Showing papers in "Lecture Notes in Control and Information Sciences in 1999"

Robust model predictive control: A survey

Abstract: This paper gives an overview of robustness in Model Predictive Control (MPC). After reviewing the basic concepts of MPC, we survey the uncertainty descriptions considered in the MPC literature, and the techniques proposed for robust constraint handling, stability, and performance. The key concept of “closedloop prediction” is discussed at length. The paper concludes with some comments on future research directions.

High-gain observers in nonlinear feedback control

Abstract: The theory of high-gain observers has been developed for about twenty years. This paper is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The paper surveys recent results on the nonlinear separation principle, conditional servo compensators, extended high-gain observers, performance in the presence of measurement noise, sampled-data control, and experimental testbeds.

Information and control: Witsenhausen revisited

Abstract: The role of information in the context of control is a deep issue To get at this, we review Witsenhausen’s notions of information patterns for control problems While staying in that basic framework, we then use ideas from traditional information theory as we re-examine Witsenhausen’s famous “counterexample” In the process, we construct a family of nonlinear “quantizing” control laws that can perform infinitely better than the best linear policies

A nonsmooth hybrid maximum principle

Abstract: We present two versions of the maximum principle for nonsmooth hybrid optimal control problems, the first one of which requires differentiability along the reference trajectory and yields an adjoint equation of the usual kind, while the second one only requires approximability to first order by Lipschitz maps, and yields an adjoint differential inclusion involving a generalized gradient of the approximating Hamiltonian

Stabilization of port-controlled Hamiltonian systems via energy balancing

Abstract: Passivity-based control (PBC) for regulation of mechanical systems is a well established tehcnique that yields robust controllers that have a clear physical interpretation in terms of interconnection of the system with its environment. In particular, the total energy of the closed-loop is the difference between the energy of the system and the energy supplied by the controller. Furthermore, since the Euler-Lagrange (EL) structure is preserved in closed-loop, PBC is robustly stable vis a vis unmodeled dissipative effects and inherits some robust performance measures from its inverse optimality. Unfortunately, these nice properties are lost when PBC is used in other applications, for instance, in electrical and electromechanical systems. Our main objective in this paper is to develop a new PBC theory for port-controlled Hamiltonian (PCH) systems, which result from the network modeling of energy-conserving lumped-parameter physical systems with independent storage elements, and strictly contain the class of EL models. We identify a class of PCH models for which PBC ensures the Hamiltonian structure is preserved, with storage function the energy balance. One final advantage of the method is that it is rather systematic and the controller can be easily derived using symbolic computation

Nonlinear passive observer design for ships with adaptive wave filtering

Abstract: In this paper we have derived a nonlinear passive observer for moored and free-floating ships. By adding low- and high-pass filtered innovation signals in the design, we have additional flexibility in the design. This augmented design is extended to a new observer with adaptive wave filtering. Experiments with a model ship shows that the adaptive observer will significantly improve the performance of the ship positioning system. This results in reduced magnitude of the observer innovation, better filtering properties and reduced control action by the propulsion system.

The problem of chattering: an averaging approach

Abstract: The singularly perturbed relay control systems (SPRCS) are examined. The mathematical apparatus for investigation of the fast periodic oscillations of SPRCS is developed. The theorem about existence of fast periodic solution of SPRCS is proved. The theorem about averaging is given. It is proved that the slow motions in SPRCS with fast periodic solutions are approximately described by equations obtained from the equations for the slow variables of SPRCS by averaging along fast periodic motions. The algorithm of asymptotic representation for the fast periodic solution of SPRCS is suggested. The algorithm for correction of the averaged equation is given. The stability of the fast periodic solution is investigated.

Synchronization through extended Kalman filtering

Abstract: We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an extended Kalman filter that is driven by a noisy drive signal from the transmitter. Extensive computer simulations show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to secure communication is also given.

