Showing papers in "IEEE Transactions on Automatic Control in 1994"

Lyapunov stability theory of nonsmooth systems

Abstract: This paper develops nonsmooth Lyapunov stability theory and LaSalle's invariance principle for a class of nonsmooth Lipschitz continuous Lyapunov functions and absolutely continuous state trajectories. Computable tests based on Filipov's differential inclusion and Clarke's generalized gradient are derived. The primary use of these results is in analyzing the stability of equilibria of differential equations with discontinuous right-hand side such as in nonsmooth dynamic systems or variable structure control. >

Stability, queue length, and delay of deterministic and stochastic queueing networks

Abstract: We present two types of stability problems: 1) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and 2) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate /spl theta/. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and MER with respect to /spl theta/. We also develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that: 1) the MER of a superposition process is less than or equal to the sum of the MER of each process, 2) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, 3) the MER of a departure process from a stable queue is less than or equal to that of the input process, and 4) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to /spl theta/ under a further assumption of independence. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the first come, first served policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to /spl theta/ is shown to be equivalent to the recently developed notion of effective bandwidth in communication networks. >

A general result on the stabilization of linear systems using bounded controls

Abstract: We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations. >

A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators

Abstract: In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero. >

Full-order observers for linear systems with unknown inputs

Abstract: This note presents a simple method to design a full-order observer for linear systems with unknown inputs. The necessary and sufficient conditions for the existence of the observer are given. >

A common Lyapunov function for stable LTI systems with commuting A-matrices

Abstract: The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x/spl dot/=A/sub i/x, i=1,2,/spl middot//spl middot//spl middot/,N, where the matrices A/sub i/ are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x/spl dot/(t)=A(t)x(t) where A(t) switches between the above constant matrices A/sub i/. >

Robust Kalman filtering for uncertain discrete-time systems

Abstract: This paper is concerned with the problem of a Kalman filter design for uncertain discrete-time systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties. Furthermore, the guaranteed cost can be optimized by appropriately searching a scaling design parameter. >

Optimal guaranteed cost control and filtering for uncertain linear systems

Abstract: The paper presents results on the design of robust state feedback controllers and steady-state robust state estimators for a class of uncertain linear systems with norm bounded uncertainty. The state feedback results extend the linear quadratic regulator to the case in which the underlying system is dependent on uncertain parameters. The state estimation results extend the steady-state Kalman filter to the case in which the underlying system is also uncertain. >

A new Smith predictor for controlling a process with an integrator and long dead-time

Abstract: A new Smith predictor for control of a process with an integrator and long dead-time is proposed in this note. The controller decouples the setpoint response from the load response. This simplifies both design and tuning. Simulation results obtained by controlling a typical process show that the new controller has superior performance compared to previous algorithms. >

Parametric identification of transfer functions in the frequency domain-a survey

Abstract: This paper gives a survey of frequency domain identification methods for rational transfer functions in the Laplace (s) or z-domain. The interrelations between the different approaches are highlighted through a study of the (equivalent) cost functions. The properties of the various estimators are discussed and illustrated by several examples. >

Improving transient response of adaptive control systems using multiple models and switching

Abstract: A well-known problem in adaptive control is the poor transient response which is observed when adaptation is initiated. In this paper we develop a stable strategy for improving the transient response by using multiple models of the plant to be controlled and switching between them. The models are identical except for initial estimates of the unknown plant parameters. The control to be applied is determined at every instant by the model which best approximates the plant. Simulation results are presented to indicate the improvement in performance that can be achieved. >

Adaptive control of plants with unknown dead-zones

Abstract: Model reference adaptive controllers are designed for plants with unknown dead-zones. Several control strategies are investigated in which two sets of adjustable parameters, one belonging to a dead-zone inverse and the other to a linear controller, are either kept fixed or adaptively updated. The developed adaptive control schemes ensure boundedness of all closed-loop signals and reduce the tracking error. >

Integrated probabilistic data association

Abstract: This paper presents an integrated probabilistic data association algorithm which provides recursive formulas for both data association and track quality (probability of track existence), allowing track initiation and track termination to be fully integrated into the association and smoothing algorithm. Integrated probabilistic data association is of similar computational complexity to probabilistic data association and as demonstrated by simulation, achieves comparable performance to the more computationally expensive interactive multiple model probabilistic data association algorithm which also integrates initiation and tracking. >

Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions

Abstract: In this note, linear discrete-time systems affected by both parameter and input uncertainties are considered. The problem of the synthesis of a feedback control, assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. It is shown that the problem has a solution if and only if there exists a certain Lyapunov function which does not belong to a preassigned class of functions (e.g., the quadratic ones), but it is determined by the target set in which ultimate boundedness is desired. One of the advantages of this approach is that we may handle systems with control constraints. No matching assumptions are made. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. The resulting compensator may be implemented as a linear variable-structure control. >

Supervisory control of timed discrete-event systems

Abstract: The Ramadge-Wonham framework for control of discrete event systems is augmented with timing features by use of Ostroff's semantics for timed transition models. It is shown that the RW concept of controllability and the existence of maximally permissive supervisory controls can be suitably generalized. The enhanced setting admits subsystem composition and the concept of forcible event as an event that preempts the tick of a global clock. An example of a simple manufacturing cell illustrates how the new framework can be used to solve synthesis problems which may include logic-based, temporal and quantitative optimality specifications. >

Coordinating locomotion and manipulation of a mobile manipulator

Abstract: A mobile manipulator in this study is a manipulator mounted on a mobile platform. Assuming the end point of the manipulator is guided, e.g., by a human operator to follow an arbitrary trajectory, it is desirable that the mobile platform is able to move as to position the manipulator in certain preferred configurations. Since the motion of the manipulator is unknown a priori, the platform has to use the measured joint position information of the manipulator for its own motion planning. This paper presents a control algorithm for the platform so that the manipulator is always positioned at the preferred configurations measured by its manipulability. Simulation results are presented to illustrate the efficacy of the algorithm. The algorithm is also implemented and verified on a real mobile manipulator system. The use of the resulting algorithm in a number of applications is also discussed. >

A function space approach to sampled data control systems and tracking problems

Abstract: This paper presents a new framework for hybrid sampled data control systems. Instead of considering the state only at sampling instants, this paper introduces a function piece during the sampling period as the state and gives an infinite-dimensional model with such a state space. This gives the advantage that sampled data systems with built-in intersample behavior can be regarded as linear, time-invariant, discrete-time systems. As a result, the approach makes it possible to introduce such time-invariant concepts as transfer functions, poles, and zeros to the sampled data systems even with the presence of the intersample behavior. In particular, tracking problems can be studied in this setting in a simple and unified way, and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions. This leads to the internal model principle for sampled data systems. >

A time-domain approach to model validation

Abstract: In this paper we offer a novel approach to control-oriented model validation problems. The problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input-output data. Our approach directly uses time-domain input-output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems. In special cases, we give analytical solutions to these problems. >

System identification using Kautz models

Abstract: In this paper, the problem of approximating a linear time-invariant stable system by a finite weighted sum of given exponentials is considered. System identification schemes using Laguerre models are extended and generalized to Kautz models, which correspond to representations using several different possible complex exponentials. In particular, linear regression methods to estimate this sort of model from measured data are analyzed. The advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters. The subsequent analysis is based on the result that the corresponding linear regression normal equations have a block Toeplitz structure. Several results on transfer function estimation are extended to discrete Kautz models, for example, asymptotic frequency domain variance expressions. >

Adaptive control of nonlinear systems with a triangular structure

Abstract: In this paper, we introduce two distinct types of nonlinear dynamical systems, /spl Tscr//sub 1/ and /spl Tscr//sub 2/, both of which possess a triangular structure. It is shown that all systems belonging to /spl Tscr//sub 1/ can be made stable and that if they belong to a subclass /spl Tscr//sub 1s/, the stability holds globally. A precise characterization of the general class of nonlinear systems transformable to /spl Tscr//sub 1/ is carried out. The second class, /spl Tscr//sub 2/, corresponds to a set of second-order nonlinear differential equations and is motivated by problems that occur in mechanical systems. It is shown that global tracking can be achieved for all systems in /spl Tscr//sub 2/. A constructive approach is used in all cases to develop the adaptive controller, and both stabilization and tracking are shown to be realizable. Simple examples are given to illustrate the different classes of nonlinear systems as well as the idea behind the approach used to stabilize them. >

Memoryless H/sup /spl infin// controllers for state delayed systems

Abstract: In this note, a memoryless H/sup /spl infin// controller for the state delayed system is presented. The controller is a delay independent stabilizer for the state delayed system, which also reduces the H/sup /spl infin// norm of the closed loop transfer function, from the disturbance to the controlled output, to a prescribed level. The controller can be obtained by solving a modified Riccati equation. >

