On the control of an uncertain water quality system

We consider a one-reach water quality system subject not only to bounded uncertain disturbances at the input and output levels but also to bounded uncertain variations of the rate coefficients. When the bounds of the time-varying uncertainties are known, two classes of robust controllers, based on the measured state, are proposed to assure some desired performance, including uniform boundedness and uniform ultimate boundedness. If only output rather than full state is available for the control, a class of estimated state-based control is proposed for the desired performance. When the bounds of the uncertainties are not known, we propose a class of controllers which, using the functional properties of the uncertainties, guarantees some desired system properties, one of which is the convergence to zero of all system responses.     

Design and application of multivariable robust optimal systems

In this paper, a design algorithm for quantitative robust optimal control of uncertain multivariable feedback systems is developed. By use of the frequency-domain approach, the two-degree-of-freedom Wiener–Hopf optimal control method and the quantitative feedback theory are employed to derive the linear quadratic optimal system design with quantitative performance robustness. Two frequency-dependent weighting matrices are shaped and two-degree-of-freedom compensators are designed to achieve quantitative robust optimal control. The proposed design algorithm is then applied to an AFTI/F-16 flight control system design to illustrate the design algorithm. © 1998 John Wiley & Sons, Ltd.     

Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances

This paper deals with the problems of robust stabilization and H_∞ control for a class of uncertain stochastic jumping systems with nonlinear disturbances and time delays. The uncertain parameters are assumed to be norm‐bounded and mode dependent, and the time delays enter into the state matrix, the stochastic perturbation term, as well as the state feedback. The stochastic robust stabilization problem addressed in this paper is to design a state feedback controller with input delay such that, for all admissible uncertainties and the nonlinear disturbances, the closed‐loop system is robustly, stochastically, exponentially stable in the mean square. Moreover, the purpose of the robust H_∞ control problem is to guarantee a specified H_∞ performance index, while still achieving the mean‐square exponential stability requirement for the closed‐loop system. By resorting to the Itô's differential formula and the Lyapunov stability theory, sufficient conditions are derived, respectively, for the robust stabilization and the robust H_∞ control problems. It is shown that the addressed problems can be solved if a set of linear matrix inequalities (LMIs) are feasible. A numerical example is employed to illustrate the usefulness of the proposed LMI‐based design methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed H2/H∞ robust output feedback sliding mode control

This paper presents an output feedback sliding mode control scheme for uncertain dynamical systems. The design problem is solved in two steps, involving first a state feedback and then an output feedback problem. First, using the null space dynamics, the sliding surface for the unmatched uncertainty is designed. Then, by tuning the sliding surface, a robust controller is constructed for the whole uncertainty; this problem takes the form of static‐output feedback. Based on this, a dynamic output feedback controller for the system augmented with the sliding surface is designed. The synthesis involves the solution of an Linear Matrix Inequality (LMI) and Bilinear Matrix Inequality (BMI) problem; the BMI problem is solved iteratively. The proposed approach is illustrated by applying it to a well‐known robust benchmark problem and also experimentally on a spring mass system with variable stiffness. Simulation and experimental results show that the proposed method outperforms previous approaches in terms of robust performance. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust preview control for uncertain discrete‐time systems based on LMI

For a class of uncertain discrete‐time systems, a preview controller based on linear matrix inequality is proposed. A new method is derived to construct an augmented error system instead of taking the difference of the error signal and the system equation. The new approach avoids applying the difference operator to the time‐varying matrix and can simplify the augmented error system. For the augmented error system of the uncertain system, state feedback is introduced. The sufficient condition of asymptotic stability of the closed‐loop system is derived for the performance index by using the relevant theorems of robust control theory. The condition can be realised by solving a linear matrix inequality optimization problem. By incorporating the controller obtained into the original system, we obtain the preview controller. Moreover, introducing an integrator allows the closed‐loop system to robustly track the desired tracking signal without steady‐state error.     

Delay‐dependent robust H ∞ control for uncertain singular time‐delay system with Markovian jumping parameters

The problem of robust H _∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H _∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

APPLICATION OF RECEDING HORIZON CONTROL STRATEGY TO PURSUIT-EVASION PROBLEMS

Time-optimal interception of an arbitrarily manoeuvering evader is investigated using a simplified kinematic model of planar constant speed motion. Against such an uncertain evader behaviour a new and robust pursuer strategy, inspired by the ‘receding horizon’ control concept, is developed. Numerical results of an extensive simulation study show that for all the cases that have been tested the optimal horizon length is approximately 60% of the minimum time required to capture a straight-flying evader. Moreover, the performance loss compared with the optimal control and game solutions is less than 1%. The proposed guidance algorithm, based on the ‘receding horizon’ control concept and using a singular perturbation approximation, is very simple to implement and leads almost always to a near-optimal outcome.     

Robust reliability method and reliability‐based performance optimization for non‐fragile robust control design of dynamic system with bounded parametric uncertainties

An efficient robust reliability method for non‐fragile robust control design of dynamic system with bounded parametric uncertainties is presented systematically, in which the uncertainties existing in the controlled plant and controller realization are taken into account simultaneously in an integrated framework. Reliability‐based design optimization of non‐fragile robust control for parametric uncertain systems is carried out by optimizing the H₂ and H_∞ performances of the closed‐loop system, with the constraints on robust reliabilities. The non‐fragile robust controller obtained by the presented method may possess a coordinated optimum performance satisfying the precondition that the system is robustly reliable with respect to the uncertainties existing in controlled plant and controller. Moreover, the robustness bounds of uncertain parameters can be provided. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. It is demonstrated by a numerical example that the presented method is effective and feasible. Copyright © 2016 John Wiley & Sons, Ltd.     