Design criteria for uncertain models with structured and unstructured uncertainties

Abstract: This paper introduces and solves a weighted game-type cost criterion for estimation and control purposes that allows for a general class of uncertainties in the model or data. Both structured and unstructured uncertainties are allowed, including some special cases that have been used in the literature. The optimal solution is shown to satisfy an orthogonality condition similar to least-squares designs, except that the weighting matrices need to be modified in a certain optimal manner. One particular application in the context of state regulation for uncertain state-space models is considered. It is shown that in this case, the solution leads to a control law with design equations that are similar in nature to LQR designs. The gain matrix, however, as well as the Riccati variable, turn out to be state-dependent in a certain way. Further applications of these game-type formulations to image processing, estimation, and communications are discussed in [1–3].

Sliding mode control of systems with delayed states and controls

Abstract: A sliding mode control (SMC) design method is proposed for a class of point-delayed systems. A linear transformation is applied to convert the delayed system to delay-free system whose spectra embed all the unstable poles of the original system with given stability margin. It is proved that the delayed system is asymptotically stable with SMC based on the delay-free system. The method is applied to internal combustion (IC) engine idle speed control, not for stabilization, but for compensation with the effects of the time delay in the system states.

A separation principle for a class of euler-lagrange systems

Abstract: We have addressed in this chapter, the problem of output feedback trajectory tracking of Euler Lagrange systems. For a subclass of these systems (including manipulators), characterised by certain factorisation, we have provided a separation principle. Our main result establishes that, if a globally exponentially stabilising state feedback controller can be implemented using the state estimates provided by a globally exponentially convergent observer; the overall closed loop system, remains uniformly globally asymptotically stable. Even though our results cannot be directly applied to robot manipulators, for these systems, we have conjectured the weaker property of UGS plus global uniform convergence of part of the state variables. These include the position and velocity tracking errors. The proof of the latter is currently under investigation.

Model-based observers for tire/road contact friction prediction

Abstract: We have presented a method to estimate on-line the changes in road condition. To achieve this goal we have introduced dynamical friction models that, one hand provide a more accurate description of the contact friction, and one the other hand, allow us to characterize road condition variations via a single parameter.

Worst-Case Simulation of Uncertain Systems

Abstract: In this paper we consider the problem of worst-case simulation for a discrete-time system with structured uncertainty The approach is based on the recursive computation of ellipsoids of confidence for the system state, based on semidefinite programming

Invariant tracking and stabilization: problem formulation and examples

Abstract: The problems of invariant tracking and invariant stabilization are considered: Design a state feedback for tracking or stabilization, respectively, such that the closed-loop dynamics is invariant under the action of a given group. Errors are then defined as invariants of the group under consideration. The approach is illustrated on two classical examples: the nonholonomic car and a continuous stirred chemical reactor. In both cases the differential flatness of the models allows for a systematic design of feedback laws for invariant tracking. The feedback synthesis is simplified by using implicit system descriptions

Issues in modelling and control of mass balance systems

Abstract: This paper devoted to mass balance systems is written in a tutorial spirit. The aim is to give a self content presentation of the modelling of engineering systems that are governed by a law of mass conservation and to briefly discuss a fundamental feedback control problem regarding these systems

The role of experimental conditions in model validation for control

Abstract: Within a stochastic noise framework, the validation of a model yields an ellipsoidal parameter uncertainty set, from which a corresponding uncertainty set can be constructed in the space of transfer functions We display the role of the experimental conditions used for validation on the shape of this validated set, and we connect a measure of the size of this set to the stability margin of a controller designed from the nominal model This allows one to check stability robustness for the validated model set and to propose guidelines for validation design

On global stabilization of nonlinear dynamical systems

Abstract: The global stabilization of nonlinear minimum phase systems with partially linear strict nonminimum phase composite dynamics is discussed in this chapter using only the state variables of the linear composite part. The concept of the terminal sliding mode is employed for the control design. The advantage of the approach is that the finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems, hence the peaking phenomenon does not occur. The global stabilization of the nonlinear systems under the developed controller is guaranteed.

