Showing papers in "IEEE Transactions on Automatic Control in 1990"

Output regulation of nonlinear systems

Abstract: The problem of controlling a fixed nonlinear plant in order to have its output track (or reject) a family of reference (or disturbance) signal produced by some external generator is discussed. It is shown that, under standard assumptions, this problem is solvable if and only if a certain nonlinear partial differential equation is solvable. Once a solution of this equation is available, a feedback law which solves the problem can easily be constructed. The theory developed incorporates previously published results established for linear systems. >

Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

Abstract: The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H/sup infinity / optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H/sup infinity / control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H/sup infinity / control theory-based methods. >

Near-far resistance of multiuser detectors in asynchronous channels

Abstract: We consider an asynchronous code-division multiple-access environment in which the receiver has knowledge of the signature waveforms of all the users. Under the assumption of white Gaussian background noise, we compare detectors by their worst case bit error rate in a low background noise near-far environment where the received energies of the users are unknown to the receiver and are not necessarily similar.

Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control

Abstract: Consideration is given to the control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The relationship between appropriately defined controllability, stabilizability properties, and the solution of the infinite time jump linear quadratic (JLQ) optimal control problems is also examined. Although the solution of the continuous-time Markov JLQ problem with finite or infinite time horizons is known, only sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite time problem appear in the literature. In this paper necessary and sufficient conditions are established. These conditions are based on new definitions of controllability, observability, stabilizability, and detectability that are appropriate for continuous-time Markovian jump linear systems. These definitions play the same role for the JLQ problem as the deterministic properties do for the linear quadratic regulator (LQR) problem. >

Receding horizon control of nonlinear systems

Abstract: The receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems. The method is especially useful for the control of slow nonlinear systems, such as chemical batch processes, where it is possible to solve, sequentially, open-loop fixed-horizon, optimal control problems online. The method has been shown to yield a stable closed-loop system when applied to time-invariant or time-varying linear systems. It is shown that the method also yields a stable closed-loop system when applied to nonlinear systems. >

Analysis of gain scheduled control for nonlinear plants

Abstract: Gain scheduling has proven to be a successful design methodology in many engineering applications. In the absence of a sound theoretical analysis, these designs come with no guarantees of the robustness, performance, or even nominal stability of the overall gain-scheduled design. An analysis is presented for two types of nonlinear gain-scheduled control systems: (1) scheduling on a reference trajectory, and (2) scheduling on the plant output. Conditions which guarantee stability, robustness, and performance properties of the global gain schedule designs are given. These conditions confirm and formalize popular notions regarding gain scheduled designs, such as that the scheduling variable should vary slowly, and capture the plant's nonlinearities. >

Stabilizing a linear system with quantized state feedback

Abstract: The problem of stabilizing an unstable, time-invariant, discrete-time, linear system by means of state feedback when the measurements of the state are quantized is addressed. It is found that there is no control strategy that stabilizes the system in the traditional sense of making all closed-loop trajectories asymptotic to zero. If the system is not excessively unstable, feedback strategies that bring closed-loop trajectories arbitrarily close to zero for a long time can be implemented. It is also found that when the ordinary linear feedback of quantized state measurements is applied, the resulting closed-loop system behaves chaotically. The asymptotic pseudorandom closed-loop system dynamics differ substantially from what would be predicted by a conventional signal-with-noise analysis of the quantization's effects. Probabilistic reformulations of the stability problem in terms of the invariant measure are considered. >

Optimal robustness in the gap metric

Abstract: The application of the gap metric to robust stabilization of feedback systems is considered. In particular, a solution to the problem of robustness optimization in the gap metric is presented. The problem of robust stabilization under simultaneous plant-controller perturbations is addressed, and the least amount of combined plant-controller uncertainty, measured by the gap metric, that can cause instability of a nominally stable feedback system is determined. Included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the T-gap metric. A key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations. This settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well-defined metric. >

