Showing papers presented at "Conference on Decision and Control in 1995"

Control of a nonholonomic mobile robot: backstepping kinematics into dynamics

Abstract: A dynamical extension that makes possible the integration of a kinematic controller and a torque controller for nonholonomic mobile robots is presented. A combined kinematic/torque control law is developed using backstepping and asymptotic stability is guaranteed by Lyapunov theory. Moreover, this control algorithm can be applied to the three basic nonholonomic navigation problems: tracking a reference trajectory, path following and stabilization about a desired posture. A general structure for controlling a mobile robot results that can accommodate different control techniques ranging from a conventional computed-torque controller, when all dynamics are known, to adaptive controllers.

Neuro-dynamic programming: an overview

Abstract: We discuss a relatively new class of dynamic programming methods for control and sequential decision making under uncertainty. These methods have the potential of dealing with problems that for a long time were thought to be intractable due to either a large state space or the lack of an accurate model. The methods discussed combine ideas from the fields of neural networks, artificial intelligence, cognitive science, simulation, and approximation theory. We delineate the major conceptual issues, survey a number of recent developments, describe some computational experience, and address a number of open questions.

Sliding mode observers. Tutorial

Abstract: Discusses the problem of designing observers for state estimation using sliding modes. The theory and design principles are presented for linear and nonlinear systems. For linear systems the observers are developed using a block-observable form which is similar to a lower triangular matrix form. Compared with known approaches such observers have better robustness properties. In the case of nonlinear systems an equivalent control concept makes it possible to develop finite-time observers for a wide class of systems.

Stability theory for hybrid dynamical systems

Abstract: Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system are of great current interest. In the present paper we first formulate a definition of hybrid dynamical system which covers a very large number of classes of hybrid systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the notion of invariant set (e.g., equilibrium) for hybrid dynamical systems and we define several types of (Lyapunov-like) stability concepts for an invariant set. We then establish sufficient conditions for the uniform stability and the uniform asymptotic stability of an invariant set of a hybrid dynamical system. Under some mild additional assumptions, we also establish necessary conditions for some of the above stability types (converse theorems). To demonstrate the applicability of the developed theory, we present two specific examples of hybrid dynamical systems and we conduct a stability analysis of one of these examples (a sampled-data feedback control system with a nonlinear (continuous-time) plant and a linear (discrete-time) controller).

The Pendubot: a mechatronic system for control research and education

Abstract: In this paper we describe the Pendubot, a mechatronic device for use in control engineering education and for research in nonlinear control and robotics. This device is a two-link planar robot with an actuator at the shoulder but no actuator at the elbow. With this system, a number of fundamental concepts in nonlinear dynamics and control theory may be illustrated. The Pendubot complements previous mechatronic systems, such as the Acrobot and the inverted pendulum of Furuta.

NP-hardness of some linear control design problems

Abstract: We show that some basic linear control design problems are NP-hard, implying that, unless P=NP, they cannot be solved by polynomial time algorithms. The problems that we consider include simultaneous stabilization by output feedback, stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix, and decentralized control. These results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is an NP-hard problem.

Stabilization of motor networks

Abstract: In some cases the most important factor limiting the performance of a distributed control system is not the availability of computational power but rather the availablity of time on a shared communication network for communication between the sensors, the control computer and the actuators. In this paper the author develops a mathematical model describing a class of multivariable control problems of this type and presents an algorithm which can be used to investigate the existence of stabilizing control laws in the presence of communication constraints. The author's model assumes that the communication facilities are to be time-shared according to a pattern which is repeated periodically. The designer has the problem of picking the pattern such that effective control laws can be implemented within the constraints it imposes. If the systems being controlled are linear, there is an affine family of possible closed-loop transition matrices associated with each communication pattern. The selection and implementation of a particular control law which is supported by the given pattern then defines the performance. This approach allows us to put the problem of designing the communication pattern in a form that can be investigated using mathematical programming techniques. In particular one can evaluate the advantages and disadvantages associated with allocating more communication resources to some control loops and less to others.

Nonlinear design of active suspensions

Abstract: We propose a new nonlinear backstepping design for active suspension systems which aims to improve the tradeoff between ride quality and suspension travel. We show that the intentional introduction of nonlinearity through the controller into an otherwise linear system can be beneficial in cases where the desired closed-loop response is different in different operating regions.

Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems

Abstract: Recent research has demonstrated that ordinal comparison converges fast despite possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address a fundamental problem of characterizing the convergence of ordinal comparison. To achieve the goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.

Rotating stall and surge control: a survey

Abstract: The paper presents an analysis of the current state of the art in the control of aero- or hydrodynamic instabilities in turbomachines. It describes the flow phenomena associated with rotating stall and surge, discusses methods devised to prevent these instabilities occuring, but concentrates mainly on the active control (stabilization) of the unstable flows. It appears that lately significant progress has been made in this area. It seems to foster to a more mature state, although several problems deserve further consideration. The consequences of this state of the art for several interested parties, researchers, developers, manufacturers, and users, are stipulated.

Nonsmooth control-Lyapunov functions

Abstract: It is shown that the existence of a continuous control-Lyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finite-dimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in set-valued analysis and the theory of differential inclusions with various names such as "upper contingent derivative". This result generalizes to the nonsmooth case the theorem of Artstein (1983) relating closed-loop feedback stabilization to smooth CLF's. It relies on viability theory as well as optimal control techniques. A "nonstrict" version of the results, analogous to the LaSalle invariance principle, is also provided.

Passivity-based controllers for the stabilization of DC-to-DC power converters

Abstract: Average models of PWM regulated DC-to-DC power supplies are shown to be Euler-Lagrange systems. As such, passivity-based dynamical feedback controllers can be derived for the indirect stabilization of the average output voltage. The derived controllers are based on a suitable stabilizing "damping injection" scheme. The approach is applied to regulate DC-to-DC power converters of the "boost" and "buck-boost" types. The effectivity and robustness of the proposed duty ratio synthesis policies are tested, via computer simulations, on a stochastically perturbed model of a switched "boost" converter.

Identifying MIMO Wiener systems using subspace model identification methods

Abstract: In this paper we show that the multivariable output-error state-space model (MOESP) class of sub-space model identification (SMI) schemes can be extended to identify Wiener systems, a series connection of a linear dynamic system followed by a static nonlinearity. In this paper, we restrict to present these extensions for the case the Taylor series expansion of the static nonlinearity contains odd terms. It is shown that the extension allows to identity the linear part of the Wiener systems as if the static nonlinearity is not present. In this way, it is related to cross-correlation analysis techniques.

LPV control design for pitch-axis missile autopilots

Abstract: The missile pitch-axis autopilot is designed using linear parameter-varying (LPV) control theory. The controller guarantees quadratic stability and bounded induced L/sub 2/-norm performance for the missile plant. Our approach is motivated by gain-scheduling methodology and provides a well founded and systematic procedure for high performance missile autopilot design.

The use of observability and controllability gramians or functions for optimal sensor and actuator location in finite-dimensional systems

Abstract: In this paper, we discuss the optimal location of sensors and actuators for both linear and nonlinear dynamical systems, in both the continuous-time and discrete-time case, on the basis of observability and controllability functions. The optimal location of sensors can be viewed as the problem of maximizing the output energy generated by a given state. On the other hand, the optimal location of actuators can be viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, such as the control of distributed parameter systems, arising in mechanical, hydraulic or chemical processes. In this paper, some new results on observability and controllability functions for nonlinear systems are also provided. Furthermore, we propose a general procedure for computing the optimal design parameters, based on both integer programming and a branch and bound method, suitable for large-scale systems. The effectiveness of this approach is demonstrated for a practical example.

Shortest 3-dimensional paths with a prescribed curvature bound

Abstract: We present the solution of the three-dimensional case of a problem regarding the structure of minimum-length paths with a prescribed curvature bound and prescribed initial and terminal positions and directions. In particular, we disprove a conjecture, according to which every minimizer is a concatenation of circles and straight lines. We show that there are many minimizers-the "helicoidal arcs"-that are not of this form. These arcs are smooth and are characterized by the fact that their torsion satisfies a second-order ordinary differential equation. The solution is obtained by applying optimal control theory. An essential feature of the problem is that it requires the use of optimal control on manifolds. The natural state space of the problem is the product of three-dimensional Euclidean space and a two-dimensional sphere. Although the problem is obviously embeddable in 6-dimensional Euclidean space, the maximum principle for the embedded problem yields no information, whereas a careful application of the maximum principle on manifolds yields a very strong result, namely, that every minimizer is either a helicoidal arc or of the form C, S, CS, SC, CSC, CCC, where C, S stand for "circle" and "segment", respectively.

