Showing papers in "IEEE Transactions on Automatic Control in 1996"
2,208 citations
TL;DR: This paper addresses the design of state- or output-feedback H/sub /spl infin// controllers that satisfy additional constraints on the closed-loop pole location by derived in terms of linear matrix inequalities (LMIs).
Abstract: This paper addresses the design of state- or output-feedback H/sub /spl infin// controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMIs), and the authors' formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H/sub 2//H/sub /spl infin// synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example.
2,036 citations
TL;DR: It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.
Abstract: This paper describes a simple "high-level" controller called a "supervisor" which is capable of switching into feedback with a SISO process, a sequence of linear positioning or set-point controllers from a family of candidate controllers so as to cause the output of the process to approach and track a constant reference input. The process is assumed to be modeled by a SISO linear system whose transfer function is in the union of a number of subclasses, each subclass being small enough so that one of the candidate controllers would solve the positioning problem if the transfer function of the process were to be one of the subclasses' members. Each subclass contains a "nominal process model transfer function" about which the subclass is centred. It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.
1,415 citations
TL;DR: The authors believe that the H-infinity-optimal control theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs.
Abstract: One of the major concentrated activities of the past decade in control theory has been the development of the so-called "H-infinity-optimal control theory", which addresses the issue of worst-case controller design for linear plants subject to unknown disturbances and plant uncertainties. Among the different time-domain approaches to this class of worst-case design problems, the one that uses the framework of dynamic, differential game theory stands out to be the most natural. This is so because the original H-infinity control problem (in its equivalent time-domain formulation) is in fact a minimax optimization problem, and hence a zero-sum game, where the controller can be viewed as the minimizing player and disturbance as the maximizing player. Using this framework, the authors present in this book a complete theory that encompasses continuous-time as well as discrete-time systems, finite as well as infinite horizons, and several different measurement schemes, including closed loop perfect state, delayed perfect state, samples state, closed-loop imperfect state, delayed imperfect state and sampled imperfect state information patterns. They also discuss extensions of the linear theory to nonlinear systems, and derivation of the lower dimensional controller for systems with regularly and singularly perturbed dynamics. This is the second edition of a 1991 book with the same title, which, besides featuring a more streamlined presentation of the results included in the first edition, and at places under more refined conditions, also contains substantial new material, reflecting new developments in the field since 1991. Among these are the nonlinear theory; connections between H-infinity-optimal control and risk sensitive stochastic control problems; H-infinity filtering for linear and nonlinear systems; and robustness considerations in the presence of regular and singular perturbations. Also included are a rather detailed description of the relationship between frequency-and time-domain approaches to robust controller design, and a complete set of results on the existence of value and characterization of optimal policies in finite- and infinite-horizon LQ differential games. The authors believe that the theory is now at a stage where it can easily be incorporated into a second-level graduate course in a control curriculum, that would follow a basic course in linear control theory covering LQ and LQG designs. The framework adopted in this book makes such an ambitious plan possible. For the most part, the only prerequisite for the book is a basic knowledge of linear control theory. No background in differential games, or game theory in general, is required, as the requisite concepts and results have been developed in the book at the appropriate level. The book is written in such a way that makes it possible to follow the theory for the continuous- and discrete-time systems independently (and also in parallel).
1,352 citations
TL;DR: A design methodology is developed that expands the class of nonlinear systems that adaptive neural control schemes can be applied to and relaxes some of the restrictive assumptions that are usually made.
Abstract: Based on the Lyapunov synthesis approach, several adaptive neural control schemes have been developed during the last few years. So far, these schemes have been applied only to simple classes of nonlinear systems. This paper develops a design methodology that expands the class of nonlinear systems that adaptive neural control schemes can be applied to and relaxes some of the restrictive assumptions that are usually made. One such assumption is the requirement of a known bound on the network reconstruction error. The overall adaptive scheme is shown to guarantee semiglobal uniform ultimate boundedness. The proposed feedback control law is a smooth function of the state.
1,255 citations
TL;DR: The authors derive sufficient ("weak coupling") conditions which guarantee the asymptotic string stability of a class of interconnected systems and ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used.
Abstract: Introduces the notion of string stability of a countably infinite interconnection of a class of nonlinear systems. Intuitively, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the interconnected system are uniformly bounded. It is well known that the input output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. The authors derive sufficient ("weak coupling") conditions which guarantee the asymptotic string stability of a class of interconnected systems. Under the same "weak coupling" conditions, string-stable interconnected systems remain string stable in the presence of small structural/singular perturbations. In the presence of parameter mismatch, these "weak coupling" conditions ensure that the states of all the subsystems are all uniformly bounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically.
