Showing papers presented at "American Control Conference in 2002"

The scaled unscented transformation

Abstract: This paper describes a generalisation of the unscented transformation (UT) which allows sigma points to be scaled to an arbitrary dimension. The UT is a method for predicting means and covariances in nonlinear systems. A set of samples are deterministically chosen which match the mean and covariance of a (not necessarily Gaussian-distributed) probability distribution. These samples can be scaled by an arbitrary constant. The method guarantees that the mean and covariance second order accuracy in mean and covariance, giving the same performance as a second order truncated filter but without the need to calculate any Jacobians or Hessians. The impacts of scaling issues are illustrated by considering conversions from polar to Cartesian coordinates with large angular uncertainties.

Aircraft trajectory planning with collision avoidance using mixed integer linear programming

Abstract: Describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written for the operations research community. In the paper, an approximate model of aircraft dynamics using only linear constraints is developed, enabling the MILP approach to be applied to aircraft collision avoidance. The formulation can also be extended to include multiple waypoint path-planning, in which each vehicle is required to visit a set of points in an order chosen within the optimization.

Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations

Abstract: The Unscented Transform (UT) approximates the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The UT works by constructing a set of points, referred to as sigma points, which has the same known statistics, e.g., first and second and possibly higher moments, as the given estimate. The given nonlinear transformation Is applied to the set, and the unscented estimate is obtained by computing the statistics of the transformed set of sigma points. For example, the mean and covariance of the transformed set approximates the nonlinear transformation of the original mean and covariance estimate. The computational efficiency of the UT therefore depends on the number of sigma points required to capture the known statistics of the original estimate. In this paper we examine methods for minimizing the number of sigma points for real-time control, estimation, and filtering applications. We demonstrate results in a 3D localization example.

Stability analysis of swarms

Abstract: We specify an "individual-based" continuous time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model.

Using deadbands to reduce communication in networked control systems

Abstract: The most effective way to improve networked control systems (NCSs) performance is to reduce network traffic. By adapting a system to a network configuration, the communication medium is more efficiently used and time-delays are minimized. Adjustable deadbands are explored as a solution to reduce network traffic in NCSs. The stability of deadband control is derived and then verified via simulation. A method to determine the size of the deadbands is presented that relies on a performance metric that takes into account system response as well as network traffic. The effectiveness of deadband control with different controllers is studied as well as the effect of disturbances and plant uncertainty.

Receding horizon control of autonomous aerial vehicles

Abstract: This paper presents a new approach to trajectory optimization for autonomous fixed-wing aerial vehicles performing large-scale maneuvers. The main result is a planner which designs nearly minimum time planar trajectories to a goal, constrained by no-fly zones and the vehicle's maximum speed and turning rate. Mixed-Integer Linear Programming (MILP) is used for the optimization, and is well suited to trajectory optimization because it can incorporate logical constraints, such as no-fly zone avoidance, and continuous constraints, such as aircraft dynamics. MILP is applied over a receding planning horizon to reduce the computational effort of the planner and to incorporate feedback. In this approach, MILP is used to plan short trajectories that extend towards the goal, but do not necessarily reach it. The cost function accounts for decisions beyond the planning horizon by estimating the time to reach the goal from the plan's end point. This time is estimated by searching a graph representation of the environment. This approach is shown to avoid entrapment behind obstacles, to yield near-optimal performance when comparison with the minimum arrival time found using a fixed horizon controller is possible, and to work consistently on large trajectory optimization problems that are intractable for the fixed horizon controller.

Modeling and control for PEM fuel cell stack system

Abstract: A nonlinear fuel cell system dynamic model that is suitable for control study is presented. The transient phenomena captured in the model include the flow characteristics and inertia dynamics of the compressor, the manifold filling dynamics, and consequently, the reactant partial pressures. Characterization of the fuel cell polarization curves based on time varying current, partial oxygen and hydrogen pressures, temperature, membrane hydration allows analysis and simulation of the transient fuel cell power generation. An observer based feedback and feedforward controller that manages the tradeoff between reduction of parasitic losses and fast fuel cell net power response during rapid current (load) demands is designed.

Nonlinear model predictive tracking control for rotorcraft-based unmanned aerial vehicles

Abstract: We investigate the feasibility of a nonlinear model predictive tracking control (NMPTC) for autonomous helicopters. We formulate a NMPTC algorithm for planning paths under input and state constraints and tracking the generated position and heading trajectories, and implement an on-line optimization controller using a gradient-descent method. The proposed NMPTC algorithm demonstrates superior tracking performance over conventional multi-loop proportional-derivative (MLPD) controllers especially when nonlinearity and coupling dominate the vehicle dynamics. Furthermore, NMPTC shows outstanding robustness to parameter uncertainty, and input saturation and state constraints are easily incorporated. When the cost includes a potential function with a possibly moving obstacle or other agents' state information, the NMPTC can solve the trajectory planning and control problem in a single step. This constitutes a promising one-step solution for trajectory generation and regulation for RUAVs, which operate under various uncertainties and constraints arising from the vehicle dynamics and environmental contingencies.

