bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonlinear uncertain systems and robustness optimization
Authors: Ryan E. P. , Townley S. 
Published: July 2007

AbstractAn approach to (adaptive) stabilization is developed for a class of uncertain nonlinearly perturbed linear dynamical systems modelled by a controlled differential inclusion on Rn. The essential features are nonlinear feedback and optimization of robustness with respect to unmatched uncertainty. The approach is geometric: (i) a family 𝒱 of proper subspaces V ⊂ Rn is introduced with the property that {0} ⊂ V is an asymptotically stable equilibrium for the projection, onto V, of the unperturbed linear flow; (ii) for the perturbed system, it is then shown that each V ϵ 𝒱 can be rendered attractive and (almost) invariant by some choice of feedback determined by the nature of the perturbation and other a priori system information; specifically, under differing hypotheses, we can render V ϵ 𝒱 almost invariant and attractive, or invariant and finite‐time attractive, or adaptively attractive via, respectively, linear high‐gain feedback or discontinuous feedback, or adaptive feedback. Associated with each V ϵ 𝒱 is a measure of robustness with respect to unmatched uncertainty (a stability radius), quantified by a real parameter η. The problem of optimizing this measure is formulated as an optimization problem over 𝒱, solvable (in a supremal sense of η‐maximizing sequences (Vj) 𝒱) via solutions of particular algebraic Riccati equations of order k ≤ (n ‐ m), where m ≤ n is the control dimension; typically k = n ‐ m..
Stability of quantitative feedback designs and the existence of robust QFT controllers
Authors: Jayasuriya Suhada , Zhao Yongdong 
Published: July 2007

AbstractQuantitative feedback theory (QFT) has received much criticism for a lack of clearly stated mathematical results to support its claims. Considered in this paper are two important fundamental questions: (i) whether or not a QFT design is robustly stable, and (ii) does a robust stabilizer exist. Both these are precursors for synthesizing controllers for performance robustness. Necessary and sufficient conditions are given to resolve unambiguously the question of robust stability in SISO systems, which in fact confirms that a properly executed QFT design is automatically robustly stable. This Nyquist‐type stability result is based on the so‐called zero exclusion condition and is applicable to a large class of problems under some simple continuity assumptions. In particular, the class of uncertain plants include those in which there are no right‐half plane pole‐zero cancellations over all plant uncertainties. A sufficiency condition for a robust stabilizer to exist is derived from the well‐known Nevanlinna‐Pick theory in classical analysis. Essentially the same condition may be used to answer the question of existence of a QFT controller for the general robust performance problem. These existence results are based on an upper bound on the nominal sensitivity function. Also considered is QFT design for a special class of interval plants in which only the poles and the DC gain are assumed uncertain. The latter problem lends itself to certain explicit computations that considerably simplify the QFT design problem.
Quantitative design of a class of nonlinear systems with parameter uncertainty
Authors: Oldak S. , Baril C. , Gutman P. O. 
Published: July 2007

AbstractThis paper considers the case in which a linear time‐invariant (LTI) but uncertain plant suffers from nonlinearities y=n(x) which can be expressed as y=Kn+η(x), |η(x)|≤M, with K, a possibly uncertain scalar. This covers a large and very important class of nonlinearities encountered in practice such as friction, backlash, dead zone and quantization.Quantitative design techniques are presented for this class for the satisfaction of specifications. Special attention is paid to the avoidance of limit cycles using describing function theory, although the design method is also amenable of application using other stability criteria such as the circle criteria. Numerical examples are developed illustrating the design procedure.
Multi‐input, multi‐output flight control system design for the YF‐16 using nonlinear QFT and pilot compensation
Authors: Miller Russel B. , Horowitz Isaac M. , Houpis Constantine H. , Finley Barfield A. 
Published: July 2007

AbstractNonlinear quantitative feedback theory (QFT) and pilot compensation techniques are used to design a 2 × 2 flight control system for the YF‐16 aircraft over a large range of plant uncertainty. The design is based on numerical input‐output time histories generated with a FORTRAN implemented nonlinear simulation of the YF‐16. The first step of the design process is the generation of a set of equivalent linear time‐invariant (LTI) plant models to represent the actual nonlinear plant. It has been proven that the solution to the equivalent plant problem is guaranteed to solve the original nonlinear problem. Standard QFT techniques are then used in the design synthesis based on the equivalent plant models. A detailed mathematical development of the method used to develop these equivalent LTI plant models is provided. After this inner‐loop design, pilot compensation is developed to reduce the pilot's workload. This outer‐loop design is also based on a set of equivalent LTI plant models. This is accomplished by modelling the pilot with parameters that result in good handling qualities ratings, and developing the necessary compensation to force the desired system responses.
Neural networks for nonlinear state estimation
Authors: Parisini T. , Zoppoli R. 
Published: July 2007

