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Automatic Control, IEEE Transactions on

Issue 6 • Date June 2006

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Displaying Results 1 - 25 of 28
  • Symbolic feedback control for navigation

    Page(s): 926 - 937
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (39 KB)  

    We discuss the generation of symbolic feedback control sequences for navigating a sparsely-described and uncertain environment, together with the problem of sensing landmarks sufficiently well to make feedback meaningful. We explore the use of a symbolic control approach for mitigating the lack of a detailed map of the environment and for reducing the complexity associated with finding control laws which steer a control system between distant locations. Under our language-based approach, control inputs take the form of symbolic strings. The decision process that generates those strings is guided by estimates of the vehicle's location within a set of important landmarks and by the statistical effectiveness of each string. This arrangement, and in particular the symbolic nature of the control set, allows us to formulate and solve a class of optimal navigation problems which would be exceedingly difficult to handle if approached at the level of sensors and actuators. Our approach is illustrated in a series of numerical indoor navigation experiments. View full abstract»

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  • IEEE Transactions on Automatic Control publication information

    Page(s): c2
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    Freely Available from IEEE
  • Special Section on Symbolic Methods for Complex Control Systems

    Page(s): 921 - 923
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    Freely Available from IEEE
  • Symbolic Feedback Control for Navigation

    Page(s): 924 - 925
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  • Symbolic Feedback Control for Navigation

    Page(s): 926 - 937
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1504 KB) |  | HTML iconHTML  

    We discuss the generation of symbolic feedback control sequences for navigating a sparsely-described and uncertain environment, together with the problem of sensing landmarks sufficiently well to make feedback meaningful. We explore the use of a symbolic control approach for mitigating the lack of a detailed map of the environment and for reducing the complexity associated with finding control laws which steer a control system between distant locations. Under our language-based approach, control inputs take the form of symbolic strings. The decision process that generates those strings is guided by estimates of the vehicle's location within a set of important landmarks and by the statistical effectiveness of each string. This arrangement, and in particular the symbolic nature of the control set, allows us to formulate and solve a class of optimal navigation problems which would be exceedingly difficult to handle if approached at the level of sensors and actuators. Our approach is illustrated in a series of numerical indoor navigation experiments. View full abstract»

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  • Reachability and control synthesis for piecewise-affine hybrid systems on simplices

    Page(s): 938 - 948
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (528 KB) |  | HTML iconHTML  

    In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise-affine hybrid systems is undecidable. View full abstract»

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  • A grammatical approach to self-organizing robotic systems

    Page(s): 949 - 962
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (944 KB) |  | HTML iconHTML  

    In this paper, we define a class of graph grammars that can be used to model and direct concurrent robotic self-assembly and similar self-organizing processes. We give several detailed examples of the formalism and then focus on the problem of synthesizing a grammar so that it generates a given, prespecified assembly. In particular, to generate an acyclic graph we synthesize a binary grammar (rules involve at most two parts), and for a general graph we synthesize a ternary grammar (rules involve at most three parts). In both cases, we characterize the number of concurrent steps required to achieve the assembly. We also show a general result that implies that no binary grammar can generate a unique stable assembly. We conclude the paper with a discussion of how graph grammars can be used to direct the self-assembly of robotic parts. View full abstract»

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  • Logic-based solution methods for optimal control of hybrid systems

    Page(s): 963 - 976
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    Combinatorial optimization over continuous and integer variables is a useful tool for solving complex optimal control problems of hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear (or quadratic) programming (MIP), which provides the solution after solving a sequence of relaxed linear (or quadratic) programs. MIP formulations require the translation of the discrete/logic part of the hybrid problem into mixed-integer inequalities. Although this operation can be done automatically, most of the original symbolic structure of the problem (e.g., transition functions of finite state machines, logic constraints, symbolic variables, etc.) is lost during the conversion, with a consequent loss of computational performance. In this paper, we attempt to overcome such a difficulty by combining numerical techniques for solving convex programming problems with symbolic techniques for solving constraint satisfaction problems (CSP). The resulting "hybrid" solver proposed here takes advantage of CSP solvers for dealing with satisfiability of logic constraints very efficiently. We propose a suitable model of the hybrid dynamics and a class of optimal control problems that embrace both symbolic and continuous variables/functions, and that are tailored to the use of the new hybrid solver. The superiority in terms of computational performance with respect to commercial MIP solvers is shown on a centralized supply chain management problem with uncertain forecast demand. View full abstract»