Qualitative analysis of discrete-time switched systems

Abstract: We investigate some qualitative properties for time-controlled switched systems consisting of several linear discrete-time subsystems. First, we study exponential stability of the switched system with commutation property, stable combination and average dwell time. When all subsystem matrices are commutative pairwise and there exists a stable combination of unstable subsystem matrices, we propose a class of stabilizing switching laws where Schur stable subsystems are activated arbitrarily while unstable ones are activated in sequence with their duration time periods satisfying a specified ratio. For more general switched system whose subsystem matrices are not commutative pairwise, we show that the switched system is exponentially stable if the average dwell time is chosen sufficiently large and the total, activation time ratio between Schur stable and unstable subsystems is not smaller than a specified constant. Secondly, we use an average dwell time approach incorporated with a piecewise Lyapunov function to study the /spl Lscr//sub 2/ gain of the switched system.

Regenerative braking system for a hybrid electric vehicle

Abstract: This paper discusses a regenerative braking system (RBS) for a parallel hybrid electric vehicle (PHEV) that performs regenerative energy recovery based on vehicle attributes, thereby providing improved performance, efficiency and reliability at minimal additional cost. A detailed description of the regenerative braking algorithm is presented along with simulation results from a dynamic model of the PHEV exhibiting the regenerative braking performance.

Min-max feedback model predictive control for distributed control with communication

Abstract: This paper concerns a distributed model predictive control (DMPC) strategy in which each controller views the signals from other subsystems as disturbance inputs in its local model. The DMPC controllers exchange predictions on the bounds of their state trajectories and incorporate this information into their local DMPC problems. They also impose their own predicted state bounds as constraints in subsequent DMPC iterations to guarantee their subsystem satisfies the bounds broadcast to the other controllers. Each controller solves a local min-max problem on each iteration to optimize performance with respect to worst-case disturbances. Parameterized state feedback is introduced into the DMPC formulation to obtain less conservative solutions and predictions. The paper presents sufficient conditions for feasibility and stability. The approach is illustrated with an example.

Complexity in UAV cooperative control

Abstract: This paper addresses complexity and coupling issues in cooperative decision and control of distributed autonomous unmanned aerial vehicle (UAV) teams. In particular, the recent results obtained by the inhouse research team are presented. Hierarchical decomposition is implemented where team vehicles are allocated to sub-teams using the set partition theory. Results are presented for single assignment and multiple assignments using the network flow and auction algorithms. Simulation results are presented for wide area search munitions where complexity and coupling are incrementally addressed in the decision system, yielding a radically improved team performance.

The capabilities and art of state-dependent Riccati equation-based design

Abstract: State-dependent Riccati equation (SDRE) techniques are general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. The paper provides an overview of the capabilities of SDRE control and goes into detail concerning the art of carrying out effective SDRE designs for both systems that conform and do not conform to the basic structure and conditions required by the method. The paper is centered around the SDRE nonlinear regulator. The following situations which prevent a straightforward application of the SDRE method to the control problem at hand are addressed: the existence of state-independent terms, the existence of state-dependent terms which do not go to zero as the state vector goes to zero, the existence of nonlinearity in the controls, and the existence of uncontrollable and unstable but bounded state dynamics.

Phase-locked loops: a control centric tutorial

Abstract: Presents a tutorial on phase-locked loops from a control systems perspective. It starts with an introduction of the loop as a feedback control problem, with both the similarities and differences to traditional control problems. Chief among the differences is the necessary inclusion of two nonlinearities in the loop that are not parasitic, but essential to the loop's operation. Analysis methods, both linear and nonlinear are discussed. Then digital loops are discussed, followed by loop components and a cursory look at noise. Finally, the paper ends with a discussion of different applications of PLLs and their relatives.

Optimization of powertrain operating policy for feasibility assessment and calibration: stochastic dynamic programming approach

Abstract: An approach based on stochastic dynamic programming is proposed to develop optimal operating policies for automotive powertrain systems. The goal is to minimize fuel consumption and tailpipe emissions. Unlike in the conventional approach, the minimization is performed not for a predetermined drive cycle, but in a stochastic "average" sense over a class of trajectories from an underlying Markov chain drive cycle generator. The objective of this paper is to introduce the approach and illustrate its applications. with several examples.