AbstractEstimating the state of a nonlinear stochastic system (observed through a nonlinear noisy measurement channel) has been the goal of considerable research to solve both filtering and control problems. In this paper, an original approach to the solution of the optimal state estimation problem by means of neural networks is proposed, which consists in constraining the state estimator to take on the structure of a multilayer feedforward network. Both non‐recursive and recursive estimation schemes are considered, which enable one to reduce the original functional problem to a nonlinear programming one. As this reduction entails approximations for the optimal estimation strategy, quantitative results on the accuracy of such approximations are reported. Simulation results confirm the effectiveness of the proposed method.
Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete‐time theory
Authors: Haddad Wassim M. , Bernstein Dennis S. 
Published: July 2007

AbstractIn a companion paper (‘Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous‐time theory’), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are developed for the discrete‐time case. As in the continuous‐time case, each result is based upon a suitable Riccati‐like matrix equation that is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time‐invariant system and a memoryless nonlinearity. Multivariable versions of the discrete‐time circle and Popov criteria are obtained as extensions of known results. Each result is specialized to the linear uncertainty case and connections with robust stability for state‐space systems is explored.
Admissible controls and attainable states for a class of nonlinear systems with general constraints
Authors: Achhab M. E. , Callier F. M. , Wertz V. 
Published: July 2007

AbstractWe consider nonlinear control systems where the control and the state variables are submitted to explicit constraints. This paper has two objectives. First, for a class of nonlinear systems with constraints, an existence result of nontrivial admissible controls and some of their interesting properties are proved. Then, we investigate the problem of local controllability in a neighbourhood of an equilibrium point, while observing state and control constraints along the whole trajectory. An iterative procedure is also given, which allows one to compute the steering admissible control function. This procedure is illustrated with a classical example.
Quantification of model uncertainty from data
Authors: de Vries Douwe K. , Van Hof Paul M. J. Den 
Published: July 2007

AbstractIdentification of linear models in view of robust control design requires the identification of a control‐relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency‐dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.
Polynomial solutions toH∞problems
Authors: Meinsma Gjerrit 
Published: July 2007

AbstractThe paper presents a polynomial solution to the standardH∞‐optimal control problem. Based on two polynomialJ‐spectral factorization problems, a parameterization of all suboptimal compensators is obtained. A bound on the McMillan degree of suboptimal compensators is derived and an algorithm is formulated that may be used to solve polynomialJ‐spectral factorization problems.
Construction of value set for robustness analysis via circular arithmetic
Authors: Polyak B. T. , Scherbakov P. S. , Shmulyian S. B. 
Published: July 2007

AbstractCircular arithmetic technique is developed for constructing value set of a characteristic polynomial. It provides necessary and sufficient conditions for robust stability of disk polynomials and their simple combinations. In more complicated cases sufficient conditions can be obtained. Various examples including multilinear (real or complex) parameter perturbations are considered.
The discrete‐timeH∞control problem with measurement feedback
Authors: Stoorvogel Anton A. , Saberi Ali , Chen Ben M. 
Published: July 2007

AbstractThis paper is concerned with the discrete‐timeH∞control problem with measurement feedback. We extend previous results by having weaker assumptions on the system parameters. We also show explicitly the structure ofH∞controllers. Finally, we show that it is in certain cases possible, without loss of performance, to reduce the dynamical order of the controllers.
Frequency‐restricted norm bounds for interval systems
Authors: Kimura Tetsuya , Hara Shinji 
Published: July 2007

AbstractWe investigate bounds of frequency‐restricted norms (FRN), a generalization ofH∞‐norm, for SISO LTI interval systems, where the numerator and the denominator are interval polynomials. Though theH∞‐norm of interval systems can be determined by 16 Kharitonov‐type systems, we can show that this fact is not true in general by a counterexample. A special class of systems for which the FRN is bounded by fixed extremal systems is derived. On the basis of this result, an example of PI‐type controller design considering both parametric and unstructured perturbations is illustrated by a parameter space design method.
Equivalence of stability concepts for discrete time‐varying systems
Authors: Bhaya Amit , Das Francisco , Mota Chagas 
Published: July 2007