Hybrid control in air traffic management systems

Abstract: In a new collaborative project involving the University of California, Berkeley, NASA Ames Research Center, and Honeywell Systems Research Center, the authors have begun the study of hierarchical, hybrid control systems in the framework of air traffic management systems (ATMS). The need for a new ATMS arises from the overcrowding of large urban airports and the need to more efficiently land and take off larger numbers of aircraft without building new runways. Technological advances that make a more advanced air traffic control system a reality include the availability of relatively inexpensive and fast real time computers (both on board the aircraft and in the control tower) and global positioning systems. The usefulness of these technological advances is currently limited by today's air traffic control system, which involves the use of "freeways" in the Terminal Radar Approach Control (TRACON) region around urban airports. These freeways are set approach patterns to runways which do not allow for the possibility of so-called "free flight" by an aircraft to its destination. Limiting the aircraft trajectories in this manner results in the addition of both planned and unplanned delays to air travel.

Forward-backward stochastic differential equations and their applications in finance

Abstract: In this paper we present some results concerning the solvability of the adapted solutions to a class of forward-backward stochastic differential equations over an arbitrarily prescribed time duration, and several applications of such equations in mathematical finance. In particular, we introduce a direct scheme (called "four step scheme") initiated by Ma-Protter-Yong (1994), which enables one to derive the explicit relations between the forward and backward components of the adapted solutions. Using the extensions of such a scheme in different directions, we then study some problems in finance including a console rate problem, a problem of hedging options for a large investor, and a stochastic Black-Scholes formula.

Algorithms for optimal hybrid control

Abstract: The authors previously (1994) proposed a general, unified framework for hybrid control problems that encompasses several types of hybrid phenomena and several models of hybrid systems An existence result was obtained for optimal controls The value function associated with this problem satisfies a set of "generalized quasi-variational inequalities" (GQVIs) We give a classification of the types of hybrid systems models covered by our framework and algorithms We review our general framework and results Then, we outline three explicit approaches for computing the solutions to the GQVIs that arise in optimal hybrid control The approaches are generalizations to hybrid systems of shooting methods for boundary value problems, impulse control for piecewise-deterministic processes (PDPs), and value and policy iteration for piecewise-continuous dynamical systems In the central case, we make clear the strong connection between impulse control for PDPs and optimal hybrid control This allows us to give exact and approximate ("epsilon-optimal") algorithms for computing the value function associated with such problems and give some theoretical results Also following previous work, we find that we can compute optimal solutions via linear programming (LP) The resulting LP problems are in general large, but sparse In each case, the underlying feedback controls can be subsequently computed Illustrative examples of each algorithm are solved in our framework

Variable time headway for string stability of automated heavy-duty vehicles

Abstract: We present adaptive nonlinear schemes for longitudinal control of automated heavy duty vehicles. An important control objective is string stability, which ensures that errors decrease as they propagate downstream through the platoon. It is well known that string stability requires intervehicle communication if a constant spacing policy is adopted. When vehicles operate autonomously, string stability can be achieved if speed-dependent spacing with constant time headway is used. This, however, results in larger steady-state spacing, which increase the platoon length hence decreasing traffic throughput. In this paper we propose a new spacing policy in which the time headway varies linearly with the velocity error. Our simulation results demonstrate that this modification significantly reduces the transient errors and allows us to use much smaller spacing in the autonomous mode of platoon operation.

Delay-dependent stability of linear systems with delayed state: an LMI approach

Abstract: This paper deals with the problem of asymptotic stability of a class of time-delay systems with constant, but unknown time-delay. Upper bounds on the time-delay that ensure the stability of the considered systems are given using a Razumikhin technique. Furthermore, the approach adopted here allows the computation of the delay bound by transforming the stability problem into an LMI optimization problem.

Backstepping designs for jet engine stall and surge control

Abstract: A new systematic method for nonlinear control design-backstepping-is applied to low-order compression system models. Backstepping achieves global asymptotic stability of both stall and surge in the presence of large uncertainties in the compressor model. Throughout our presentation, we explore the control design implications of the nonlinear equilibrium properties of compressors.