Harmonic generation in adaptive feedforward cancellation schemes

Abstract: The paper investigates the generation of harmonics in adaptive feedforward cancellation schemes. Specifically, it is shown that an algorithm designed to reject a certain number of frequency components may in fact be capable of reducing higher-order harmonics as well. This effect originates in the time-variation of the adaptive parameters. A consequence is that the adaptive system may perform better than the algorithm with the fixed, ideal parameters. Surprisingly, the response to higher-order harmonics can be calculated precisely, using a Laplace transform analysis. The origin of the numerical procedure is in the equivalence between the adaptive feedforward cancellation scheme and a control scheme based on the internal model principle. The implication of the results on design and implementation issues is discussed. >

Computational complexity of /spl mu/ calculation

Abstract: The structured singular value /spl mu/ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing /spl mu/. This paper considers the complexity of calculating /spl mu/ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the /spl mu/ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating /spl mu/ of general systems with pure real or mixed uncertainty for other than small problems. >

Adaptively controlling nonlinear continuous-time systems using multilayer neural networks

Abstract: Multilayer neural networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable continuous-time system. The control law is defined in terms of the neural network models of system nonlinearities to control the plant to track a reference command. The network parameters are updated online according to a gradient learning rule with dead zone. A local convergence result is provided, which says that if the initial parameter errors are small enough, then the tracking error will converge to a bounded area. Simulations are designed to demonstrate various aspects of theoretical results. >

Multiscale recursive estimation, data fusion, and regularization

Abstract: We describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. In particular multiscale signal representations lead naturally to pyramidal or tree-like data structures in which each level in the tree corresponds to a particular scale of representation. A class of multiscale dynamic models evolving on dyadic trees is introduced. The main focus of this paper is on the description, analysis, and application of an extremely efficient optimal estimation algorithm for this class of models. This algorithm consists of a fine-to-coarse filtering sweep, followed by a coarse-to-fine smoothing step, corresponding to the dyadic tree generalization of Kalman filtering and Rauch-Tung-Striebel smoothing. The Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to-coarse prediction step, and a fusion step. We illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of "fractal regularizations" of ill-posed signal and image processing problems encountered. >

Passivity-based adaptive attitude control of a rigid spacecraft

Abstract: An adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion. The tracking error is described with the Euler parameter vector. Global convergence of the tracking error to zero is shown using passivity theory. This allows for the use of time-varying positive-definite feedback gain matrices, and the results can easily be extended to other passive parameter update laws. >

A Nash game approach to mixed H/sub 2//H/sub /spl infin// control

Abstract: The established theory of nonzero sum games is used to solve a mixed H/sub 2//H/sub /spl infin//, control problem. Our idea is to use the two pay-off functions associated with a two-player Nash game to represent the H/sub 2/ and H/sub /spl infin// criteria separately. We treat the state-feedback problem and we find necessary and sufficient conditions for the existence of a solution. Both the finite and infinite time problems are considered. In the infinite horizon case we present a full stability analysis. The resulting controller is a constant state-feedback law, characterized by the solution to a pair of cross-coupled Riccati equations, which may be solved using a standard numerical integration procedure. We begin our development by considering strategy sets containing linear controllers only. At the end of the paper we broaden the strategy sets to include a class of nonlinear controls. It turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers. >

Solution to the positive real control problem for linear time-invariant systems

Abstract: In this paper we study the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear time-invariant plant such that a given closed-loop transfer function is extended strictly positive real. Necessary and sufficient conditions for the existence of a controller are obtained. State-space formulas for the controller design are given in terms of solutions to algebraic Riccati equations (or inequalities). The order of the constructed controller does not exceed that of the plant. >

Adaptive control in the presence of input constraints

Abstract: This paper deals with the problem of adaptively controlling a linear time-invariant plant in the presence of constraints on the input amplitude. We introduce a new adaptive algorithm which ensures that the plant can be locally stabilized. In addition to the standard assumptions which are required for adaptive control in the ideal case, an upper bound on the plant control parameter is required to be known. The results are evaluated by simulation studies. >

Risk-sensitive control and dynamic games for partially observed discrete-time nonlinear systems

Abstract: Solves a finite-horizon partially observed risk-sensitive stochastic optimal control problem for discrete-time nonlinear systems and obtains small noise and small risk limits. The small noise limit is interpreted as a deterministic partially observed dynamic game, and new insights into the optimal solution of such game problems are obtained. Both the risk-sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states, dynamic programming, and associated separated policies. A certainty equivalence principle is also discussed. The authors' results have implications for the nonlinear robust stabilization problem. The small risk limit is a standard partially observed risk-neutral stochastic optimal control problem. >