Fault detection in flight control systems via innovation sequence of Kalman filter

Abstract: In the paper, an approach based on the ratio of two quadratic forms of which matrices are theoretic and selected covariance matrices of Kalman filter innovation sequence for sensor fault detection, is presented. The optimal arguments of the quadratic forms are found to quickly detect the faults in sensors. The approach does not require a priori information about the faults and statistical characteristics of the system. Although the approach, like other fault detection approaches based on innovation sequence, cannot isolate the faults, it is quite useful to detect the faults considerably affecting the statistical characteristics of the innovation sequence, and will be augmented to isolate sensor faults.

Learning processes and logic-algebraic method in knowledge-based control systems

Abstract: A great variety of definitions and approaches in the field of knowledge-based and learning control systems have been described. This chapter concerns a specific class of knowledge-based systems with a static plant described by a knowledge representation in the form of a set of facts given by an expert (logic knowledge representation). For the static plant described by a function y = r the control problem may consist in finding the decision Z such that = r is the required output value. For the plant described by the knowledge representation presented in this chapter, the control problem consists in finding the proper input p rope r ty which implies the required o u t p u t property. In the case with the logic knowledge representation the facts, input property and output property are logic formulas concerning x, y and some additional variables. For this class of knowledge-based systems the logicalgebraic m e t h o d has been developed [1, 2, 3, 4, 5, 6]. The main idea of the logic-algebraic method consists in replacing the individual reasoning concepts based on inference rules by unified algebraic procedures based on the rules in two-value logic algebra. The results may be considered as a unification and generalisation of the different individual reasoning algorithms for the class of systems determined by the form of the knowledge representation in Sec. 2. The purpose of this chapter is to show how the logic-algebraic method may be used for the determination of learning algorithms in control systems with unknown parameters in the knowledge representation. Sec. 3 presents a formulation and solution of the control problem for the known parameters. The main idea of the learning process consists in a modification of the control decisions based on a current estimation of the unknown parameters. The

Variants of nonlinear normal form observer design

Abstract: The study of the normal form observer design and its variants is confirming the experience that the observer design is far more complicated to solve than the feedback or controller design of nonlinear systems. The presented normal form observer design variants illustrate that a progress in the solution of the nonlinear observer design problem is possible in various directions: via the application of a semi-diffeomorphic state transformation derived from the observability properties in case of the continuous observer; through an extended Taylor linearization and the additional output transformation used by the extended Luenberger observer; and by a subtle utilization of degrees of freedoms of multiple outputs for a subsystem design of the block-triangular observer.

Application of nonlinear observers to fault detection and isolation

Abstract: The fundamental problem of residual generation for linear systems has been reviewed, and the principle behind its solution has been described. Next, a formulation of the the same problem for nonlinear systems which are affine in the control signals and the failure modes was derived. Sufficient conditions for the existence of a solution have been presented. The possibility to use high gain nonlinear observers in the design of a residual generator has been investigated. The theoretical results have been illustrated by simulations on a hydraulic process.

A convex approach to a class of minimum norm problems

Abstract: This paper considers the problem of determining the minimum euclidean distance of a point from a polynomial surface in R n. It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global minimum can be achieved via the solution of a one-parameter family of LMIs. Each LMI problem consists in the minimization of the maximum eigen value of a symmetric matrix. It is also pointed out that for some classes of problems the solution of a single LMI provides the lower bound. The second result concerns the tightness of the bound. It is shown that optimality of the lower bound can be readily checked via the solution of a system of linear equations. In addition, it is pointed out that lower bound tightness is strictly related to some properties concerning real homogeneous forms. Finally, an application example is developed throughout the paper to show the features of the approach.

Sliding mode tracking control of systems with unstable zero dynamics

Abstract: In this paper, a sliding mode tracking control methodology, based on the block control principle, for an arbitrary reference signal of multivariable systems with unstable zero dynamics is developed. The proposed approach does not require an exosystem and is applicable to any relative degree systems. It is shown that the two step design procedure of the sliding mode theory is applicable to provide tracking without an error. Nonlinear systems reducable to a regular form can also be incorporated in this approach. As an illustrative example, tracking controller for EGR/VGT diesel engine was designed which is a 7th order 2-input 2-output nonminimum phase system.