Output tracking for a non-minimum phase dynamic CTOL aircraft model

Abstract: A dynamic model for the longitudinal axis of a conventional takeoff and landing (CTOL) aircraft is presented. Non-minimum phase characteristics in this model result from the fact that the process of generating an upward pitch moment produces a small downward force, causing the aircraft to lose altitude. The model is not full state linearizable and the internal dynamics which remain after input-output linearization using the coordinates of the center of mass as outputs are unstable. The CTOL model is not flat with respect to fixed points on the aircraft body. The nonlinear inversion technique produces stable trajectories for the states of the internal dynamics, but the corresponding feedforward force inputs required to track these trajectories are large. Approximate linearization techniques which ignore the coupling between the pitch moment and the vertical and horizontal aircraft dynamics, may be used to calculate inputs of smaller magnitude.

Steering and independent braking control for tractor-semitrailer vehicles in automated highway systems

Abstract: A steering and independent braking control for a tractor-semitrailer vehicle is proposed to achieve lane following in automated highway systems. Independent braking force of the semitrailer is utilized to stabilize the trailer yaw motion and thus to prevent the potential occurrence of jack-knifing. The control algorithm is designed by the input/output linearization and the adaptive backstepping design methodologies.

LMITOOL: a package for LMI optimization

Abstract: Many problems in systems and control can be formulated as "linear matrix inequality" (LMI) problems. Previously, efficient algorithms have been developed for solving LMIs of reasonable size. Using these programs for solving control problems however requires a reformulation of the problem, which often implies a great deal of tedious algebraic manipulations. In this paper, the authors present a complete package (toolbox) for Matlab (a version of which is available in the free Matlab-like scientific software package Scilab) that allows the user to solve his control problem using LMI methods with very little effort. Applications of LMIs in systems and control, and the use of LMITOOL are illustrated by a number of examples.

Identification of linear parametrically varying systems

Abstract: Addresses the problem of identification of linear parametrically varying systems with one measurable varying parameter. Under the assumption of full state measurements, the authors show that the problem can be reduced to a set of n (dimension of state space) recursive least squares problems. Further, the authors show that these recursions do estimate the parameters of the original model accurately under certain assumptions on the parameter variations. In the case of noisy state measurements the authors set up the problem as a set of n instrument variable recursions. Once again the authors demonstrate strong consistency of estimates. Simulations are presented to illustrate the results.

Maneuvering target tracking using adaptive turn rate models in the interacting multiple model algorithm

Abstract: This paper presents an interacting multiple model algorithm (IMM) utilizing adaptive turn rate models to track a maneuvering target. The turning rate is calculated at each time step from the velocity and acceleration estimates of the center filter as the magnitude of the acceleration divided by the speed of the target. The comparison of the tracking performance of the proposed algorithm is made with that of an IMM algorithm, utilizing a straight line motion model in conjunction with a single turn rate model which uses an estimate of the turn rate and also to that of an IMM algorithm utilizing three constant turn rate models.

An effective approach to smartly allocate computing budget for discrete event simulation

Abstract: Ordinal Optimization concentrates on isolating a subset of good designs with high probability and reduces the required simulation time dramatically for discrete event simulation. To obtain the same probability level, we may smartly allocate our computing budget among different designs, instead of equally simulating all designs. In this paper we present an effective approach to smartly allocate computing budget for DES simulation. While Ordinal Optimization can dramatically reduce computation cost, our approach can further reduce the already-low cost. Numerical testing shows an additional factor of ten speed-up.

New results for Hammerstein system identification

Abstract: A novel approach is presented for the analysis and design of identification algorithms for Hammerstein models, which consist of a static nonlinearity followed by an LTI system. The authors examine two identification problems. In the first problem, the system is excited with white noise and the LTI system is FIR, and they find a simple explicit solution for the optimal parameter estimate and show that for sufficiently large data lengths a standard iterative technique globally converges to this optimal value. In the second problem, the LTI system is given in state-space form and the authors show that standard state-space algorithms can be easily modified to identify Hammerstein models.

Adaptive repetitive control of a compact disc mechanism

Abstract: Radial track following of a compact disc player servo mechanism is severely exposed to periodic disturbances, induced by the eccentric rotation of the disc. The period of this disturbance is not available for measurement and varies slowly in time. Periodic disturbances can be adequately attenuated using the concept of repetitive control, provided the period is known. To deal with time varying periodic disturbances, a repetitive controller is tuned based on a simple though inaccurate physical model of the time varying character of the period. The model is tuned based on an estimate of the period, obtained through recursive identification. Experimental results show that the proposed scheme enables a significant improvement of the tracking accuracy of the radial servo mechanism.