MIMO control of an Apache web server: modeling and controller design

Abstract: This paper considers the efficacy of feedback control in improving the performance of computing systems. Computing systems typically have many competing performance goals which are affected by several external variables. A feedback control strategy is desirable because well established techniques exist to handle these performance trade-offs and external disturbances. In order to employ such a strategy, decisions need to be made about the inputs, outputs, sample time, model type, and performance measures. This paper describes this process, which is often nebulous for computing systems, in the context of an Apache web server. A linear multi-input multi-output model of the system is identified experimentally and used to design several feedback controllers. Experimental results are presented showing the problems associated with a pure pole placement design and effectiveness of LQ control based techniques. The paper concludes with a discussion of future work.

Model predictive control of blood glucose in type I diabetics using subcutaneous glucose measurements

Abstract: A constrained model predictive controller is implemented on a simulated type I diabetic patient. A Kalman filter is used to estimate the blood glucose concentration based on a subcutaneous glucose measurement. The model predictive controller returns blood glucose to normoglycemic ranges when subjected to a meal disturbance. The settling time is similar to that of a non-diabetic.

Reconfigurable LPV control design for Boeing 747-100/200 longitudinal axis

Abstract: Presents the design of a reconfigurable linear parameter varying (LPV) controller for the Boeing 747-100/200 longitudinal axis in the up-and-away flight regime. The control objectives are to obtain decoupled flight-path angle and velocity command tracking and achieve good disturbance rejection characteristics during normal operation and in the presence of an elevator fault. The LPV controller is synthesized using a quasi-LPV model of the aircraft longitudinal axis based on the Jacobian linearization approach. The controller schedules on three parameters: flight altitude and velocity and a fault identification signal. During normal flight operations, the LPV controller uses the elevators and thrust for flight maneuvers. The stabilizer is used to trim the aircraft. Two elevator fault scenarios are contemplated-lock and float. The proposed control strategy is to use the stabilizer as the alternative longitudinal control surface. Simulation results with elevator faults present show that the reconfigured controller stabilizes the faulted system at the expense of a factor of a designed one-third reduction in the tracking responsiveness of the longitudinal axis and has good disturbance rejection properties.

Task allocation for wide area search munitions

Abstract: Addresses the problem of task allocation for wide area search munitions. The munitions are required to search for, classify, attack, and perform battle damage assessment on potential targets. It is assumed that target field information is communicated between all elements of the swarm. A network flow optimization model is used to develop a linear program for optimal resource allocation. Periodically re-solving this optimization problem results in coordinated action by the search munitions. The network optimization model can be initialized such that multiple vehicles can be assigned to service a single target. Memory of previous task assignments is included in the task benefit calculations to reduce churning due to frequent reassignments. Simulation results are presented for a swarm of eight vehicles searching an area containing three potential targets. All targets are quickly classified, attacked, and verified as destroyed.

Efficient moving horizon estimation and nonlinear model predictive control

Abstract: State estimation from plant measurements should play an essential role in any advanced process control technology. Unlike the model predictive control (MPC) regulator, however, this area has received little attention. In this paper, we address the computational issues surrounding constrained moving horizon estimation (MHE) by presenting an algorithm for the efficient computation of moving horizon estimates. In our discussion, we present structured solvers for use with MHE, derive formulas for a nonlinear covariance smoothing update, and describe interactions between MHE and nonlinear target calculations. We conclude with relevant examples of MHE operating in a closed loop to remove non-zero mean disturbances, poor initial estimates, and random noise.

Stability of asynchronous dynamical systems with rate constraints and applications

Abstract: A class of asynchronous dynamical systems with rate constraints that is a modification of the class defined by Hassibi et al. (1999) is introduced. A numerical procedure for a quadratic stability analysis, based on a combination of LMI and a genetic algorithm is proposed. Applications to networked control systems with packet dropout and to convergence of asynchronous fixed point iterations are described. The results obtained are put in perspective as well as compared with those obtained earlier in the literature.

Real-time computational methods for SDRE nonlinear control of missiles

Abstract: Computational speed and performance issues arising in the practical implementation of the state dependent Riccati equation (SDRE) technique are discussed. A software package for real-time implementation of the SDRE technique was developed during the present research. The execution of this software at speeds up to 2 kHz sample rates on problems of the size commonly encountered in missile flight control applications is then demonstrated on commercial off-the-shelf processors.