Fusion steady-state robust filtering for uncertain multisensor networked systems with application to autoregressive moving average signal estimates

This article is concerned with the centralized fusion (CF) robust steady-state Kalman filtering problem for a class of multisensor networked systems with mixed uncertainties including state-dependent and noise-dependent multiplicative noises, missing measurements, packet dropouts, and uncertain noise variances. By using a model transformation approach, the initial multisensor system under study is transformed into a multi-model multisensor system only with uncertain noise variances. By introducing an augmented state vector, the CF system is obtained. In the light of the minimax robust estimation method, and based on the worst-case fusion system with conservative upper bounds of uncertain noise variances, the CF robust steady-state Kalman estimators (predictor, filter, and smoother) are proposed in a unified form. By means of the permutation matrices and Lyapunov equation method, the robustness of CF estimators is proved. The accuracy relations among the robust local and fusion steady-state estimators are proved. An example applied to autoregressive moving average signal estimation is put forward, and the robust CF steady-state signal estimators are proposed. Simulation experiment shows the correctness of the proposed approach.     

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

By integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Bilinear matrix inequality approaches to robust guaranteed cost control for uncertain discrete‐time delay system

The robust guaranteed cost control problem for uncertain discrete‐time delay system is considered in this paper. Sufficient conditions for the existence of the robust guaranteed cost controllers via memoryless state feedback and static output feedback are expressed as bilinear matrix inequality (BMI). Furthermore, the design methods of optimal robust guaranteed cost controllers, which minimize the upper bound of a given quadratic cost function are presented. Alternate iterative algorithms are proposed to solve the nonconvex optimization problems with BMI constrains. A numerical example is given to illustrate the effectiveness of the proposed methods.Copyright © 2012 John Wiley & Sons, Ltd.     

Model reference adaptive minimum‐energy control for a mechatronic elevator system

The mechatronic elevator system driven by a permanent magnet synchronous motor is modeled using mechanical and electrical equations. In addition, the dimensionless forms are derived for practicable movements. This paper proposes and demonstrates the reference model of a minimum‐input absolute electrical energy control scheme based on the Hamiltonian function. Furthermore, a model reference adaptive control scheme based on the Lyapunov function is proposed for tracking the reference model to achieve a robust control performance, thus combining the minimum‐energy reference model of the minimum‐input absolute electrical energy control and the robust control offered by the model reference adaptive control. The proposed model reference adaptive minimum‐energy control yields robust minimum‐energy control performance. Subsequently, the experimental parameters of the elevator system were identified through self‐learning particle swarm optimization. The experimental results demonstrate the robust minimum‐energy control performance of the proposed model reference adaptive minimum‐energy control. Copyright © 2016 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.     

Non-linear excitation control of a synchronous generator using robust feedback linearization

The objective of this paper is to design non-linear excitation controllers for synchronous generators using robust feedback linearization. Since disturbances acting on power systems are of random nature and since the variations in the interconnection variables, the machine currents, cannot be known with certainty, such systems have to be treated as non-linear uncertain stochastic systems. To take advantage of well-developed robust linear control techniques, geometry and stochastic calculus are used to transform the non-linear system to an equivalent linear uncertain system. Simulation results of a single-machine infinite-bus system indicate that the proposed controller provides a larger stability margin than that obtained using existing linear and non-linear controllers. © 1997 John Wiley & Sons, Ltd.     

Design of robust quadratic‐optimal controllers for uncertain singular systems using orthogonal function approach and genetic algorithm

This paper discusses the robust‐optimal state feedback controller design problems of linear singular systems under the structured (elemental) parameter uncertainties by using the orthogonal function approach (OFA) and the hybrid Taguchi genetic algorithm (HTGA). A sufficient condition is proposed to ensure that the linear singular systems with the structured parameter uncertainties are regular, impulse free, and asymptotically stable. Based on the OFA, an algorithm only involving algebraic computation is derived in this paper and then is integrated with the HTGA to design the robust‐optimal state feedback controller of linear uncertain singular systems subject to robust stability constraint and the minimization of a quadratic performance index. A design example of a two degree of freedom mass–spring–damper system is given to demonstrate the applicability of the proposed approach. Copyright © 2008 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 combined feedback/feedforward control for fractional FOPDT systems

In this paper, a combined feedback/feedforward design methodology is proposed for fractional systems in order to cope with model uncertainty and to minimize performance degradation. Based on a fractional commensurate uncertain model, a parametric robust controller is first designed. Then, a parametric command signal for the unity feedback loop is designed. Finally, an optimal set of tuning parameters is found by solving a constrained min–max optimization problem in order to minimize the worst‐case settling time. Simulation results show the effectiveness of the methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal trajectory generation and robust flatness–based tracking control of quadrotors

This work proposes an optimal trajectory generation and a robust flatness–based tracking controller design to create a new performance guidance module for the quadrotor in dense indoor environments. The properties of the differential flatness, the B‐spline, and the direct collocation method are exploited to convert the constrained optimization problem into a nonlinear programming one, which can be easily resolved by a classic solver. After that, the obtained optimal reference trajectory is applied to the dynamic quadrotor model and two different flatness‐based controllers, namely, one based on feedback linearization and one based on feedforward linearization, are developed and compared to ensure the trajectory tracking despite the existence of disturbances and parametric uncertainties. Numerical simulation is executed to evaluate the proposed optimal trajectory generation approach and the robust tracking strategies. It turns out that the controller based on feedforward linearization outperforms the feedback linearization one in robustness and permits obtaining a performance guidance law for an uncertain quadrotor system.