Robot control by using only joint position measurements

Abstract: An observer for reconstructing the joint velocities of rigid-joint robots is proposed. The approach consists of exploiting the structural properties of the robot dynamics. The associated error dynamics are shown to be asymptotically stable. The observer furnishes the state estimate directly in the physical coordinates, so that no transformation is needed. The stability of some state feedback controllers having the proposed observer inserted in the feedback loop is proved. The structure of the observer and its convergence are shown. The stability of the whole system is analyzed when the observer is used in connection with a point-to-point controller and a trajectory controller. >

Further facts about input to state stabilization

Abstract: Previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback is allowed Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are briefly discussed >

Synthesis of feedback control logic for a class of controlled Petri nets

Abstract: An efficient solution is developed for a class of forbidden state problems for discrete event systems (DESs). DESs are considered which can be modeled as cyclic controlled marked graphs (CMGs), a special class of controlled Petri nets (CPNs). The distributed representation of the DES state in terms of the CMG marking permits an efficient specification of the forbidden states in terms of individual place markings. More important, it is shown that the graphical representations of the state transition logic in a CMG can be used to synthesize state feedback logic which is maximally permissive while guaranteeing the forbidden states will not occur. The practical application of the theoretical results is illustrated for an example of automated guided vehicle (AGV) coordination in a flexible manufacturing facility. >

Generalized controller canonical form for linear and nonlinear dynamics

Abstract: A generalized controller canonical form for linear and nonlinear dynamics is proposed. It is obtained using the theorem of the primitive element from differential algebra. The derivation of the controller form does not apply to multivariable constant linear systems. With the transformations, all nonlinear dynamics can be exactly linearized by dynamic feedback. The main departure from standard theory is that transformations may depend on input derivatives. Once differential-algebraic tools are introduced, the proofs of the results are easy. >

Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems

Abstract: The paper concerns policies for sequencing material through a flexible manufacturing system to meet desired production goals for each part type. The authors demonstrate by examples that cyclic material flow and certain distributed scheduling policies can lead to instability in the sense that the required buffer levels are unbounded. This can be the case even when the set-up times for changing part types are zero. Sufficient conditions are then derived under which a class of distributed policies is stable. Finally, a general supervisory mechanism is presented which will stabilize any scheduling policy (i.e. maintain bounded buffer sizes at all machines) while satisfying the desired production rates. >

Manufacturing flow control and preventing maintenance: a stochastic control approach

Abstract: A stochastic control model for simultaneously planning production and maintenance in a flexible manufacturing system (FMS) is proposed, and an efficient technique for computing the optimal control policy is developed. The model extends previous formulations by including an age-dependent machine failure rate and by allowing the control to influence some jump rates (namely the preventive maintenance activities). By using an adaptation to the case of piecewise-deterministic systems of the approximation technique initially proposed by H.J. Kushner (1977) in the realm of the optimal control of diffusions, one shows how it is possible to computer the optimal control for a two-machine system. >

Observability of discrete event dynamic systems

Abstract: A finite state automaton is adopted as a model for discrete event dynamic systems (DEDS). Observations are assumed to be a subset of the event alphabet. Observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions. A polynomial test for observability is given. It is shown that an observer may be constructed and implemented in polynomial time and space. A bound on the cardinality of the observer state space is also presented. A notion of resiliency is defined for observers, and a test for resilient observability and a procedure for the construction of a resilient observer are presented. >

Decentralized control and coordination of discrete-event systems with partial observation

Abstract: Decentralized supervision and coordination are studied for partially observed discrete-event systems. The authors' (1988) previous results on decentralized supervision and supervision under partial observation are extended by incorporating both these features in the control structure. In addition, a concept of coordination is introduced, and conditions for the existence of a coordinating supervisor are established. It is concluded that decentralized supervision will be easier to design and implement that centralized supervision; under suitable conditions it will be equivalent with respect to overall closed-loop system behavior. In achieving this equivalence a key role is played by the linguistic property of normality. As shown by an illustrative example, the results have application to such complex systems as manufacturing systems, which the qualitative modeling framework adopted. >