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  • Complexity of control on finite automata

    Page(s): 977 - 986
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (408 KB) |  | HTML iconHTML  

    We consider control questions for finite automata viewed as input/output systems. In particular, we find estimates of the minimal number of states of an automaton able to control a given automaton. We prove that, on average, feedback closed-loop control automata do not have fewer states than open-loop control automata when the control objective is to steer the controlled automaton to a target state. We compare our approach to other ways of formalizing of formalizing analogous control objectives. View full abstract»

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  • Feedback encoding for efficient symbolic control of dynamical systems

    Page(s): 987 - 1002
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1024 KB) |  | HTML iconHTML  

    The problem of efficiently steering dynamical systems by generating input plans is considered. Plans are considered which consist of finite-length words constructed on an alphabet of input symbols, which could be, e.g., transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. Efficiency is considered in terms of the computational complexity of plans, and in terms of their description length (in number of bits). We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. The paper also investigates how the efficiency of planning is affected by the choice of inputs, and provides some results as to optimal performance in terms of accuracy and range. View full abstract»

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  • Symbolic control of linear systems based on symbolic subsystems

    Page(s): 1003 - 1013
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (408 KB) |  | HTML iconHTML  

    This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification. View full abstract»

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  • Manufacturing systems: LMI approach

    Page(s): 1014 - 1018
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB) |  | HTML iconHTML  

    This note deals with the control of production systems that produce many part types with limited capacity. First, a simple model is used to show that the inventory control problem can be solved using modern control theory. A state feedback controller that forces the cumulative production of the system to track precisely the cumulative demand is proposed. The tracking problem is formulated as an H control problem and the synthesis of the gains of the state feedback controller that guarantees the H tracking performance of the equivalent dynamics is done by solving a given set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the developed results. The simple model is then extended to include real facts like inspection and processing times. View full abstract»

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  • A method for stability and bifurcation control

    Page(s): 1019 - 1023
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    In this note, we use the Rössler system as an illustrative example to present a method for controlling stability and bifurcations of nonlinear dynamical systems. This approach employs the idea used in computing the transition variety sets of constrained bifurcations to find the stability boundaries of equilibrium points in parameter space. With this method and feedback control, one can obtain appropriate parameter values to delay either static, dynamic, or both bifurcations. A feedback controller is designed to stabilize the Rössler system using all feasible control parameters. A numerical example is given to demonstrate the theoretical results. View full abstract»

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  • Adaptive Jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models

    Page(s): 1024 - 1029
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (384 KB) |  | HTML iconHTML  

    Most research so far on robot trajectory control has assumed that the kinematics of the robot is known exactly. However, when a robot picks up tools of uncertain lengths, orientations, or gripping points, the overall kinematics becomes uncertain and changes according to different tasks. Recently, we derived a new adaptive Jacobian tracking controller for robots with uncertain kinematics and dynamics. This note extends the results to include redundant robots and adaptation to actuator parameters. Experimental results are presented to illustrate the performance of the proposed controller. View full abstract»

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  • Discrete sliding mode control of systems with unmatched uncertainty using multirate output feedback

    Page(s): 1030 - 1035
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    Systems with uncertainties and disturbances are common in practice. In some cases, these disturbances are unmatched. Moreover, in most cases the entire state information is also not available for control purpose. This note proposes a control algorithm for achieving quasi-sliding mode in discrete-time linear time-invariant (LTI) systems with bounded unmatched uncertainties. A multirate output feedback based strategy is used for this purpose. The proposed algorithm is illustrated through an example. View full abstract»

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  • Global positioning of robot manipulators with mixed revolute and prismatic joints

    Page(s): 1035 - 1040
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB) |  | HTML iconHTML  

    The existing controllers for robot manipulators with uncertain gravitational force can globally stabilize only robot manipulators with revolute joints. The main obstacles to the global stabilization of robot manipulators with mixed revolute and prismatic joints are unboundedness of the inertia matrix and the Jacobian of the gravity vector. In this note, a class of globally stable controllers for robot manipulators with mixed revolute and prismatic joints is proposed. The global asymptotic stabilization is achieved by adding a nonlinear proportional and derivative term to the linear proportional-integral-derivative (PID) controller. By using Lyapunov's direct method, the explicit conditions on the controller parameters to ensure global asymptotic stability are obtained. View full abstract»

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  • H control for discrete-time nonlinear stochastic systems

    Page(s): 1041 - 1046
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (296 KB) |  | HTML iconHTML  

