Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

Robust H∞ guaranteed cost control for discrete‐time switched singular systems with time‐varying delay

This paper investigates the problem of control design for a class of uncertain switched singular systems with time‐varying delay. Under mode‐dependent average dwell time and using an appropriate Lyapunov‐Krasovskii functional, the exponential admissibility of the system is analyzed. In order to obtain less conservative conditions, the delay partitioning technique is adopted as well as the improved reciprocally convex approach. By means of the developed admissibility condition, a static output feedback controller is then designed using linear matrix inequality approach. Moreover, by solving an optimization convex problem with constraints, the switched controller is developed to ensure simultaneously the stability of the closed‐loop system and satisfy an optimized upper bound of both the linear quadratic guaranteed cost and the H_∞ norm. Numerical examples are proposed to verify the efficiency and the merits of the method proposed.     

A new method for suboptimal control of a class of non‐linear systems

In this paper, a new non‐linear control synthesis technique (θ–D approximation) is discussed. This approach achieves suboptimal solutions to a class of non‐linear optimal control problems characterized by a quadratic cost function and a plant model that is affine in control. An approximate solution to the Hamilton–Jacobi–Bellman (HJB) equation is sought by adding perturbations to the cost function. By manipulating the perturbation terms both semi‐global asymptotic stability and suboptimality properties are obtained. The new technique overcomes the large‐control‐for‐large‐initial‐states problem that occurs in some other Taylor series expansion based methods. Also this method does not require excessive online computations like the recently popular state dependent Riccati equation (SDRE) technique. Furthermore, it provides a closed‐form non‐linear feedback controller if finite number of terms are taken in the series expansion. A scalar problem and a 2‐D benchmark problem are investigated to demonstrate the effectiveness of this new technique. Both stability and convergence proofs are given. Copyright © 2004 John Wiley & Sons, Ltd.     

A partitioning approach for H∞ control of singular time‐delay systems

This paper presents a new approach for delay‐dependent H_∞ stability analysis and control synthesis for singular systems with delay. By constructing an augmented Lyapunov–Krasovskii functional with a triple‐integral term, and using the partitioning technique, a bounded real lemma is presented to ensure the singular state‐delay system to be regular, impulse free and stable with γ‐disturbance rejection. The proposed result leads to significant performance improvement in system analysis and synthesis. Based on the criterion obtained, a homotopy‐based iterative LMI algorithm is developed to design a static output feedback controller. The feasibility and the effectiveness of theoretical developments are illustrated through numerical examples.Copyright © 2012 John Wiley & Sons, Ltd.     

Robust ℋ︁2 static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

This paper investigates the problem of computing robust ??₂ static output feedback controllers for discrete‐time uncertain linear systems with time‐invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter‐dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an ??₂ guaranteed cost. The conditions are based on parameter‐dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass–spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of ℋ︁∞ fuzzy controllers for nonlinear systems with random data dropouts

The problem of ??_∞ control of nonlinear networked control systems subject to random data dropout is concerned in this paper. The random data dropout, because of the limited bandwidth of the network channels, could exist in the communication channels both from the sensor to the controller and from the controller to the actuator simultaneously. The nonlinear plant is represented by the well‐known Takagi–Sugeno fuzzy model and the random data dropout is expressed by the Bernoulli random binary distribution. In the presence of random data dropout, two control schemes, state feedback and static output feedback, are proposed to design ??_∞ controllers such that the closed‐loop system is stochastically stable and preserves a guaranteed ??_∞ performance. The addressed controller design problem is transformed to an auxiliary convex optimization problem, which can be solved by a linear matrix inequality approach. Three examples are provided to illustrate the applicability and less conservativeness of the developed theoretical results. It is easy to see that our approach is simple but our results are much less conservative than the recently published results. Copyright © 2010 John Wiley & Sons, Ltd.     

Reference output tracking control for a flexible air‐breathing hypersonic vehicle via output feedback

This paper addresses the problem of reference output tracking control for the longitudinal model of a flexible air‐breathing hypersonic vehicle (FAHV) by utilizing the output feedback control approach. The dynamic characteristics of the FAHV along with the aerodynamic effects of hypersonic flight make the flight control of such systems highly challenging. Moreover, there exist some intricate couplings between the engine and flight dynamics as well as complex interaction between rigid and flexible modes in the longitudinal model. These couplings bring difficulty to the flight control design for the intractable hypersonic vehicle systems. This paper deals with the problem of reference output tracking control for the longitudinal model of the FAHV. By utilizing the trim condition information including the state of altitude, velocity, angle of attack, pitch angle, pitch rate and so on, the linearized model is established for the control design objective. Then, the reference output velocity and altitude tracking control design problem is proposed for the linearized model. The flexible models of the FAHV system are hardly measured because of the complex dynamics and the strong couplings of the FAHV. Thus, by using only limited flexible model information, the reference output tracking performance analysis criteria are obtained via Lyapunov stability theory. Then, based on linear matrix inequality optimization algorithm, the static output feedback controller is designed to stabilize the closed‐loop systems, guarantee a certain bound for the closed‐loop value of the cost function, and can make the control output achieve the reference velocity and altitude tracking performance. Subsequently, the condition of dynamic output feedback controller synthesis is given in terms of linear matrix inequalities and a numerical algorithm is developed to search for a desired dynamic output feedback controller which minimizes the cost bound and obtains the excellent reference altitude and velocity tracking performance simultaneously. The effectiveness of the proposed reference output tracking control method is demonstrated in simulation part. Furthermore, the superior reference velocity and altitude performance commands could be achieved via using static and dynamic output feedback controllers under lacking some unmeasured flexible states information in the measurement output vector. Copyright © 2011 John Wiley & Sons, Ltd.     

