Showing papers in "IEEE Transactions on Automatic Control in 1993"
TL;DR: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated and suboptimal trajectories are derived for systems that are not in canonical form.
Abstract: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given. >
1,787 citations
TL;DR: Key features of one automated intelligent vehicle/highway system (IVHS) are outlined, it is shown how core driver decisions are improved, and a basic IVHS control system architecture is proposed and a design of some control subsystems is offered.
Abstract: Key features of one automated intelligent vehicle/highway system (IVHS) are outlined, it is shown how core driver decisions are improved, a basic IVHS control system architecture is proposed, and a design of some control subsystems is offered. Some experimental work is summarized. A system that promises a threefold increase in capacity is outlined, and a four-layer hierarchical control architecture that decomposes this problem into more manageable units is proposed. >
1,334 citations
TL;DR: This paper presents a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error, and requires considerably less online computation than existingReceding horizon controllers for nonlinear, constrained systems.
Abstract: We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems. >
1,163 citations
TL;DR: An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed and guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law.
Abstract: An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed. For both stable and unstable linear plants, feasibility of the contraints guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law. The constraints' feasibility can be checked efficiently with a linear program. It is always possible to remove state constraints in the early portion of the infinite horizon to make them feasible. The controller's implementation requires only the solution of finite-dimensional quadratic programs. >
1,046 citations
TL;DR: A nonlinear adaptive state feedback input-output linearizing control is designed for a fifth-order model of an induction motor which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits.
Abstract: A nonlinear adaptive state feedback input-output linearizing control is designed for a fifth-order model of an induction motor which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The control algorithm contains a nonlinear identification scheme which asymptotically tracks the true values of the load torque and rotor resistance which are assumed to be constant but unknown. Once those parameters are identified, the two control goals of regulating rotor speed and rotor flux amplitude are decoupled, so that power efficiency can be improved without affecting speed regulation. Full state measurements are required. >
723 citations
TL;DR: A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm.
Abstract: For pt.I, see ibid., p.17-32 (1993). The problem of designing global output-feedback robust stabilizing controls for a class of single-input single-output minimum-phase uncertain nonlinear systems with known and constant relative degree is addressed. They are assumed to be linear with respect to the input and nonlinear with respect to an unknown constant parameter vector. The nonlinearities depend on the output only. The nonlinearities may be uncertain and are only required to be bounded by known smooth functions. The order of the robust compensator is equal to the relative degree minus one and is static when the relative degree is one. A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm. When the parameter vector enters linearly, the self-tuning regulator does not require the knowledge of parameter bounds and guarantees set point regulation for the same class of systems considered in Part I. >
607 citations
TL;DR: A new metric on linear, time-invariant systems is defined that is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds.
Abstract: A new metric on linear, time-invariant systems is defined. This metric is no greater than the gap metric, and is in fact the smallest metric for which a certain robust stabilization result holds. Unlike other known metrics which induce the graph topology, it has a clear frequency response interpretation. This allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric. >
482 citations
TL;DR: It is shown that the iterated Kalman filter (IKF) update is an application of the Gauss-Newton method for approximating a maximum likelihood estimate.
Abstract: It is shown that the iterated Kalman filter (IKF) update is an application of the Gauss-Newton method for approximating a maximum likelihood estimate. An example is presented in which the iterated Kalman filter update and maximum likelihood estimate show correct convergence behavior as the observation becomes more accurate, whereas the extended Kalman filter update does not. >
462 citations
TL;DR: The basic question of nonlinear H/sup infinity / control theory is to decide, for a given two-port system, when feedback that makes the full system dissipative and internally stable exists.
Abstract: The basic question of nonlinear H/sup infinity / control theory is to decide, for a given two-port system, when feedback that makes the full system dissipative and internally stable exists. This problem can also be viewed as a question about circuits, and, after translation, also has a game-theoretic statement. Several necessary conditions for solutions to exist are presented, and sufficient conditions for a certain construction to lead to a solution are given. >
419 citations
TL;DR: An algorithm is presented for iterative learning of the control input for a linear discrete-time multivariable system and its synthesis and analysis are based on two-dimensional system theory.
Abstract: An algorithm is presented for iterative learning of the control input for a linear discrete-time multivariable system. Necessary and sufficient conditions are stated for convergence of the proposed algorithm. The algorithm synthesis and analysis are based on two-dimensional (2-D) system theory. A numerical example is given. >
363 citations
TL;DR: A class of systems which can be transformed into a global normal form with no zero dynamics is treated, and an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction can be designed.