Adaptive observers for single output nonlinear systems

Abstract: An adaptive version of the nonlinear observer obtained by A.J. Krener et al. (1983) is presented. This version involves the cancellation of nonlinear terms by output injection. As an intermediate step, necessary and sufficient conditions are given for transforming a nonlinear system by state-space change of coordinates into the special adaptive observer form that was used by Y. Bastin et al. (1988) to design adaptive observers. >

On the consistency of hierarchical supervision in discrete-event systems

Abstract: Hierarchical structure in the supervisory control of discrete-event systems is formalized in the automaton framework of P.J. Ramadge and W.M. Wonham (SIAM J. Cont. Optimiz., vol.25, no.1, p.206-30, 1987). The setup embodies a low-level real-world model controlled by an operator and a high-level abstract model virtually controlled by a manager. The two levels are connected by command and information channels. Concepts of hierarchical consistency are proposed, relating high-level behavior required by the manager to low-level behavior achievable by the operator. It is shown that consistency can be realized by appropriately refining the information sent up by the operator to the manager. >

Hamiltonian adaptive control of spacecraft

Abstract: A new approach to the accurate attitude tracking control of rigid spacecraft handling large loads of unknown mass properties is proposed. The method, based on the construction of a physically motivated Lyapunov-like function, is inspired by the adaptive robot control algorithm of J.J.E. Slotine and W. Li (Int. J. Robot. Res., vol.6, no.3, 1987), and presents similar advantages over techniques based on inverse dynamics in terms of simplicity, easier approach to robustness issues, and adaptive capabilities. The approach is illustrated in simulations. >

Hybrid dynamical systems theory and the Signal language

Abstract: The logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDS) are studied. The theory is related to discrete event dynamical system theory, but handles numerics as well as symbolics. It is supported by the programming language Signal and a mathematical model of general implicit dynamical systems. The core of the theory is the notion of HDS resolution which is based on a coding of any HDS into a dynamic graph which consists of a skew product of a polynomial dynamical system on the finite field of integers modulo 3 (to describe the transitions of the underlying automation) and directed graphs (to describe how data dependencies dynamically evolve). The resolution algorithms are based on the study of this dynamical system. >

H/sub infinity /-minimum error state estimation of linear stationary processes

Abstract: A state estimator is derived which minimizes the H/sub infinity /-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution. The second approach establishes a duality between the problem of H/sub infinity /-filtering and the problem of unconstrained input H/sub infinity /-optimal regulation. Using this duality, previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding Kalman filter. The two approaches usually lead to different results. They are compared by a simple example which also demonstrates a clear advantage of the H/sub infinity /-estimate over the conventional l/sub 2/-estimate. >

A framework for real-time discrete event control

Abstract: The TTM/RTTL (timed transition model with real-time temporal logic) framework is presented for modeling, specifying, and analyzing real-time discrete-event systems. TTMs are used to represent the process of the plant and its controller. RTTL is the assertion language for specifying plant behavior and verifying that a controller satisfies the specification. The framework adapts features from the program verification literature which are useful for posing problems of interest to the control engineer, such as modular synthesis and design. Examples are used to illustrate the ideas presented. The authors' published analytical results are summarized and referenced. >

Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances

Abstract: The problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered. The only information required about the disturbances is a finite convex polyhedral bound. Discrete- and continuous-time systems are considered. The property of positive D-invariance of a region is introduced, and it is proved that a solution of the problem is achieved by the selection of a polyhedral set S and the computation of a feedback matrix K such that S is positively D-invariant for the closed-loop system. It is shown that if polyhedral sets are considered, the solution involves simple linear programming algorithms. However, the procedure suggested requires a great amount of computational work offline if the state-space dimension is large, because the feedback matrix K is obtained as a solution of a large set of linear inequalities. All of the vertices of S are required. >

