Showing papers presented at "American Control Conference in 2004"

A survey of spacecraft formation flying guidance and control. Part II: control

Abstract: Formation flying is defined as a set of more than one spacecraft whose states are coupled through a common control law. This paper provides a comprehensive survey of spacecraft formation flying control (FFC), which encompasses design techniques and stability results for these coupled-state control laws. We divide the FFC literature into five FFC architectures: (i) multiple-input multiple-output, in which the formation is treated as a single multiple-input, multiple-output plant, (ii) leader/follower, in which individual spacecraft controllers are connected hierarchically, (iii) virtual structure, in which spacecraft are treated as rigid bodies embedded in an overall virtual rigid body, (iv) cyclic, in which individual spacecraft controllers are connected non-hierarchically, and (v) behavioral, in which multiple controllers for achieving different (and possibly competing) objectives are combined. This survey significantly extends an overview of the FFC literature provided by Lawton, which discussed the L/F, virtual structure and behavioral architectures. We also include a brief history of the formation flying literature, and discuss connections between spacecraft FFC and other multi-vehicle control problems in the robotics and automated highway system literatures.

A stochastic control strategy for hybrid electric vehicles

Abstract: The supervisory control strategy of a hybrid vehicle coordinates the operation of vehicle sub-systems to achieve performance targets such as maximizing fuel economy and reducing exhaust emissions. This high-level control problem is commonly referred as the power management problem. In the past, many supervisory control strategies were developed on the basis of a few pre-defined driving cycles, using intuition and heuristics. The resulting control strategy was often inherently cycle-beating and lacked a guaranteed level of optimality. In this study, the power management problem is tackled from a stochastic viewpoint. An infinite-horizon stochastic dynamic optimization problem is formulated. The power demand from the driver is modeled as a random Markov process. The optimal control strategy is then obtained by using stochastic dynamic programming (SDP). The obtained control law is in the form of a stationary full-state feedback and can be directly implemented. Simulation results over standard driving cycles and random driving cycles are presented to demonstrate the effectiveness of the proposed stochastic approach. It was found that the obtained SDP control algorithm outperforms a sub-optimal rule-based control strategy trained from deterministic DP results.

Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one

Abstract: We consider the problem of (asymptotic) stabilization of mechanical systems with underactuation degree one. A state-feedback design is derived applying the interconnection and damping assignment passivity-based control methodology. Its application relies on the possibility of solving a set of partial differential equations that identify the energy functions that can be assigned to the closed-loop. The following results are established: 1) identification - in terms of some algebraic inequalities - of a subclass of these systems for which the partial differential equations are trivially solved; 2) characterization of all systems which are feedback-equivalent to this subclass; and 3) introduction of a suitable parametrization of the assignable energy functions that provides the designer with a handle to address transient performance and robustness issues. An additional feature of our developments is that the open-loop system need not be described by a port-controlled Hamiltonian (or Lagrangian) model, a situation that arises often in applications due to model reductions or preliminary feedbacks that destroy the structure. The new result is applied to obtain an (almost) globally stabilizing controller for the inertia wheel pendulum, a controller for the chariot with pendulum system that can swing-up the pendulum from any position in the upper half plane and stop the chariot at any desired location, and an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling. In all cases we obtain very simple and intuitive solutions that do not rely on, rather unnatural and technique-driven, linearization or decoupling procedures but instead endows the closed-loop system with a Hamiltonian structure with desired potential and kinetic energy functions.

Gaussian process model based predictive control

Abstract: Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimized. This paper illustrates possible application of Gaussian process models within model-based predictive control. The extra information provided within Gaussian process model is used in predictive control, where optimization of control signal takes the variance information into account. The predictive control principle is demonstrated on control of pH process benchmark.

Rank minimization and applications in system theory

Abstract: In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The rank minimization problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NP-hard. We give an overview of the problem, its interpretations, applications, and solution methods. In particular, we focus on how convex optimization can be used to develop heuristic methods for this problem.