AbstractStability concepts arising in the literature on absolute stability, difference inclusions and interval matrices are all shown to be equivalent to simultaneous asymptotic stability of a class of linear time‐varying discrete systems and, in turn, to exponential stability. This enables the classification of an interval matrix stability test due to Baueret al., a Lyapunov indicator test due to Barabanov and a constructive Lyapunov function test due to Brayton and Tong into a hierarchy of stability tests. Some applications of these tests are given and it is observed that they are not, in general, polynomial‐time tests.
Loop shaping and a zero‐placement technique as applied to the benchmark problem
Authors: Schmidt David K. , Benson Dwayne 
Published: July 2007

AbstractA classical and a ‘quasi‐modern’ approach are taken to develop robust control laws for the 1992 ACC benchmark problem of Wie and Bernstein. In both approaches, copious use of loop‐shaping à la Bode design is employed. The quasi‐modern approach reported herein is a zero‐placement technique, which is a variant on LQG/LTR. This approach allows for the direct selection of the zeros of the loop transfer function, leading to the desired loop shape. Therefore, undesirable pole‐zero cancellations may be avoided. The modern and quasi‐modern approaches are closely related, and can lead to similar control laws. Though the problem addressed here is SISO, the zero‐placement approach can be used on MIMO systems. However, in the case discussed herein, the classically designed controller has superior performance and stability robustness.
Robust controller design for a non‐colocated spring‐mass system via mixed 𝓁/∞ optimization
Authors: Sznaier Mario , Rotstein Héctor 
Published: July 2007

AbstractA successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addressed using the ℋ︁∞robust control framework. However, this framework cannot accommodate the realistic case where in addition to robustness considerations, the system is subject to time‐domain specifications. We recently proposed design procedures to explicitly incorporate time‐domain specifications into the ℋ︁∞framework. In this paper we apply these design procedures to the simple mass‐spring system used as a benchmark in the 1990–1992 ACC, with the goal of minimizing the peak control effort while satisfying disturbance rejection, settling time, tracking and robustness specifications. The results show that there exist a severe trade‐off between peak control action and robustness to unstructured model uncertainty.
A zero compensation approach to singular H2 and H∞ problems
Authors: Copeland B. R. , Safonov M. G. 
Published: July 2007

AbstractIn this work we analyse singular H2 and H∞ problems for which the usual Riccati equations become ill‐posed owing to the existence of plant zeros at infinity.We adopt a two‐step approach to the analysis. First we replace the usual Riccati equations with two generalized eigenproblems; these problems are always well‐posed. Next we extract those structural elements which pertain to the troublesome plant zeros. We do this by introducing pre‐compensators which cancel the offending zeros. In so doing, we temporarily relax the controller properness constraint that is traditionally imposed in H2 and H∞ problems by allowing pole‐zero cancellations between the plant and controller at infinity. Since no significant added complexity of analysis results, we also treat the case of singularity due to finite jω‐axis plant zeros by relaxing the internal stability requirement and allowing finite jω‐axis pole‐zero cancellations.The resultant theory allows us to specify necessary and sufficient conditions for the existence of solutions to singular H2 and H∞ problems. The existence conditions and the resultant control laws are expressed directly in terms of the eigenvalues and eigenvectors of two Hamiltonian matrices associated with the problem. The theory also gives some insight into the character of the subset of all proper, internally stabilizing solutions, including whether this set is nonempty. An example is included.
A design procedure for the exact H∞ siso‐robust performance problem
Authors: Nordgren R. E. , Franchek M. A. , Nwokah O. D. I. 
Published: July 2007

AbstractPresented in this paper is a loop‐shaping solution to the H∞ robust performance problem for a class of SISO systems. The key feature of this work is the explicit incorporation of phase information into the controller synthesis to facilitate loop‐shaping over all frequencies. Consequently, a significant reduction in the required controller gain/bandwidth is achieved. It is also shown that the optimal solution, in the sense of controller gain/bandwidth minimization, to the robust performance problem is that which makes μ = 1 over all frequencies. This is different from the usual definition of optimality in the H∞/μ literature. An example is included for completeness.
Minimax optimal control of uncertain systems with structured uncertainty
Authors: Savkin Andrey V. , Petersen Ian R. 
Published: July 2007