Target tracking problems subject to kinematic constraints

Abstract: Filtering problems with kinematic constraints which may arise in target tracking problems are considered. A novel approach which treats kinematic constraints as additional fictitious or pseudomeasurements is proposed. A numerical example is provided to show the technical feasibility of the proposed idea for target tracking problems. This example shows that the proposed method can improve estimation accuracy significantly for velocity and acceleration states in the tracking problem. However, it is noted that the tracking performance may be deteriorated if the constraints do not properly represent the target characteristics and a small R/sub c/ is chosen. >

Modeling and estimation of discrete-time Gaussian reciprocal processes

Abstract: Discrete-time Gaussian reciprocal processes are characterized in terms of a second-order two-point boundary-value nearest-neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics. This second-order model is the analog for reciprocal processes of the standard first-order state-space models for Markov processes. The model is used to obtain a solution to the smoothing problem for reciprocal processes. The resulting smoother obeys second-order equations whose structure is similar to that of the Kalman filter for Gauss-Markov processes. It is shown that the smoothing error is itself a reciprocal process. >

On adaptive inverse dynamics control of rigid robots

Abstract: The authors derive an adaptive inverse dynamics control law for rigid robots that overcomes the most restrictive difficulty of such schemes to date, namely, the requirement that the inverse of the estimated inertia matrix remain bounded. The control scheme still requires the joint accelerations for its implementation. In practice, one would implement this scheme by estimating the acceleration from the measured velocity. Good performance could still be expected without direct acceleration measurement, assuming sufficient encoder resolution and sufficiently fast sampling. Another practical advantage of the authors' scheme is that since the 'nominal' inverse dynamics or inner loop portion of their control law is fixed, it is more amenable to the development of a dedicated interface and can be 'burned' onto a chip to reduce online computation requirements. >

Decentralized stabilization and pole assignment for general proper systems

Abstract: Considered is the problem of finding existence conditions and a controller synthesis procedure, using decentralized control, for assigning the poles of a linear time-invariant proper system described by a state-space model (C, A, B, D), where no assumption is made regarding the structure of D. This problem has direct application to the decentralized stabilization problem, decentralized robust servomechanism problem, etc., and is a nontrivial extension to the standard decentralized problem where it is assumed that the direct feedthrough terms either are absent or have a block-diagonal structure. >

Optimal Hankel model reduction for nonminimal systems

Abstract: A basis-free descriptor system representation is shown to facilitate the computation of all minimum-degree and optimal kth-order all-pass extensions and Hankel-norm approximants. The descriptor representation has the same simple form for both the optimal and suboptimal cases. The method makes Hankel model reduction practical for nonminimal and nearly nonminimal systems by eliminating the ill-conditioned calculation of a minimal balanced realization. A simple, numerically sound method based on singular-value decomposition enables the results to be expressed in state-space form. >

Estimating time-varying parameters by the Kalman filter based algorithm: stability and convergence

Abstract: Convergence and stability properties of the Kalman filter-based parameter estimator are established for linear stochastic time-varying regression models. The main features are: both the variances and sample path averages of the parameter tracking error are shown to be bounded; the regression vector includes both stochastic and deterministic signals, and no assumptions of stationarity or independence are requires; and the unknown parameters are only assumed to have bounded variations in an average sense. >

Asymptotically optimal estimation of MA and ARMA parameters of non-Gaussian processes from high-order moments

Abstract: A description is given of an asymptotically-minimum-variance algorithm for estimating the MA (moving-average) and ARMA (autoregressive moving-average) parameters of non-Gaussian processes from sample high-order moments. The algorithm uses the statistical properties (covariances and cross covariances) of the sample moments explicitly. A simpler alternative algorithm that requires only linear operations is also presented. The latter algorithm is asymptotically-minimum-variance in the class of weighted least-squares algorithms. >