1,055 citations
TL;DR: These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations, and they often compare favorably with /spl mu/ analysis for time-invariant parameter uncertainty.
Abstract: This paper presents new tests to analyze the robust stability and/or performance of linear systems with uncertain real parameters. These tests are extensions of the notions of quadratic stability and performance where the fixed quadratic Lyapunov function is replaced by a Lyapunov function with affine dependence on the uncertain parameters. Admittedly with some conservatism, the construction of such parameter-dependent Lyapunov functions can be reduced to a linear matrix inequality (LMI) problem and hence is numerically tractable. These LMI-based tests are applicable to constant or time-varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations. They also avoid the frequency sweep needed in real-/spl mu/ analysis, and numerical experiments indicate that they often compare favorably with /spl mu/ analysis for time-invariant parameter uncertainty.
999 citations
TL;DR: New characterizations of the input-to-state stability property are presented and the equivalence between the ISS property and several (apparent) variations proposed in the literature are shown.
Abstract: We present new characterizations of the input-to-state stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature.
863 citations
TL;DR: An inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory which leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case.
Abstract: An inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory. In the case of minimum phase systems, the trajectory produced agrees with that generated by Hirschorn's inverse dynamic system; however, the preimage trajectory is noncausal (rather than unstable) in the nonminimum phase case. In addition, the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case. With the addition of stabilizing feedback to the preimage trajectory, asymptotically exact output tracking is achieved. Tracking is demonstrated with a numerical example and compared to the well-known Byrnes-Isidori regulator. Rather than solving a partial differential equation to construct a regulator, the inverse is calculated using a Picard-like interaction. When preactuation is not possible, noncausal inverse trajectories can be truncated resulting in the tracking-error transients found in other control schemes.
825 citations
TL;DR: A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation.
Abstract: A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation. The theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear, feedforward form. This result, in turn, is applied to the control of: 1) linear systems (stable and unstable) with inputs subject to magnitude and rate saturation and time delays; 2) the cascade of globally asymptotically stable nonlinear systems with certain linear systems (those that are stabilizable, right invertible, and such that all of their invariant zeros have nonpositive real part); 3) the inverted pendulum on a cart; and 4) the planar vertical takeoff and landing aircraft.
791 citations
TL;DR: It is proved, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one.
Abstract: We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one.
TL;DR: A graph-theoretic formulation of multiple-model estimation is given which leads to a systematic treatment of model-set adaptation and opens up new avenues for the study and design of the MM estimation algorithms.
Abstract: Existing multiple-model (MM) estimation algorithms have a fixed structure, i.e. they use a fixed set of models. An important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used. Limitations of the fixed structure algorithms are addressed first. In particular, it is shown theoretically that the use of too many models is performance-wise as bad as that of too few models, apart from the increase in computation. This paper then presents theoretical results pertaining to the two ways of overcoming these limitations: select/construct a better set of models and/or use a variable set of models. This is in contrast to the existing efforts of developing better implementable fixed structure estimators. Both the optimal MM estimator and practical suboptimal algorithms with variable structure are presented. A graph-theoretic formulation of multiple-model estimation is also given which leads to a systematic treatment of model-set adaptation and opens up new avenues for the study and design of the MM estimation algorithms. The new approach is illustrated in an example of a nonstationary noise identification problem.
TL;DR: Two noniterative subspace-based algorithms which identify linear, time-invariant MIMO (multi-input/multioutput) systems from frequency response data are presented.
Abstract: Two noniterative subspace-based algorithms which identify linear, time-invariant MIMO (multi-input/multioutput) systems from frequency response data are presented. The algorithms are related to the recent time-domain subspace identification techniques. The first algorithm uses equidistantly, in frequency, spaced data and is strongly consistent under weak noise assumptions. The second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions, promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure.
TL;DR: The authors take a semiglobal approach to solve some of the central control problems for linear systems with saturating actuators, including stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties.
Abstract: This paper deals with the design of linear systems with saturating actuators where the actuator limitations have to be incorporated a priori into control design. The authors take a semiglobal approach to solve some of the central control problems for such systems. These problems include stabilization, input-additive disturbance rejection, and robust stabilization in the presence of matched nonlinear uncertainties. The authors develop further the semiglobal design technology which was initiated in their earlier work (Lin and Saberi, 1995) and utilize it to deal with these control problems.