Simultaneous disturbance attenuation and fault detection using proportional integral observers

Abstract: This paper considers the design of a proportional integral observer (PIO) for simultaneous disturbance attenuation and fault detection. Unlike the proportional observer, an integral observer alone suffices to achieve good convergence and filtering properties when sensor noise is present in the system. On the other hand, a proportional integral observer makes it possible to decouple the modeling uncertainties while estimating the states and faults with satisfactory convergence properties. We show that a generalized PIO structure, a proportional integral fading observer, facilitates the design procedure for achieving the above goal.

Analysis and design of multivariable extremum seeking

Abstract: The paper provides a multivariable extremum seeking scheme, the first for systems with general time-varying parameters. We derive a stability test in a simple SISO format and develop a systematic design algorithm based on standard LTI control techniques to satisfy the stability test. We also supply an analytical quantification of the level of design difficulty in terms of the number of parameters and in terms of the shape of the unknown equilibrium map. Moreover, we remove the requirement of slow forcing for plants with strictly proper output dynamics (and consequent slow convergence) present in earlier works.

Concepts, methods and techniques in adaptive control

Abstract: This tutorial paper looks back at almost 50 years of adaptive control trying to establish how much more we need to be able to offer the industrial community an adaptive controller which will be used and referred to with the same ease as existing PID controllers. Since the first commercial adaptive controller, significant progress in the design and analysis of these controllers has been achieved. Various forms of adaptive controllers are now readily available targeting a significant range of industries from process to aerospace. A general overview of adaptive control will allow the reader to place on the map several industrial architectures for such controllers, all with the aim of bridging the gap between academic and industrial views of the topic. Such a presentation of design and analysis tools currently opens a more philosophical question "Has the critical mass in adaptive control been reached?".

Estimation via Markov chain Monte Carlo

Abstract: Markov chain Monte Carlo (MCMC) is a powerful means for generating random samples that can be used in computing statistical estimates, numerical integrals, and marginal and joint probabilities. The approach is especially useful in applications where one is forming an estimate based on a multivariate probability distribution or density function that would be hopeless to obtain analytically. In particular, MCMC provides a means for generating samples from joint distributions based on easier sampling from conditional distributions. Over the last 10 to 15 years, the approach has had a large impact on the theory and practice of statistical modeling. On the other hand, MCMC has had relatively little impact (yet) on estimation problems in control. The paper is a survey of popular implementations of MCMC, focusing especially on the two most popular specific implementations of MCMC: Metropolis-Hastings and Gibbs sampling.

A comparison of run-to-run control algorithms

Abstract: Run-to-run control is the term used for the application of batch process control as practiced in the semiconductor industry. This paper gives a brief introduction to the fundamental parts of a run-to-run control algorithm and surveys several of the popular techniques for the application of this control methodology. In particular, model predictive control is explored as a robust and flexible technique for implementing run-to-run control.

On velocity estimation using position measurements

Abstract: Velocity measurement is often required in control system design of mechanical machines including robot manipulators. However, precise velocity measurement/estimation remains a challenging task, especially for very slow motions. Several methods have been published to estimate velocity from position measurements, typically the output of an incremental optical encoder. In the present work, a simple and efficient method is proposed to estimate velocity from an incremental encoder pulse train. Based on the physical characteristics of incremental encoders, the proposed method allows the user to select the estimation precision and tune the time delay, and yet requires less calculation than other methods. The proposed method is evaluated experimentally using a direct drive robot arm. An external laser dynamic calibrator is used to obtain accurate reference velocity measurements for comparison. Experimental results confirm the advantages of the proposed method.

Applied receding horizon control of the Caltech Ducted Fan

Abstract: This paper details the application of a constrained receding horizon control strategy to an indoor vectored-thrust flight experiment known as the Caltech Ducted Fan. The strategy is used to stabilize the experiment about one operating point, and step response and disturbance rejection are examined with different configurations and in comparison to a gain-scheduled LQR controller. Issues related to non-zero computation times, choice of horizon length and terminal cost are discussed.

Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology

Abstract: Coordinated dynamical swarm behavior occurs when certain types of animals forage for food or try to avoid predators. Analogous behaviors can occur in engineering systems (e.g. in groups of autonomous mobile robots or UAVs). In this paper, we study a model of an M-dimensional (M /spl ges/ 2) asynchronous swarm with a communication topology, where each member only communicate with fixed neighbors, to provide conditions under which collision-free convergence can be achieved with finite-size swarm members that have proximity sensors and neighbor position sensors that only provide delayed position information. Moreover, we give conditions under which an M-dimensional asynchronous mobile swarm following an "edge-leader" can maintain cohesion during movements even in the presence of sensing delays and asynchronism, and analyze the swarm movement flexibility. Such stability analysis is of fundamental importance if one wants to understand the coordination mechanisms for groups of autonomous vehicles or robots where inter-member communication channels are less than perfect and collisions must be avoided.