Receding horizon path planning with implicit safety guarantees

Abstract: This paper extends a recently developed approach to optimal path planning of autonomous vehicles, based on mixed integer linear programming (MILP), to account for safety. We consider the case of a single vehicle navigating through a cluttered environment which is only known within a certain detection radius around the vehicle. A receding horizon strategy is presented with hard terminal constraints that guarantee feasibility of the MILP problem at all future time steps. The trajectory computed at each iteration is constrained to end in a so called basis state, in which the vehicle can safely remain for an indefinite period of time. The principle is applied to the case of a UAV with limited turn rate and minimum speed requirements, for which safety conditions are derived in the form of loiter circles. The latter need not be known ahead of time and are implicitly computed online. An example scenario is presented that illustrates the necessity of these safety constraints when the knowledge of the environment is limited and/or hard real-time restrictions are given.

Consensus of information under dynamically changing interaction topologies

Abstract: This paper considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. The paper shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs across some time intervals has a spanning tree frequently enough as the system evolves. Simulation results show the effectiveness of our update schemes.

Estimation of vehicle roll and road bank angle

Abstract: This work presents a new method for identifying road bank and vehicle roll separately using a disturbance observer and a vehicle dynamic model. The authors have previously shown that vehicle states and parameters of a vehicle model can be precisely estimated using measurements from Global Positioning System (GPS) and Inertial Navigation System (INS) sensors. Based on these results, a dynamic model, which includes vehicle roll as a state and road bank as a disturbance, is first introduced. A disturbance observer is then implemented from the vehicle model using estimated vehicle states. Experimental results verify that the estimation scheme is giving appropriate estimates of the vehicle roll and road bank angles separately.

A decentralized algorithm for robust constrained model predictive control

Abstract: A decentralized formulation is presented for model predictive control of systems with coupled constraints. The single large planning optimization is divided into small subproblems, each planning only for the states of a particular subsystem. Relevant plan data is exchanged between subsystems to ensure that all decisions are consistent with satisfaction of the coupled constraints. A typical application would be autonomous guidance of a fleet of UAVs, in which the systems are coupled by the need to avoid collisions, but each vehicle plans only its own path. The key property of the algorithm in this paper is that if an initial feasible plan can be found, then all subsequent optimizations are guaranteed to be feasible, and hence the constraints will be satisfied, despite the action of unknown but bounded disturbances. This is demonstrated in simulated examples, also showing the associated benefit in computation time.

Quadratic stabilization of a switched affine system about a nonequilibrium point

Abstract: This work deals with the problem of quadratic stabilization of switched affine systems, where the state of the switched system has to be driven to a point ("switched equilibrium") which is not in the set of subsystems equilibria. Quadratic stability of the switched equilibrium is assessed using a continuous Lyapunov function, having piecewise continuous derivative. A necessary and sufficient condition is given for the case of two subsystems and a sufficient condition is given in the general case. Two switching rules are presented: a state feedback, in which sliding modes may occur, and an hybrid feedback, in which sliding modes can be avoided. Two examples illustrate our results.

Late motor processing in low-impedance robots: impedance control of series-elastic actuators

Abstract: We have been working on several control and actuation improvements applicable to the design of biomimetic robots and assistive (e.g. prosthetic or orthotic) devices. This paper focuses on the implementation of a joint-level impedance controller for series-elastic actuators that eliminates the use of joint angle sensor information, instead using information from co-located commutation sensors on the back of a brushless motor and a compression sensor on the series elasticity. This approach is both more robust than previous systems and less subject to instabilities due to stiction and backlash.

On the stability of the Kuramoto model of coupled nonlinear oscillators

Abstract: We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary interconnection topology with uncertain natural frequencies. Using tools from spectral graph theory and control theory, we prove that for couplings above a critical value all the oscillators synchronize, resulting in convergence of all phase differences to a constant value, both in the case of identical natural frequencies as well as uncertain ones. We also provide a series of bounds for the critical values of the coupling strength.