Abstract: The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback, is considered. In particular, a class of systems which can be transformed into a global normal form with no zero dynamics is treated. Semiglobal stabilization means that for every compact set of initial conditions, an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction can be designed. The system equations are allowed to depend on constant unknown parameters which do not change the vector relative degree of the system, and the controller is robust with respect to these parameters. Global Lipschitz conditions are not required. >
TL;DR: An application of supervisory control theory to a piece of semiconductor manufacturing equipment is presented, which allows the flexible design and reliable update of processing recipes to accommodate frequently changing manufacturing requirements.
Abstract: An application of supervisory control theory to a piece of semiconductor manufacturing equipment is presented. The approach allows the flexible design and reliable update of processing recipes to accommodate frequently changing manufacturing requirements. An input-output interpretation of supervisory control theory is given. This interpretation leads to a generic implementation scheme for manufacturing systems. A synthesis fixpoint algorithm implementation using binary decision diagrams enables the design of supervisors of realistic size. A sample synthesis for an oxide growth recipe is performed on a state space of the order of 10/sup 6/ states. The actual implementation of the logic sequencing control software for the application under investigation is described. >
TL;DR: Algorithms are proposed for the solution of the robotic (eye-in-hand configuration) visual tracking and servoing problem and the computational complexity and the experimental results demonstrate that the proposed algorithms can be implemented in real time.
Abstract: The use of a vision sensor in the feedback loop is addressed within the controlled active vision framework. Algorithms are proposed for the solution of the robotic (eye-in-hand configuration) visual tracking and servoing problem. Visual tracking is stated as a problem of combining control with computer vision. The sum-of-squared differences optical flow is used to compute the vector of discrete displacements. The displacements are fed to an adaptive controller (self-tuning regulator) that creates commands for a robot control system. The procedure is based on the online estimation of the relative distance of the target from the camera, but only partial knowledge of the relative distance is required, obviating the need for offline calibration. Three different adaptive control schemes have been implemented, both in simulation and in experiments. The computational complexity and the experimental results demonstrate that the proposed algorithms can be implemented in real time. >
TL;DR: The introduction of the concept of (strict) A-dependent operators is introduced, which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in Hilbert spaces.
Abstract: This paper addresses control problems for flexible robot arms by using direct strain feedback. The purpose is to make clear why direct strain feedback can damp out vibration of flexible arms satisfactorily. We concentrate on one-link flexible robot arms whose dynamic models can be represented by linear partial differential equations with appropriate boundary conditions which have been well examined in a number of papers. A key contribution of this paper is the introduction of the concept of (strict) A-dependent operators, which allows us to prove rigorously the closed loop stability of direct strain feedback and the existence and uniqueness of nonstandard second order abstract differential equations in Hilbert spaces. Several control experiments are performed, verifying the main theoretical points of this paper, demonstrating satisfactory control results of direct strain feedback, and leading to potential application of this simple control method for flexible robot control. >
TL;DR: A conclusive demonstration for the first time that integral gain control is the best basic strategy for force control of manipulators and the concept of a novel second order low pass filter controller is presented.
Abstract: This paper presents a complete overview of basic strategies that have been proposed for force control of robot manipulators. First, the model of the plant to be controlled is reviewed. Next, the strategies are divided into force-based and position-based categories, according to previously reported implementations. Each of the controller types within these categories is analyzed, and predictions of stability and efficacy are made. Then it is shown that these two categories are actually the same, and this recognition leads to the concept of a novel second order low pass filter controller. Finally, all of the controllers are experimentally tested on the CMU DD Arm II, confirming the theoretical predictions. Among the important results presented is the conclusive demonstration for the first time that integral gain control is the best basic strategy for force control of manipulators. >
TL;DR: Sampled-data systems with continuous-time inputs and outputs, where some state variables evolve in continuous time and others evolve in discrete time, are considered and the L/sub 2/-induced norm of a sampled-data system is smaller than gamma.
Abstract: Sampled-data systems with continuous-time inputs and outputs, where some state variables evolve in continuous time and others evolve in discrete time, are considered. Methods are presented for computing and optimizing the L/sub 2/-induced norm of such systems, considered as operators relating square integral signals. These worst-case analysis and design results are counterparts of the H/sub infinity /-norm analysis and synthesis for purely continuous- or discrete-time systems. The analysis shows that the L/sub 2/-induced norm of a sampled-data system is smaller than gamma if certain discrete-time descriptor systems have no eigenvalue of magnitude one, and if a certain discrete-time linear time-invariant plant depending on gamma has H/sub infinity / norm smaller than gamma . The synthesis shows that the optimal attenuation problem for a four-block continuous-time plant with a digital controller can be solved with a gamma -iteration on a certain discrete-time four-block plant which depends on gamma . >
TL;DR: H/ sub infinity / control and filtering problems for sampled-data systems are studied and explicit formulas for a controller and a filter satisfying the H/sub infinity / performance bound are given.
Abstract: H/sub infinity / control and filtering problems for sampled-data systems are studied. Necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified H/sub infinity / performance bound. When these conditions hold, explicit formulas for a controller and a filter satisfying the H/sub infinity / performance bound are also given. >
TL;DR: Two examples of the discrete control of a continuous variable system are analyzed and each exhibits what may be regarded as the two extremes of complexity of the closed-loop behavior.
Abstract: Two examples of the discrete control of a continuous variable system are analyzed. These examples exhibit what may be regarded as the two extremes of complexity of the closed-loop behavior: one is eventually periodic, the other is chaotic. The examples are derived from sampled deterministic flow models. These are of interest in their own right but have also been used as models for certain aspects of manufacturing systems. In each case, the authors give a precise characterization of the closed-loop behavior. >
TL;DR: Langrangian relaxation is used to decompose each of the scheduling problems into job- or operation-level subproblems which results in algorithms which generate near-optimal schedules efficiently, while giving a lower bound on the optimal cost.
Abstract: The practical solutions for three manufacturing scheduling problems are examined. As each problem is formulated, constraints are added or modified to reflect increasing real world complexity. The first problem considers scheduling single-operation jobs on identical machines. The second problem is concerned with scheduling multiple-operation jobs with simple fork/join precedence constraints on identical machines. The third problem is the job shop problem in which multiple-operation jobs with general precedence constraints are scheduled on multiple machine types Langrangian relaxation is used to decompose each of the scheduling problems into job- or operation-level subproblems. The subproblems are easier to solve than the original problem and have intuitive appeal. This technique results in algorithms which generate near-optimal schedules efficiently, while giving a lower bound on the optimal cost. In resolving the scheduling problem from one time instant to the next, the Lagrange multipliers from the last schedule can be used to initialize the multipliers, further reducing the computation time. >
TL;DR: In this article, the authors apply H/sub infinity-designed controllers to a generic VSTOL (vertical and short takeoff and landing) aircraft model GVAM, and develop a gain scheduling algorithm based on the normalized comprime factor robust stabilization problem formulation.
Abstract: The authors apply H/sub infinity /-designed controllers to a generic VSTOL (vertical and short takeoff and landing) aircraft model GVAM. The design study motivates the use of H/sub infinity / techniques, and addresses some of the implementation issues which arise for multivariable and H/sub infinity /-designed controllers. An approach for gain scheduling H/sub infinity / controllers on the basis of the normalized comprime factor robust stabilization problem formulation used for the H/sub infinity / design is developed. It utilizes the observer structure unique to this particular robustness optimization. A weighting selection procedure, has been developed for the associated loop-shaping technique used to specify performance. Multivariable controllers pose additional problems in the event of actuator saturations, and a desaturation scheme which accounts for this is applied to the GVAM. A comprehensive control law was developed and evaluated using the Royal Aerospace Establishment piloted simulation facility. >
TL;DR: A complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented.
Abstract: Two new simple, complete, analytical, and restriction-free solutions with complete and explicit freedom of the matrix equation AV+BW=VF are proposed. Here (AB) is known and is controllable, and F is in the Jordan form with arbitrary given eigenvalues. Based on the proposed solutions of this matrix equation, a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented. The proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective. >
TL;DR: It is shown that within the VDES framework a useful class of control systems can be compactly modeled, and some of the associated control problems of Ramadge and Wonham can be more efficiently solved.
Abstract: A vector discrete-event system (VDES) is a discrete-event system model in which the system state is represented by a vector with integer components, and state transitions by integer vector addition. The authors investigate such structures from the viewpoint of control theory. The objective is to specialize to VDES the general automation-based control theory of P.J. Ramadge and W.M. Wonham (1987) and W.M. Wonham and P.J. Ramadge (1988). It is shown that within the VDES framework a useful class of control systems can be compactly modeled, and some of the associated control problems of Ramadge and Wonham can be more efficiently solved. >
TL;DR: A variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers.
Abstract: A class of variable structure output feedback controllers for uncertain dynamic systems with bounded uncertainties is proposed. No statistical information about the uncertain elements is assumed. A variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers. >
TL;DR: Dimensional and perturbation analysis are applied to the problem of stick slip encountered during the motion of machines and predicts the onset of stick Slip as a function of plant and controller parameters.
Abstract: Dimensional and perturbation analysis are applied to the problem of stick slip encountered during the motion of machines. The friction model studied is motivated by current tribological results and is appropriate for lubricated metal contacts. The friction model incorporates Coulomb, viscous, and Stribeck friction with frictional memory and rising static friction. Through dimensional analysis an exact model of the nonlinear system can be formed using five parameters rather than ten, greatly facilitating study and explicitly revealing the interaction of parameters. By converting the system of differential equations into a set of integrations, the perturbation technique makes approximate analysis possible where only numerical techniques had been available before. The analysis predicts the onset of stick slip as a function of plant and controller parameters; these results are compared with experimental data. >
TL;DR: Cases of first-order plants, second-order underdamped plants, and plants with multiunit delay are discussed and an optimum time scale such that an index is minimized is derived.
Abstract: Any discrete-time stable transfer function can be expressed by a discrete-time Laguerre series with a chosen time scale. An optimum time scale such that an index is minimized is derived. This index ensures that the coefficients of higher-order Laguerre functions go toward zero quickly. The solution derived requires the knowledge of the impulse response of the discrete plant. Cases of first-order plants, second-order underdamped plants, and plants with multiunit delay are also discussed. >
TL;DR: An explicit expression is given for the worst-case H/sub 2/ norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L/ sub 2/-induced operator norm.
Abstract: The worst-case effect of a disturbance system on the H/sub 2/ norm of the system is analyzed. An explicit expression is given for the worst-case H/sub 2/ norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L/sub 2/-induced operator norm. An upper bound for this measure, which is equal to the worst-case H/sub 2/ norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature. >
TL;DR: It is shown that the sixth-order nonlinear dynamical model of the induction motor consisting of rotor speed, two stator currents, two rotor fluxes and an integrator in the feedback controller can be made equivalent to two third-order decoupled linear systems by nonlinear state feedback through the stator input voltages.
Abstract: Dynamic state feedback is used to achieve feedback linearization of the induction motor. It is shown that the sixth-order nonlinear dynamical model of the induction motor consisting of rotor speed, two stator currents, two rotor fluxes and an integrator in the feedback controller can be made equivalent to two third-order decoupled linear systems by nonlinear state feedback through the stator input voltages. It is further shown that a nonsingular dynamic feedback linearizing transformation exists as long as the (electromagnetic) torque put out by the motor is nonzero. >
TL;DR: A simple algorithm to decrease the number of constraints and a modification to a standard algorithm for solving the linear complementarity problem are proposed in order to reduce the amount of computation required.
Abstract: A generalized predictive controller for systems with constrained input and output signals is presented. The optimum values of the future control signals are obtained by transforming the quadratic optimization problem into a linear complementarity problem. A simple algorithm to decrease the number of constraints and a modification to a standard algorithm for solving the linear complementarity problem are proposed in order to reduce the amount of computation required. >
TL;DR: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented and further insight is gained into the structure of the optimal solution.
Abstract: A comprehensive study of the general l/sub 1/-optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions. >
TL;DR: A robust supervisory control and observation problem of synthesizing a robust supervisor whose behavior is both legal and acceptable is solved andAdaptive supervision in discrete-event systems is discussed.
Abstract: Both robust and adaptive supervisory control in discrete-event systems are discussed. It is assumed that the system G to be controlled is not known exactly. It is only known either that it belongs to a set or that it has certain lower and upper bounds. The task of robust supervision is to synthesize a supervisor that realizes a given desired behavior for all possible G. A necessary and sufficient condition for the existence of such a robust supervisor is derived. Based on this condition, a robust supervisory control and observation problem of synthesizing a robust supervisor whose behavior is both legal and acceptable is solved. Adaptive supervision is discussed. As the system progresses, the information on occurrences of events may help to resolve or reduce uncertainties. >