Fixed‐order robust H∞ control and control‐oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities. A polynomial method is employed to design a fixed‐order controller that assigns closed‐loop poles within a given region of the complex plane and that satisfies an H_∞ performance specification. The main feature of the proposed method is that it can be extended easily for control‐oriented uncertainty set shaping using a standard input design approach. Consequently, the results can be extended to joint robust control/input design procedure whose controller structure and performance specifications are translated into the requirements on the input signal spectrum used in system identification. This way, model uncertainty set can be tuned for the robust control design procedure. The simulation results show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust dynamic ship positioning control system design and applications

This paper describes the robust control system design for a ship dynamic positioning system. The control design is based on an approximate linear model derived from the nonlinear hydrodynamic equations governing the horizontal motions of the ship. The nonlinear models of the ship, seawaves, current, wind and thrusters are derived and simulated for control design verification. The H_∞ control design technique is employed to design the controller. The control problem is formulated in state‐space form and the design specifications are translated into requirements on the weighting functions of the error signal and the thrusters input. A tuning procedure is proposed based on the wind and wave disturbances. The controller is initially tested on the nonlinear ship model and simulation results are presented to demonstrate the robustness of the H_∞ controller. Tank tests results are then presented to assess the controller performance. Copyright © 2001 John Wiley & Sons, Ltd.     

Robust reliable H∞ control design for networked control systems with nonlinear actuator faults and randomly missing measurements

In this paper, the robust reliable H_∞ controller is designed for the problem of nonlinear actuator fault case in the uncertain networked control systems with randomly occurring missing data. More precisely, the occurrence of missing measurements is modeled by a stochastic variable in terms of Bernoulli random distribution. Also, the consideration of a nonlinear term in the input control scheme is a novel work for the proposed model. Suitable robust reliable design of control for a practical actuator fault model is constructed to guarantee the asymptotic stability of the system with H_∞ performance level. A new form of Lyapunov‐Krasovskii functional with triple integral terms are formulated, and the reciprocally convex technique is utilized to establish the sufficient stability criterion in the form of linear matrix inequalities. Finally, the effectiveness of the proposed control method is shown through numerical examples, and we can confirm that the derived condition attained less conservatism than the existing results.     

Robust H∞ filtering for 2D continuous systems with finite frequency specifications

This paper investigates the design problem of robust H_∞ filtering for uncertain two-dimensional (2D) continuous systems described by Roesser model with polytopic uncertainties and frequency domain specifications. Our aim is to design a new filter guaranteeing an H_∞ performance level in specific finite frequency (FF) domains. Using the well-known generalised Kalman Yakubovich Popov lemma and homogeneous polynomially parameter-dependent matrices of arbitrary degrees, sufficient conditions for the existence of H_∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities. Illustrative examples are provided to show the usefulness and potential of the proposed results.     

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.     

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

Multiobjective robust control of LTI systems subject to unstructured perturbations

We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance (H₂-norm) bounds and time-domain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closed-loop system satisfies all specifications simultaneously. These conditions can be numerically checked using finite-dimensional, convex optimization over LMIs, associated with a two-dimensional search. When considering only a subset of the specifications, we recover previous results from the literature, such as those obtained in mixed H₂/H_∞ control.     

Robust H ∞ filtering for uncertain discrete piecewise time-delay systems

This paper investigates the problem of robust H _∞ filter design for uncertain discrete piecewise time-delay systems based on a piecewise Lyapunov functional. The parametric uncertainties are assumed to be time-varying but norm bounded. The purpose is the design of a piecewise filter such that, for all admissible uncertainties, the resulting filtering error system is asymptotically stable and satisfies a prescribed H _∞ performance level. By introducing some different extra matrix variables, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of a desired piecewise filter is given. Two numerical examples are provided to demonstrate the effectiveness of the proposed design method.     

Robust Controller Design And Pid Tuning For Multivariable Processes

In this paper, a robust controller design method is first formulated to deal with both performance and robust stability specifications for multivariable processes. The optimum problem is then dealt with using a loop‐shaping H_∞ approach, which gives a sub‐optimal solution. Then a PID approximation method is proposed to reduce a high‐order controller. The whole procedure involves selecting several parameters and the computation is simple, so it serves as a PID tuning method for multivariable processes. Examples show that the method is easy to use and the resulting PID settings have good time‐domain performance and robustness.     

H∞ approach to monotonically convergent ILC for uncertain time-varying delay systems

This paper deals with iterative learning control (ILC) design for uncertain time-delay systems. Monotonic convergence of the resulting ILC process is studied, and a sufficient condition within an H_∞-based framework is developed. It is shown that under this framework, delay-dependent conditions can be obtained in terms of linear matrix inequalities (LMIs), together with formulas for gain matrices design. A numerical example is provided to illustrate the effectiveness of the robust H_∞-based approach to ILC designed via LMIs.     

