Intelligent robust control design of a precise positioning system

This paper addresses an intelligent uncertainty function to improve the robust stability and performance of H _∞ controlled system in terms of reduced conservatism. The system is identified, output performance and control signal requirements are controlled by proper selection of performance and control weighting functions. Adaptive Neuro Fuzzy Inference System (ANFIS) learns the uncertainty bounds of model uncertainty that results from unmodeled dynamics and parameter variations, then the developed uncertainty weighting function will be included in the synthesis of the H _∞ controller. ν-gap measure is utilized to validate the intelligent identified uncertainty bounds and measure the stability of the designed H _∞ controlled system as well. Experimental results on a servo motion system reveal the advantages of combining intelligent uncertainty identification and robust control. Improved performance is achieved. The proposed approach also allows for iterative experiment design.     

Robust finite-time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of stochastic jump systems

This paper provides the stochastic finite-time stabilization and H _∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H _∞ controller via state feedback is provided to guarantee the stochastic finite-time bounded-ness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.     

H∞ controller design for linear systems with time-invariant uncertainties

This paper considers the problem of designing robust H _∞ state feedback controller for linear continuous-time systems with time-invariant uncertainties. The main result given here concerns H _∞ controller design using the parameter dependent Lyapunov function approach and a new control law. A new condition ensuring the linear systems to be is asymptotically stable with a prescribed H _∞ performance is proposed in terms of a set of linear matrix inequalities (LMIs). Theoretic proof is given to show that the proposed condition is less conservative than existing results in the literature. An example is provided to demonstrate the efficiency of the proposed method.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> fault detection for linear singular systems with time-varying delay

This paper deals with the problem of H _∞ fault detection for a kind of linear singular systems with time-varying delay. A generalized form of observer-based fault detection filter (FDF) is first used as a residual generator. Then the design of H _∞-FDF is formulated in the framework of H _∞ filtering. By applying Lyapunov-Kravoskii function approach, delay-dependent conditions on the existence of the H _∞-FDF, which ensure asymptotic stability and a prescribed H _∞ performance level, are derived. With the aid of a cone complementarity linearization technique, an iterative algorithm is proposed to calculate the parameter matrices of the H _∞-FDF in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed algorithm.     

H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

H∞ filtering for linear periodic systems with parameter uncertainty

This paper focuses on H_∞ filtering for a class of linear periodic systems with a certain type of norm-bounded time-varying parameter uncertainty which appears in both the state and output matrices. The problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed H_∞ performance on infinite horizon for the estimation error for all admissible parameter uncertainties. A solution to this problem is obtained via a Riccati equation approach.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.     

H∞ estimation for discrete-time linear uncertain systems

This paper is concerned with the problem of H_∞ estimation for linear discrete-time systems with time-varying norm-bounded parameter uncertainty in both the state and output matrices. We design an estimator such that the estimation error dynamics is quadratically stable and the induced operator norm of the mapping from noise to estimation error is kept within a prescribed bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riccati equations.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> consensus control of uncertain multi-agent systems with time delays

This paper is devoted to the robust H _∞ consensus control of multi-agent systems with model parameter uncertainties and external disturbances. In particular, switching networks of multiple agents with general linear dynamics are considered, and uncertain communication delays are also taken into account. It shows that a sufficient condition in terms of linear matrix inequalities (LMIs) is derived for the robust consensus performance with a given H _∞ disturbance attenuation level, and meanwhile the unknown feedback matrix of the proposed distributed state feedback protocol is also determined. A numerical example is included to validate the theoretical results.     

New reduced-order <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filter design method for discrete-time singular systems with lossy measurements by strict LMI approach

In this paper, the new design problems of full and reduced-order H _∞ filters including static filters are investigated for discrete-time singular systems with lossy measurements. The lossy measurement is described by a stochastic variable satisfying Bernoulli random binary distribution to model the measured output. Being different from the previous results, the filter existence condition by a new Lyapunov function for singular systems with lossy measurements is given using a strict linear matrix inequality (LMI) in terms of all variables. The proposed full and reduced-order H _∞ filter guarantees regularity, causality, and mean-square stochastic stability with a H _∞ performance bound of filtering error singular system. Moreover, it is shown that the reduced-order H _∞ filter design method is general for both singular systems and non-singular systems with lossy measurements. Numerical examples are worked out to illustrate the effectiveness and applicability of the proposed method.     

Non-fragile observer-based H �� control for neutral stochastic hybrid systems with time-varying delay

The non-fragile observer-based stabilization and H _∞ control problems for neutral stochastic hybrid systems with time-varying delay are studied in this paper. The time-delay is unknown and time-varying with known bounds. Based on Lyapunov functional approach combined with LMIs techniques, the delay-dependent sufficient conditions for the existence of the non-fragile observer-based H _∞ controller are given. Under the control of the non-fragile observer-based H _∞ controller, the resulting closed-loop system not only is robust stochastic exponential stable in the mean square but also satisfies the H _∞ performance level. A numerical example with simulation is given to demonstrate the feasibility and effectiveness of the proposed methods.     

Robust H∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H_∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H_∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H_∞ control methods.     

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.     

New approaches to robust l2?l∞ and H∞ filtering for uncertain discrete-time systemsfiltering for uncertain discrete-time systems

The problems of robust l ₂−l _∞ and H _∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l ₂−l _∞ or H _∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.     

Improved Parameter-dependent H∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.     

Adaptive robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of time delay systems with unknown uncertainty bounds

The problem of adaptive robust H _∞ control for uncertain systems with multiple delays is considered in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds are not necessarily known. The objective is to design adaptive robust H _∞ state-feedback controller such that the resulting closed-loop system is asymptotically stable and a prescribed H _∞ performance level of the closed loop system for disturbance attenuation is guaranteed. To solve this problem, a new sufficient condition is presented in terms of a linear matrix inequality (LMI). The effectiveness of proposed method is verified by its application to an unstable system.     

Finite-time disturbance attenuation of nonlinear systems

This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems. Based on the finite time Lyapunov stability theory, some finite-time H _∞ performance criterions are derived. Then the state-feedback control law is designed and the structure of such a controller is investigated. Furthermore, it is shown that the H _∞ controller can also make the closed-loop system satisfy finite-time H _∞ performance for nonlinear homogeneous systems. An example is provided to demonstrate the effectiveness of the presented results.     

Linear Time Algorithms for Exact Distance Transform

In 2003, Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) published a paper describing an algorithm that computes the exact distance transform in linear time (with respect to image size) for the rectangular binary images in the k-dimensional space ℝ ^k and distance measured with respect to L _p -metric for 1≤p≤∞, which includes Euclidean distance L ₂. In this paper we discuss this algorithm from theoretical and practical points of view. On the practical side, we concentrate on its Euclidean distance version, discuss the possible ways of implementing it as signed distance transform, and experimentally compare implemented algorithms. We also describe the parallelization of these algorithms and discuss the computational time savings associated with them. All these implementations will be made available as a part of the CAVASS software system developed and maintained in our group (Grevera et al. in J. Digit. Imaging 20:101–118, 2007). On the theoretical side, we prove that our version of the signed distance transform algorithm, GBDT, returns the exact value of the distance from the geometrically defined object boundary. We provide a complete proof (which was not given of Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) that all these algorithms work correctly for L _p -metric with 1<p<∞. We also point out that the precise form of the algorithm from Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) is not well defined for L ₁ and L _∞ metrics. In addition, we show that the algorithm can be used to find, in linear time, the exact value of the diameter of an object, that is, the largest possible distance between any two of its elements.