TL;DR: The proposed approach provides feedback laws with several degrees of freedom which can be exploited to tackle design constraints and serves as a basic tool to be used, in a recursive design, to deal with more complex systems.
Abstract: Our study relates to systems whose dynamics generalize x/spl dot/=h(y,u), y/spl dot/=f(y,u), where the state components x integrate functions of the other components y and the inputs u. We give sufficient conditions under which global asymptotic stabilizability of the y subsystem (respectively, by saturated control) implies global asymptotic stabilizability of the overall system (respectively, by saturated control). It is obtained by constructing explicitly a control Lyapunov function and provides feedback laws with several degrees of freedom which can be exploited to tackle design constraints. Also, we study how appropriate changes of coordinates allow us to extend its domain of application. Finally, we show how the proposed approach serves as a basic tool to be used, in a recursive design, to deal with more complex systems. In particular the stabilization problem of the so-called feedforward systems is solved this way.
TL;DR: A novel approach for the fault diagnosis of actuators in known deterministic dynamic systems by using an adaptive observer technique under the assumption that the system state observer can be designed such that the observation error is strictly positive real (SPR).
Abstract: This paper presents a novel approach for the fault diagnosis of actuators in known deterministic dynamic systems by using an adaptive observer technique. Systems without model uncertainty are initially considered, followed by a discussion of a general situation where the system is subjected to either model uncertainty or external disturbance. Under the assumption that the system state observer can be designed such that the observation error is strictly positive real (SPR), an adaptive diagnostic algorithm is developed to diagnose the fault, and a modified version is proposed for the general system to improve robustness. The method is demonstrated through its application to a simulated second-order system.
TL;DR: It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant, and sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion reminiscent of Popov's stability criterion.
Abstract: In this paper, the problem of robust stability of systems subject to parametric uncertainties is considered. Sufficient conditions for the existence of parameter-dependent Lyapunov functions are given in terms of a criterion which is reminiscent of, but less conservative than, Popov's stability criterion. An equivalent frequency-domain criterion is demonstrated. The relative sharpness of the proposed test and existing stability criteria is then discussed. The use of parameter-dependent Lyapunov functions for robust controller synthesis is then considered. It is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant. A possible synthesis procedure and a numerical example are then discussed.
TL;DR: This note shows that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement, and exploits the inherent passivity of the system.
Abstract: It is well known that the linear feedback of the quaternion of the attitude error and the angular velocity globally stabilizes the attitude of a rigid body. In this note, we show that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion, thus removing the need for direct angular velocity measurement. In contrast to other approaches, this design exploits the inherent passivity of the system; a model-based observer reconstructing the velocity is not needed. An application of the proposed scheme is illustrated for the robot control problem. Simulation results are included to illustrate the theoretical results.
TL;DR: The authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold.
Abstract: Estimating the three-dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although "visual motion estimation" is an old problem (the first formulations date back to the beginning of the century), only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions. In this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold. Such a formulation has structural advantages over previous recursive schemes, since the estimation of motion is decoupled from the estimation of the structure of the object being viewed, and therefore it is possible to handle occlusions in a principled way.
TL;DR: A global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results and gives conditions for continuous differentiability of the Lyapunov function and the resulting control law.
Abstract: We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results. Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems. This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation.
TL;DR: A modification of the Smith predictor for controlling higher-order processes with integral action and long dead-time is proposed, and high performance can be obtained both for the setpoint response and for the load disturbance rejection.
Abstract: A modification of the Smith predictor for controlling higher-order processes with integral action and long dead-time is proposed. The controller has a quite simple structure which is obtained based on the model consisting of an ideal integrator and dead-time and which includes only three tuning parameters: the dead-time, velocity gain of the model, and the desired time constant of the first-order closed-loop setpoint response. By adjusting these three parameters, high performance can be obtained both for the setpoint response and for the load disturbance rejection.
TL;DR: A shortest path synthesis is determined by providing, at each point, an optimal control law to steer the robot to the origin by combining the necessary conditions given by Pontryagin's maximum principle with geometric reasoning.