Network‐based robust H∞ control of continuous‐time systems with uncertainty

This paper studies the problem of robust H_∞ control for continuous‐time networked control systems (NCSs). A new type of Lyapunov functionals is exploited to derive sufficient conditions for guaranteeing the robust exponential stability and H_∞ performance of the considered system. It is shown that the new result is less conservative than the existing corresponding ones. Meanwhile, a method of eliminating redundant variables to reduce computational complexity is given, which is also applied to design state feedback H_∞ controllers, and the design condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

In this paper, we present a new scheme for designing a H_∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

In this article, the problem of robust sampled-data H _∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H _∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H _∞ output tracking design.     

Robust observer–controller compensator design using the loop shaping design procedure and the algebraic method

This paper investigates robust observer‐controller compensator design using Vidyasagar's structure (VS). VS has a unit matrix parameter H similar to the Q parameter for the Youla–Kucera parameterization. VS can be designed based on the left coprimeness of the central controller in the H_∞‐loop shaping design procedure (H_∞‐LSDP) and therefore can preserve the intrinsic properties of the H_∞‐LSDP. This paper introduces algebraic methods to simplify the design of H in the VS controller by solving specific algebraic equations. In particular, the algebraic design of H can achieve two things. First, a dynamic H adjusts the tracking performance and yields the integral action. Second, a dynamic H rejects the input and output sinusoidal disturbances with known frequencies. These attributes are indications of the flexibility of the proposed method since the output‐feedback controller design of the H_∞‐LSDP cannot easily deal with such conditions. This paper discusses the achieved loop and the closed‐loop behavior of the system with VS, and also gives two numerical examples. The first example shows that the proposed method results in a better design in many aspects than the resulting from H_∞‐LSDP. The second example shows the application of the proposed method to rejecting input and output step disturbances, and input and output multiple sinusoidal disturbances, for which the H_∞‐LSDP can hardly be used. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling

This paper is concerned with the H_∞ performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time‐varying norm‐bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input‐delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous‐time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean‐square exponential stability of the system with an H_∞ performance. What's more, an H_∞ controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

The robust model predictive control based on mixed H2/H∞ approach with separated performance formulations and its ISpS analysis

In practical applications, systems are always influenced by parameter uncertainties and external disturbance. Both the H₂ performance and the H_∞ performance are important for the real applications. For a constrained system, the previous designs of mixed H₂/H_∞ robust model predictive control (RMPC) optimise one performance with the other performance requirement as a constraint. But the two performances cannot be optimised at the same time. In this paper, an improved design of mixed H₂/H_∞ RMPC for polytopic uncertain systems with external disturbances is proposed to optimise them simultaneously. In the proposed design, the original uncertain system is decomposed into two subsystems by the additive character of linear systems. Two different Lyapunov functions are used to separately formulate the two performance indices for the two subsystems. Then, the proposed RMPC is designed to optimise both the two performances by the weighting method with the satisfaction of the H_∞ performance requirement. Meanwhile, to make the design more practical, a simplified design is also developed. The recursive feasible conditions of the proposed RMPC are discussed and the closed-loop input state practical stable is proven. The numerical examples reflect the enlarged feasible region and the improved performance of the proposed design.     

Inertia‐free saturated output feedback attitude stabilization for uncertain spacecraft

In this article, the problem of robust output feedback attitude stabilization control for a class of uncertain spacecraft is investigated, which contains external disturbances, model parameter uncertainty, unknown and uncertain inertia, controller's gain perturbations, measurement errors, and input saturation. The aim of this work is to design a dynamic output feedback controller such that the closed‐loop attitude system is stabilized, while the H_∞ norm of the transfer function from the lumped disturbance and measurement error to output is ensured to be less than a pre‐specified disturbance attenuation level, and the actual control input is confined into a certain range simultaneously. Based on the Lyapunov theory, the existence conditions of such controller are derived in terms of linear matrix inequalities. It is worth mentioning that the controller's additive and multiplicative perturbations are accounted for respectively. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed control design method.     

Robust eigenstructure assignment combining time- and frequency-domain performance specifications

This paper is concerned with robust eigenstructure assignment for multivariable systems. It combines time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H^∞ control to realize joint optimal robust control design. A unified parametric solution for state-feedback eigenstructure assignment is derived for both the case where the sets of closed- and open-loop eigenvalues do not intersect and the case where these sets do intersect. This is based on a set of free parameters. All complex operations are converted into the real field so that the algorithm which is developed for the controller design can be easily implemented on computers. It uses a robustness index defined in the frequency domain as the cost function to be optimized. The analytical gradient calculation of the cost function with respect to the free parameters is given. Using gradient-based optimization, the robustness index is minimized by making full use of the freedom provided by eigenstructure assignment. © 1998 John Wiley & Sons, Ltd.