AbstractThis paper considers a minimax control problem for an uncertain system containing structured uncertainties. The uncertainties in this system are assumed to satisfy a certain integral quadratic constraint. For a given initial condition, the minimax optimal controller is constructed by solving a parameter‐dependent Riccati equation of the game type. This controller leads to a closed‐loop uncertain system which is absolutely stable.
Input to state stabilizability for parametrized families of systems
Authors: Lin Yuandan , Sontag Eduardo D. , Wang Yuan 
Published: July 2007

AbstractThis paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov‐theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state‐space stability to ‘input to state’ (bounded‐input bounded‐state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analysed.
Joint‐space orthogonalization and passivity for physical interpretations of dextrous robot motions under geometric constraints
Authors: Arimoto Suguru 
Published: July 2007

AbstractA principle of ‘joint‐space orthogonalization’ is proposed as an extended notion of hybrid (force and position) control for robot manipulators under geometric constraints. The principle realizes the hybrid control in a strict sense by letting position feedback signals be orthogonal in joint space to the contact force vector whose components exert at corresponding joints. This orthogonalization is executed via a projection matrix computed in real‐time from a Jacobian matrix of the constraint equation in joint coordinates.To show the important role of the principle in control of robot manipulators, two basic set‐point control problems are analysed. One is a hybrid PID control problem for robot manipulators under geometric endpoint constraint and another is a coordinated control problem of two arms. It is shown that passivity properties of residual dynamics of robots follow from the introduction of a quasi‐natural potential and the joint‐space orthogonalization. Various stability problems of PID‐type feedback control schemes without compensating for the gravity force and with or without use of a force sensor are discussed from passivity properties of robot dynamics with the aid of the hyper‐stability theory.
Control of constrained robots including effects of joint flexibility and actuator dynamics
Authors: Krishnan Hariharan 
Published: July 2007

AbstractWe consider mathematical representations of constrained robot systems in which the effects of joint flexibility and actuator dynamics are significant. The objective is to design a feedback control law so that the position output variables and the force output variables of the robot follows the desired position and the desired force trajectories respectively despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. The development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility. Thus using the force/position control law developed in this paper one can achieve better tracking performance in cases where such effects are significant.
NonlinearH∞disturbance attenuation for robots with flexible joints
Authors: Tomei Patrizio 
Published: July 2007

AbstractThe tracking problem is considered for robots having flexible joints. We propose a state feedback control algorithm which guarantees arbitrary attenuation on the outputs of the effects of time‐varying disturbances as well as of parameter uncertainties. Only a lower bound on the values of the elastic constants is required to be known.
A semi‐global low‐and‐high gain design technique for linear systems with input saturation—stabilization and disturbance rejection
Authors: Lin Zongli , Saberi Ali 
Published: July 2007

AbstractIn this paper we propose a linear low‐and‐high gain design technique to solve the semi‐global stabilization problem for a class of linear systems subject to input saturation. The central idea behind this new technique is to increase the utilization of the available control capability of the system. The power of this new semi‐global design technique is shown by solving the problem of semi‐global stabilization with input‐additive disturbance rejection which is formulated as a semi‐global practical stabilization problem.
Linear systems with input nonlinearities: Global stabilization by scheduling a family ofH∞‐type controllers
Authors: Teel Andrew R. 
Published: July 2007

AbstractA new global stabilization algorithm is presented for linear systems that have (A,B) stabilizable, the eigenvalues ofAin the closed left‐half plane, but where the controls pass through nonlinearities of a general type. This algorithm is based on a semi‐global stabilization solution for the same class of systems. The global solution is constructed by dynamically scheduling the adjustable parameter of the semi‐global solution according to the size of the state. The semi‐global solution is a family of linear control laws generated by a family ofH∞‐type algebraic Riccati equations. We show that the closed‐loop state feedback system has the property that additive disturbances which converge exponentially to zero cannot produce unbounded states. This fact is used to show that, under a linear detectability assumption, the state feedback results are recovered when the solution is implemented via a standard linear‐based observer.
Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities
Authors: Michel Anthony N. , Liu Derong , Wang Kaining 
Published: July 2007

AbstractFor linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback.Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities).We demonstrate the applicability of the present results by means of several specific examples.