Delay‐dependent feedforward control of time‐delay systems with parametric uncertainties via dynamic IQCs

This paper studies the design problem of a robust delay‐dependent H _∞ feedforward controller design for a class of linear uncertain time‐delay system having state and control delays when the system is subject to ‐type disturbances. The proposed controller scheme involves two main controllers, which are static state‐feedback and dynamic feedforward controllers. The state‐feedback controller is used for stabilizing the delay and uncertainty‐free system, whereas the feedforward controller performs disturbance attenuation. Dynamic type integral quadratic constraints (IQCs), which consist of frequency‐dependent multipliers, have been introduced to represent the delays and parametric uncertainties in the system where the degree of the multiplier used in IQC representation is in an adjustable nature. This scheme allows the designer to obtain less conservative controllers with increasing precision. Sufficient delay‐dependent criteria in terms of linear matrix inequalities are obtained such that the uncertain linear time‐delay system is guaranteed to be globally, uniformly, asymptotically stable with a minimum disturbance attenuation level. Several numerical examples together with the simulation studies provided at the end illustrate the usefulness of the proposed design. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical design of stable delta‐domain generalized predictive control

This paper addresses certain fundamental issues related to the discrete‐time design problem of the delta‐domain generalized predictive control (δ‐GPC) for both minimum phase and non‐minimum phase linear SISO plants including nominal stability and nominal performance of the closed‐loop system. The approach being presented is completely analytical, and the nominal performance of the control system is directly achieved by a prototype design of the closed‐loop system characteristics resulting in definite time‐domain specifications. Two design methods are offered in which a model‐based prediction paradigm is applied to achieve the future output and the future filtered output trajectory of the plant. Prediction of the first type is based on suitable emulations of the output δ‐derivatives and is used in the GPC controller design for minimum‐phase models of the plant. Prediction of the second type utilizes emulation of derivatives of the output filtered by the numerator polynomial of the transfer function of the controlled part of the plant. It can be employed both for minimum phase and non‐minimum phase plants. A numerical example is given that illustrates the δ‐GPC method for controller design. Copyright © 2002 John Wiley & Sons, Ltd.     

Delay‐dependent robust passive control for a class of nonlinear systems with time‐varying delays

In this paper, the problem of robust passive control for a class of nonlinear systems with time‐varying delays is considered. The uncertainties investigated in this paper are norm bounded and time varying, and they enter all system matrices. Based on the Lyapunov–Krasovskii functionals approach, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of time delay. We also design a state feedback controller that guarantees a robust asymptotically stable and strictly passive closed‐loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques. Copyright © 2007 John Wiley & Sons, Ltd.     

Neural net control of nonlinear plants through state feedback

A heuristic design method for state feedback fixed (non‐adaptive) neural net controller in nonlinear plants is presented. The design method evolves as a natural extension of the optimal control strategies employed in linear systems. A multi‐layered feed‐forward neural network is used as the feedback controller. The controller is trained to directly minimize a suitable cost function comprised of the plant output, states and the input. The optimization is carried out using a gradient scheme that employs the recently developed concept of block partial derivatives. The applicability of the proposed design method is demonstrated through simulated examples. Simulation studies include a variety of optimal control problems in nonlinear plants such as: minimum energy and minimum fuel problems, state tracking, output servo with integrator, and unconstrained and constrained regulation. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust H∞ control for uncertain linear neutral delay systems

This paper deals with the problem of robust H_∞ control for uncertain linear neutral delay systems. The parameter uncertainty under consideration is assumed to be norm‐bounded time‐invariant and appears in all the matrices of the state‐space model. The problem we address is the design of memoryless state feedback controllers such that the closed‐loop system is asymptotically stable and the H_∞ norm of the closed‐loop transfer function from disturbance to the controlled output is strictly less than a prescribed positive scalar for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the above problem is proposed. When this matrix inequality is feasible, an explicit expression for the desired state feedback controller is given. Furthermore, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust continuous‐time controller design via structural Youla–Kučera parameterization with application to predictive control