Abstract: This paper deals with the complete characterization of the shortest paths for a car-like robot. Previous works have shown that the search for a shortest path may be limited to a simple family of trajectories. Our work completes this study by providing a way to select inside this family an optimal path to link any two configurations. We combine the necessary conditions given by Pontryagin's maximum principle with a geometric reasoning. This approach enables us to complete the local information with a global analysis of different wave fronts. We construct a partition of the configuration space in regions where the same kind of path is optimal to reach the origin. In other words, we determine a shortest path synthesis by providing, at each point, an optimal control law to steer the robot to the origin.
TL;DR: The authors use a state feedback restriction policy which prevents some enabled transitions from firing for avoiding deadlock in the system and presents the PN realization of these restriction policies when the closed-loop system can be modeled by a live PN.
Abstract: Multiple products through a flexible manufacturing system (FMS) with limited resources can lead to deadlock. In this paper, the authors study the problem of deadlock avoidance by using the Petri net (PN) model for FMSs and introducing the concept of deadlock structure. The necessary and sufficient conditions to prevent deadlock are characterized. The authors use a state feedback restriction policy which prevents some enabled transitions from firing for avoiding deadlock in the system. In particular, when the number of any key kind of resources is greater than one, this policy is minimally restrictive and allows the maximal use of resources in the system. The authors present the PN realization of these restriction policies when the closed-loop system can be modeled by a live PN. The restriction policies can be easily implemented. An example is provided for illustration.
TL;DR: Model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation on a repeated scalar uncertainty structure and a related necessary and sufficient condition for the exact reducibility of stable uncertain systems are presented.
Abstract: Model reduction methods are presented for systems represented by a linear fractional transformation on a repeated scalar uncertainty structure. These methods involve a complete generalization of balanced realizations, balanced Gramians, and balanced truncation model reduction with guaranteed error bounds, based on solutions to a pair of linear matrix inequalities which generalize Lyapunov equations. The resulting reduction methods immediately apply to uncertainty simplification and state order reduction in the case of uncertain systems but also may be interpreted as state order reduction for multidimensional systems.
TL;DR: The internal model principle has been used to generalize the design for the class of nonlinear systems being considered and new functions for chattering reduction and error convergence inside the boundary layer are proposed which are discontinuous in magnitude but not in sign.
Abstract: To reduce chattering in sliding-mode control, a boundary layer around the switching surface is used, and a continuous control is applied within the boundary. The effects of various control laws within the boundary layer on chattering and error convergence in different systems are studied. New functions for chattering reduction and error convergence inside the boundary layer are proposed which are discontinuous in magnitude but not in sign. The internal model principle has been used to generalize the design for the class of nonlinear systems being considered.
TL;DR: The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns, and by considering the appropriate state space models and error Gramians, the Krein-space estimation theory.
Abstract: We have shown that several interesting problems in H/sup /spl infin//-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns.
TL;DR: A new method for the design of reduced-order observers for descriptor systems with unknown inputs based on the generalized constrained Sylvester equation and sufficient conditions for the existence of the observer are given.
Abstract: A new method for the design of reduced-order observers for descriptor systems with unknown inputs is presented. The approach is based on the generalized constrained Sylvester equation. Sufficient conditions for the existence of the observer are given.
TL;DR: The authors develop a self-contained theory for linear estimation in Krein spaces based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms.
Abstract: The authors develop a self-contained theory for linear estimation in Krein spaces. The derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between Krein space projection and the recursive computation of the stationary points of certain second-order (or quadratic) forms. The authors use the innovations process to obtain a general recursive linear estimation algorithm. When specialized to a state-space structure, the algorithm yields a Krein space generalization of the celebrated Kalman filter with applications in several areas such as H/sup /spl infin//-filtering and control, game problems, risk sensitive control, and adaptive filtering.
TL;DR: The technique is to compute a noncausal "particular solution" based on the desired trajectory over each segment and the movement from one segment to the next, and this "partic solution" consists of a " particular control" and a "Particular state trajectory".
Abstract: Suppose we are to guide a plant with a square transfer matrix through a series of way points. This can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner. Each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof. Our technique is to compute: 1) a noncausal "particular solution" based on the desired trajectory over each segment and the movement from one segment to the next, and this "particular solution" consists of a "particular control" and a "particular state trajectory"; and 2) a regulator to handle modeling errors, disturbances, etc. We concentrate on the "particular solution".
TL;DR: A recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented, and an efficient algorithm is proposed that is similar to that of the commonly used ellipsoidal approximation schemes.
Abstract: In this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered. The system model is linear in the unknown parameters. A recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented, and an efficient algorithm is proposed. Its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes. Numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm.