Showing papers in "IEEE Transactions on Automatic Control in 1984"

Analytical redundancy and the design of robust failure detection systems

Abstract: The failure detection and identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology.

Adaptive control of mechanical impedance by coactivation of antagonist muscles

Abstract: This paper examines the postulate that an important function of the activity of antagonist muscle groups is to modulate mechanical impedance. Some biomechanical modeling and analyses are presented leading to a prediction of simultaneous activation of antagonist muscles in the maintenance of upright posture of the forearm and hand. An experimental observation of antagonist coactivation in this situation is presented.

Controllability, observability, and duality in singular systems

Abstract: The concepts of controllability and observability for systems of the form E\dot{x} = Ax + Bu, y = Cx, E singular are considered. A theory is presented which unifies the three main approaches to this topic already existing in the literature. The development includes a generalization of the duality theorem from state-space theory.

Fundamental properties and performance of conventional bearings-only target motion analysis

Abstract: This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform. The process is inherently nonlinear and exhibits unusual observability properties that are geometry-dependent. A maximum likelihood estimate (MLE) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the MLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MIV) and the pseudo-linear estimate (PLE). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the MLE. The limits on performance that can be expected from processing bearing data are detailed. Specifically, for long range-to-baseline geometries, approximate expressions for the Cramer-Rao bound are derived. Extension of the results to the practical filters approximately predicts numerically observed behavior. For less restrictive geometries, bounds are presented. Incorporation of a target speed constraint on the MLE results in a transition to a lower dimensional problem as noise level and range increases. Monte Carlo experimental results are presented and the improvements realized by the MLE techniques are evident.

Linear approximation of transfer function with a pole of fractional power

Abstract: Two methods for the linear approximation of a transfer function with a pole of fractional power are presented. Analog circuit models are developed, and their frequency response curves and step response curves are compared. It was found that the Pade method gives a better approximation than Wang and Hsia's method within the frequency limit as specified.

A connection between state-space and doubly coprime fractional representations

Abstract: Explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped LTI system are given in terms of a stabilizable and detectable state-space realization of the transfer function. These formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations. Several additional implications of this result are briefly discussed, as are some immediate extensions and future research directions.

Spacecraft attitude control and stabilization: Applications of geometric control theory to rigid body models

Abstract: In this paper, we study the attitude control problem for spacecraft with gas jet or momentum exchange actuators, using the recent nonlinear geometric control theory. We give necessary and sufficient conditions for controllability of the system in the case that the gas jet actuators yield one, two, or three independent torques. In the case of momentum exchange devices, controllability is studied with three independent actuators, and controllability is shown to be impossible with fewer devices. The former conditions with gas jet actuators are presented in three equivalent ways, and an equivalence is established with an earlier condition by Baillieul. The local controllability problem is also studied in the case of gas jet actuators yielding two independent torques. Using these results, an algorithm stabilizing the controllable system around an equilibrium state and trajectory is outlined, as proposed by Hermes. In the situations considered, however, the linearized systems are not controllable.

The optimal projection equations for fixed-order dynamic compensation

Abstract: First-order necessary conditions for quadratically optimal, steady-state,fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form. In contrast to the pair of matrix Riccati equations for the full-order LQG case, the optimal steady-state fixed-order dynamic compensator is characterized by four matrix equations (two modified Riccati equations and two modified Lyapunov equations) coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains. The coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced-order controller case.

Optimal control of two interacting service stations

Abstract: Optimal controls described by switching curves in the two-dimensional state space are shown to exist for the optimal control of a Markov network with two service stations and linear cost. The controls govern routing and service priorities. Finite horizon and long run average cost problems are considered and value iteration is a key tool. Nonconvex value functions are shown to exist for slightly more general networks. Nonconvex value functions are also shown to arise for a simple single station control problem in which the instantaneous cost is convex but not monotone. Nevertheless, optimality of threshold policies is established for the single station problem. The proof is based on a novel use of stochastic coupling and policy iteration.

On H ∞ -optimal sensitivity theory for SISO feedback systems

Abstract: This paper deals with the design of feedback controllers which minimize the H^{\infty} -norm of the sensitivity function, suitably weighted. This approach to the theory of feedback design was introduced by Zames [1] and developed by Zames and Francis [2]. In this paper the theory of Sarason [3] is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm. The problem of achieving small sensitivity over a specified frequency band is studied, and the effect of nonminimum phase is elucidated. Finally, a method is introduced for handling plant poles and zeros on the imaginary axis.

Robust stabilizability for a class of transfer functions

Abstract: This paper is concerned with the robust stabilizability for single-input single-output plants. Robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency-dependent uncertainty band function around the transfer function of a nominal model. A necessary and sufficient condition for robust stabilizability is derived based on the well-known Nevanlinna-Pick theory in classical analysis. It is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model, in order for the class to be robustly stabilizable. A procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown.

Optimal control of a queueing system with two heterogeneous servers

Abstract: The problem considered is that of optimally controlling a queueing system which consists of a common buffer or queue served by two servers. The arrivals to the buffer are Poisson and the servers are both exponential, but with different mean service times. It is shown that the optimal policy which minimizes the mean sojourn time of customers in the system is of threshold type. The faster server should be fed a customer from the buffer whenever it becomes available for service, but the slower server should be utilized if and only if the queue length exceeds a readily computed threshold value.

H ∞ -optimal feedback controllers for linear multivariable systems

Abstract: This paper treats the problem of designing, for a linear multivariable plant, a feedback controller which minimizes the H^{\infty} -norm of a weighted sensitivity matrix. There exists a family of optimal improper feedbacks. This family is determined by application of a theory of Ball and Helton. A method for computing optimal feedbacks is described in detail and a numerical example is included. It is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices.

Application of state estimation to target tracking

Abstract: In this paper, we present a survey of problems and solutions in the area of target tracking. The discussion includes design tradeoffs, performance evaluation, and current issues.

Robust redesign of adaptive control

Abstract: Effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed. In the regulation problem global stability properties are no longer guaranteed, but a region of attraction exists for exact adaptive regulation. The dependence of the region of attraction on unmodeled parasitics is examined first. Then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties. A modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking. The size of this set depends on design parameters, the frequency range of parasitics, and the reference input signal characteristics.

Convergence and asymptotic agreement in distributed decision problems

Abstract: We consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements, possibly at different random times, related to the same uncertain random vector. Each agent has the same objective function and prior probability distribution. We assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received, possibly at random times, by a subset of other agents. Conditions for asymptotic convergence of each agent's decison sequence and asymptotic agreement of all agents' decisions are derived.

A transformation approach to stochastic model reduction

Abstract: A new and direct approach to stochastic model reduction is developed. The order reduction algorithm is obtained by establishing an equivalence between canonical correlation analysis and solutions to algebraic Riccati equations. Also the concept of balanced stochastic realization (BSR) plays a fundamental role. Asymptotic stability of the reduced-order realization is established, and spectral domain interpretations for the BSR are given.

The graph metric for unstable plants and robustness estimates for feedback stability

Abstract: In this paper, a "graph metric" is defined that provides a measure of the distance between unstable multivariable plants. The graph metric induces a "graph topology" on unstable plants, which is the weakest possible topology in which feedback stability is robust. Using the graph metric, it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of RHP poles. If the perturbed and unperturbed systems have the same RHP poles, then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations. As an application of these results, the design of stabilizing controllers for unstable singularly perturbed systems is studied. Finally, the relationship of the graph metric to the "gap metric" introduced by Zames and El-Sakkary is studied in detail. In particular, it is shown that the robustness results of Zames and El-Sakkary do not enable one to conclude the causality, of the perturbed system, whereas the present results do.

Invariance of the strict Hurwitz property for polynomials with perturbed coefficients

Abstract: Given a strictly Hurwitz polynomial f(\lambda) = \lambda^{n} + a_{n-1} \lambda^{n-1} + a_{n-2}\lambda^{n-2}+...+ a_{1}\lambda + a_{0} , it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict Hurwitz property. For systems with n \leq 4 , maximal intervals of the a i are given in a recent paper by Guiver and Bose [1]. In this note, a theorem of Kharitonov is exploited to obtain a general result for polynomials of any degree.

Joint probabilistic data association for multitarget tracking with possibly unresolved measurements and maneuvers

Abstract: In a multitarget environment, when tracking crossing targets, a model is needed for the situation where the measurements from two targets are merged into one due to an inherent resolution threshold. A multidimensional model for the merged measurements is proposed and the resulting pdf is presented. This model is applied to augment the Joint Probabilistic Data Association (JPDA) algorithm used for tracking multiple targets in a cluttered environment, so that it can handle, in a more realistic manner, the situation of crossing targets. An extension to maneuvering targets is also presented.

Exact nonlinear control of large angle rotational maneuvers

Abstract: The rigid body attitude control problem with external torques is transformed into an equivalent linear form implementable by three double integrators. The linearizing transformations themselves are formulated in vector algebra, requiring no integrators for implementation. It is thereby shown that optimal command generation for fast slewing maneuvers can be carried out exactly in the transformed system, together with regulator design without gain scheduling for correction of unmodeled disturbances. In particular, a general rest-to-rest maneuver is computed in closed form, and coupled with a previously obtained exact detumbling maneuver so that arbitrary initial conditions can be accommodated. An illustrative simulation is appended.

Convergence properties of the Riccati difference equation in optimal filtering of nonstabilizable systems

Abstract: This paper studies the convergence and properties of the solutions of the Riccati difference equation Special emphasis is given to systems which are not necessarily stabilizable (in the filtering sense), particularly those having uncontrollable roots on the unit circle Besides generalizing and unifying previous work, the results have application to a number of important problems including filtering and control of systems with purely deterministic disturbances such as sinusoids and drift components

Optimal disturbance reduction in linear multivariable systems

Abstract: This paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory. The approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation. The resulting computations are easily implemented using existing methods.

An inclusion principle for dynamic systems

Abstract: The purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems, which is a suitable mathematical framework for comparing systems with different dimensions. The framework offers immediate results in reduced-order modeling and the overlapping decentralized control of complex systems. The presentation, which is limited to linear constant systems, relies on both the matrix algebra (computations) and the geometric elements (structure) to provide a balanced view of the issues involved in the concept of inclusion. The framework is quite broad, and has been used to consider nonlinear and time-varying systems, as well as systems with hereditary and stochastic effects.

A solution method for the static constrained Stackelberg problem via penalty method

Abstract: This note presents a new solution method for the static constrained Stackelberg problem. Through our approach, the Stackelberg problem is completely transformed into a one-level unconstrained problem such that the newly introduced overall augmented objective function is minimized with repect to the leader's and the follower's variables jointly. It can be proved that a sequence of solutions to the transformed problems converges to the solution of the original problem, when the penalty parameters are updated.

Controllability and observability criteria for multivariable linear second-order models

Abstract: Criteria are discussed for the determination of controllability, stabilizability, observability, or detectability of linear second-order multivariable models of, for example, large space structures. An initial modal transformation is not required and the criteria are thus applicable to models with arbitrary damping coefficients. Moreover, the criteria are modal in the sense that some or all of the modes may be tested for controllability, or observability. This aspect has advantages if not all the modes are known or easily computable. The criteria are further illustrated for a number of important special cases in a series of corollaries.

An adaptive control strategy for mechanical manipulators

Abstract: This paper focuses on the study of an adaptive perturbation control which tracks a desired time-based trajectory as close as possible for all times over a wide range of manipulator motion and payloads. The proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component computes the nominal torques from the Newton-Euler equations of motion to compensate all the interaction forces among the various joints. The feedback component consisting of recursive least-square identification and an optimal adaptive self-tuning control algorithm for the linearized system computes the perturbation torques which reduce the position and velocity errors of the manipulator along the nominal trajectory. A computer simulation study was conducted to evaluate the performance of the proposed adaptive control.

Minimax linear observers and regulators for stochastic systems with uncertain second-order statistics

Abstract: The problem of minimax design of linear observers and regulators for linear time-varying multivariable stochastic systems with uncertain models of their second-order statistics is treated in this paper. General classes of allowable covariance matrices and means of the process and observation noises and of the random initial condition are considered. A game formulation of the problem is adopted and it is shown that the optimal filter for the least favorable set of covariances is minimax robust for each of the filtering situations analyzed. Conditions satisfied by the saddle-point solutions are given, and their utility for finding the worst case covariances is illustrated by way of several examples of uncertainty classes of practical interest.

The control of a prosthetic arm by EMG pattern recognition

Abstract: An electromyographic (EMG) signal pattern recognition system is constructed for real-time control of a prosthetic arm through precise identification of motion and speed command. A probabilistic model of the EMG patterns is first formulated in the feature space of integral absolute value (IAV) to describe the relation between a command, represented by motion and speed variables, and location and shape of the corresponding pattern. The model provides the sample probability density function of pattern classes in the decision space of variance and zero crossings based on the relations between IAV, variance, and zero crossings established in this paper. Pattern classification is carried out through a multiclass sequential decision procedure designed with an emphasis on computational simplicity. The upper bound of probability of error and the average number of sample observations are investigated. Speed and motion predictions are used in conjunction with the decision procedure to enhance decision speed and reliability. A decomposition rule is formulated for the direct assignment of speed to each primitive motion involved in a combined motion. A learning procedure is also designed for the decision processor to adapt long-term pattern variation. Experimental results are discussed in the Appendix.