    In this note, we develop an H-type theory for a large class of discrete-time nonlinear stochastic systems. In particular, we establish a bounded real lemma (BRL) for this case. We introduce the notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems, and utilize it in the derivation of the BRL. In particular, this BRL establishes a necessary and sufficient condition, in terms of a certain Hamilton Jacobi inequality (HJI), for a discrete-time nonlinear stochastic system to have l2-gain≤γ. The time-invariant case is also considered as a special case. In this case, the BRL guarantees necessary and sufficient conditions for the system to have l2-gain≤γ, by means of a solution to a certain algebraic HJI. An application of this theory to a special class of systems which is a characteristic of numerous physical systems, yields a more tractable HJI which serves as a sufficient condition for the underlying system to possess l2-gain≤γ. Stability in both the mean square sense and in probability, is also discussed. Systems that possess a special structure (norm-bounded) of uncertainties in their model are considered. Application of the BRL to this class of systems yields a linear state-feedback stabilizing controller which achieves l2-gain≤γ, by means of certain linear matrix inequalities (LMIs). View full abstract»

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  • Observer design for unknown input nonlinear descriptor systems via convex optimization

    Page(s): 1047 - 1052
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (352 KB) |  | HTML iconHTML  

    This paper treats the design problem of full-order observers for nonlinear descriptor systems with unknown input (UI). Depending on the available knowledge on the UI dynamics, two cases are considered. First, a UI proportional observer (UIPO) is proposed when the spectral domain of the UI is unknown. Second, a PIO is proposed when the spectral domain of the UI is in the low frequency range. Sufficient conditions for the existence and stability of such observers are given and proved. Based on the linear matrix inequality (LMI) approach, an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective. An example is included to illustrate the method. View full abstract»

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  • Formalizing real-time scheduling using priority-based supervisory control of discrete-event systems

    Page(s): 1053 - 1058
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (280 KB) |  | HTML iconHTML  

    In this note, we formalize real-time task scheduling by applying an extension of supervisory control theory (SCT) of discrete-event systems to real-time models. The set of all possible timed traces of the system is specified by a discrete timed automaton where each transition is associated with an event occurrence or the passage of one unit of time. We introduce priorities to SCT, and apply them to the setting of discrete timed automata in order to develop a formal and unified framework for task scheduling on a single CPU. View full abstract»

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  • Analysis of coordination in multi-agent systems through partial difference equations

    Page(s): 1058 - 1063
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (288 KB) |  | HTML iconHTML  

    In this note, we introduce the framework of partial difference equations (PdEs) over graphs for analyzing the behavior of multi-agent systems equipped with decentralized control schemes. Both leaderless and leader-follower models are considered. PdEs mimic partial differential equations (PDEs) on graphs and can be studied by introducing concepts of functional analysis strongly inspired to the corresponding ones arising in PDEs theory. We generalize different models proposed in the literature by introducing errors in the agent dynamics and analyze agent coordination through the joint use of PdEs and automatic control tools. Moreover, for the simplest control schemes, we show that the resulting PdEs enjoy properties that are similar to those of well-known PDEs like the heat equation, thus allowing to exploit physical-based reasoning for conjecturing formation properties. View full abstract»

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  • Stability of linear neutral time-delay systems: exact conditions via matrix pencil solutions

    Page(s): 1063 - 1069
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (304 KB) |  | HTML iconHTML  

    In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems. View full abstract»

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  • On the dead-time compensation from L1 perspectives

    Page(s): 1069 - 1073
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    It is known that both H2 and H optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L1 control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L1 problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor. View full abstract»

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  • Globally stabilizing adaptive control design for nonlinearly-parameterized systems

    Page(s): 1073 - 1079
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (320 KB) |  | HTML iconHTML  

    In this note, a new adaptive control design is proposed for nonlinear systems that are possibly nonaffine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate; it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or nonaffine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability and estimation convergence, the proposed adaptive control has the unique feature that it does not contains any robust control part which typically overpowers unknown dynamics, may be conservative, and also interferes with parameter estimation. View full abstract»

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  • Discrete-Time Markov Chains

    Page(s): 1080 - 1081
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    Freely Available from IEEE
  • Explore IEL IEEE's most comprehensive resource [advertisement]

    Page(s): 1082
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    Freely Available from IEEE

Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering.  Two types of contributions are regularly considered

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Editor-in-Chief
P. J. Antsaklis
Dept. Electrical Engineering
University of Notre Dame