of rotor flux magnitude and motor torque. The advantages of this method are: (1) The rotor flux and the generated torque can be accurately controlled. (2) Robustness with respect to matched and mismatched uncertainties is obtained. Additionally, a varying continuous control term is proposed. As a result, chattering is eliminated without sacrificing robustness and precision. The control strategy is based on all motor states being available. In practice the rotor fluxes are not usually measurable, and a sliding‐mode observer is derived to estimate the rotor flux. The observer is designed to possess invariant dynamic modes which can be assigned independently to achieve the desired performance. Furthermore, it can be shown that the observer is robust against model uncertainties and measurement noise. Simulation and practical results are presented to confirm the characteristics of the proposed control law and rotor flux observer. Copyright © 2004 John Wiley & Sons, Ltd.     

ROBUST OUTPUT FEEDBACK GUARANTEED COST CONTROL FOR 2‐D UNCERTAIN STATE‐DELAYED SYSTEMS

This paper considers the robust guaranteed cost control problem of two‐dimensional (2‐D) state‐delayed systems. First, the definition of guaranteed cost matrix is proposed and an upper bound of the cost function is given. Then, the guaranteed cost control problem is resolved. Furthermore, the minimum upper bound of the closed‐loop cost function is obtained by solving an optimization problem with LMIs' constraints. A numerical example demonstrates the effectiveness of our results.     

Packet‐Loss‐Dependent Stabilization of Model‐Based Networked Control Systems

In this paper, the stabilization problem and controller design of model‐based networked control systems (MB‐NCSs) with both arbitrary and Markovian packet dropouts are discussed via the switched system approach. Different from the common way of using the last successfully transmitted information, the approximate state produced by the explicit plant model is applied to deal with the packet loss problem in our method. Based on the Lyapunov functional methodology and inequality techniques, some sufficient stabilization conditions are derived and stabilizing state feedback controllers are constructed. Moreover, by using the cone complementary linearation (CCL) method, a non‐linear minimization problem subject to some linear matrix inequalities (LMIs) is provided here to help find a sub‐optimal solution. Numerical examples and accompanying simulations illustrate the effectiveness and validity of our techniques, and also evidence of improvements over the existing literature.