This paper addresses the continuous‐time control of uncertain linear SISO plants and its nominal and robust stability and nominal and robust performance objectives. A specific application of the Youla–Ku?era (Q) parameterization concept leads to a new development of observer‐like controller structures. This method is combined with a nominal design of continuous‐time generalized predictive control suitable for both minimum‐phase and non‐minimum‐phase plants. The subsequent design procedure consists of two steps. Firstly, the nominal stability and nominal performance of the control system are established by using an analytical design methodology, based on a collection of closed‐loop prototype characteristics with definite time‐domain specifications. And secondly, a generic structure of the controller is enhanced by suitable Q‐parameters guaranteeing that the control system has the required robustness properties. The proposed structural (reduced‐order) Q‐parameterization relies on an observer structure of controllers, which can be easily enhanced with certain filters necessary for control robustification. To reduce the complexity of the resulting robust controllers, we suggest using a structural factorization, which allows for simple forms of robustifying (phase‐lag) correctors of low order, easy for implementation, and convenient for optimization and tuning. Two numerical examples are given to illustrate the composed technique and its practical consequences. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust load–frequency regulation: A real-time laboratory experiment

This paper addresses a new method for robust decentralized design of proportional-integral-based load–frequency control (LFC) with communication delays. In the proposed methodology, the LFC problem is reduced to a static output feedback control synthesis for a multiple delays power system, and then the control parameters are easily carried out using robust H_∞ control technique. To demonstrate the efficiency of the proposed control strategy, an experimental study has been performed on the Analog Power System Simulator at the Research Laboratory of the Kyushu Electric Power Co. in Japan. Copyright © 2007 John Wiley & Sons, Ltd.     

A back propagation through time‐like min–max optimal control algorithm for nonlinear systems

This paper presents a conjugate gradient‐based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward‐in‐time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one‐layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation, to provide an effective, numerically robust algorithm for solving optimal min–max control problems. The proposed algorithm is evaluated on a robotic system with two DOFs. Copyright © 2012 John Wiley & Sons, Ltd.     

Reduced‐order observer‐based fault estimation and fault‐tolerant control for a class of discrete Lipschitz nonlinear systems

This paper addresses an issue on reduced‐order observer‐based robust fault estimation and fault‐tolerant control for a class of uncertain nonlinear discrete‐time systems. By introducing a nonsingular coordinate transformation, a new nonlinear reduced‐order fault estimation observer (RFEO) is proposed with a wide application range in order to achieve an accurate estimation of both states and faults. Next, an improved algorithm is given to obtain the optimal estimation by using a novel iterative linear matrix inequality technique. Furthermore, an RFEO‐based output feedback fault‐tolerant controller, which is independent of the RFEO, can maintain the stability and performance of the faulty system. Simulation results of an aircraft application show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

H∞ control for sampled‐data linear systems with two Markov processes

This paper is concerned with the design problem of H_∞ digital switching control for linear continuous systems with Markovian jumping parameters. The controller is digital and monitored by the jumping parameters of the plant. The closed‐loop system is a hybrid one defined on a hybrid time space (composed of a continuous‐time and a discrete‐time) and a sample space. The sample space is specified by two separable continuous‐time discrete‐state Markov processes, one appearing in the open‐loop system, and the other appearing in control action, which is different with the traditional Markovian jumping process. Our attention is focused on designing digital output feedback controllers for the system with two Markovian jumping processes such that both stochastic stability and a prescribed H_∞ performance are achieved. The problem of robust H_∞ control for systems with parameters uncertainties is also studied. It is shown that the sampled‐data control problems for linear Markovian jumping systems with and without parameter uncertainties can be solved in terms of the solutions to a set of intercoupled matrix inequalities. Two numerical examples are given to show the design procedures. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust observer‐based control for uncertain discrete time‐delay systems with nonlinearities electric‐hydraulic system under Hölder condition

In this paper, the robustness and control problems of output dynamic observer‐based control for uncertain discrete time‐delay systems with nonlinearities under a class of Hölder condition are considered. The parameter uncertainties enter into all the system matrices, the time‐varying delay is unknown with given lower and upper bounds, and the nonlinearities are described by satisfying a class of α Hölder condition. The asymptotic stabilization for uncertain time‐delay nonlinear system will be guaranteed. Linear matrix inequality optimization approach is used to design the robust observer‐based output dynamic controls. The feedback control and observer gains are got from linear matrix inequality optimization feasible solution. Electric‐hydraulic system is described and used to illustrate the method.     

Temporal and differential stabilizability and detectability of piecewise constant rank systems

In a past note we drew attention to the fact that time‐varying continuous‐time linear systems may be temporarily uncontrollable and unreconstructable and that this is vital knowledge to both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability require considering piecewise constant rank (PCR) systems and the differential Kalman decomposition. In this note for conventional as well as PCR systems measures of temporal and differential stabilizability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closed‐loop system when designing a static state or dynamic output feedback controller. It is indicated how to compute the measures from the system matrices. The importance of our developments for control system design is illustrated through three numerical examples concerning LQ and LQG perturbation feedback control of a non‐linear system about an optimal control and state trajectory. Copyright © 2011 John Wiley & Sons, Ltd.