Model predictive control for starvation prevention in a hybrid fuel cell system

Abstract: When current is drawn from a fuel cell, it is critical that the reacted oxygen is replenished rapidly by the air supply system to avoid stack starvation and damage. We first explain that in a stand-alone fuel cell, there is lack of control authority in avoiding excessive oxygen starvation during high current demand. In the hybrid configuration introduced A small auxiliary power source significantly extends the control authority in avoiding oxygen starvation. To achieve best possible results without violating operational constraints of the system, a well-devised current split strategy is required. We formulate distribution of current demand between the fuel cell and the auxiliary source in a constrained optimization (model predictive control) framework. As a result, the reactant deficit during sudden increases in stack power was reduced from 50% in stand-alone architecture to less than 1% in the hybrid configuration.

Methodological calibration of the cell transmission model

Abstract: A semi-automated method has been developed for calibrating the parameters of a modified version of Daganzo's cell transmission model (CTM). A least-squares data fitting approach was applied to loop detector data to determine free-flow speeds, congestion-wave speeds, and jam densities for specified subsections of a freeway segment. Bottleneck capacities were estimated from measured mainline and on-ramp flows. The calibration method was tested on a 14-mile portion of Interstate 210 Westbound in southern California. The calibrated CTM was able to reproduce observed bottleneck locations and the approximate behavior of traffic congestion, yielding approximately 6%, or less, error in the predicted total travel time.

Adaptive regulation of amplitude limited robot manipulators with uncertain kinematics and dynamics

Abstract: Common assumptions in most of the previous robot controllers are that the robot kinematics and manipulator Jacobian are perfectly known and that the robot actuators are able to generate the necessary level of torque inputs. In this paper, an amplitude-limited torque input controller is developed for revolute robot manipulators with uncertainty in the kinematic and dynamic models. The adaptive controller yields semi-global asymptotic regulation of the task-space set-point error. The advantages of the proposed controller include the ability to actively compensate for unknown parametric effects in the dynamic and kinematic model and the ability to ensure that actuator constraints are not breached by calculating the maximum required torque a priori.

Mixture Kalman filter based highway congestion mode and vehicle density estimator and its application

Abstract: We present our latest results on developing and implementing a traffic congestion mode and vehicle density estimator for a segment of Interstate 210 in Southern California. Using a mixture Kalman filtering (MKF) algorithm on the switching-mode traffic model, the estimator is able to provide estimated vehicle densities at unmeasured locations, as well as the congestion statuses (free-flow or congested), which are not directly observed. The program runs efficiently, thus making it possible to carry out estimation in real time.

Reinforcement learning-based output feedback control of nonlinear systems with input constraints

Abstract: A novel neural network (NN) -based output feedback controller with magnitude constraints is designed to deliver a desired tracking performance for a class of multi-input-multi-output (MIMO) discrete-time strict feedback nonlinear systems. Reinforcement learning in discrete time is proposed for the output feedback controller, which uses three NN: 1) a NN observer to estimate the system states with the input-output data; 2) a critic NN to approximate certain strategic utility function; and 3) an action NN to minimize both the strategic utility function and the unknown dynamics estimation errors. The magnitude constraints are manifested as saturation nonlinearities in the output feedback controller design. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the state estimation errors, the tracking errors and weight estimates is shown.

A tutorial on convex optimization

Abstract: In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it's ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the reader can more readily recognize and formulate engineering problems using modern convex optimization. This tutorial coincides with the publication of the new book on convex optimization, by Boyd and Vandenberghe, who have made available a large amount of free course material and links to freely available code. These can be downloaded and used immediately by the audience both for self-study and to solve real problems.

Geometry of network security

Abstract: The main point of this paper is that network security has a geometric component, in the sense that some architectures promote some aspects of security. Such security issues closely related to the topological architecture of the network graph are multi-path routing to mitigate "eavesdropping" or "packet sniffing", worm propagation and defense, and distributed denial of service (DDoS) attack mitigation. Those geometric aspects relevant to network security are encapsulated in the concept of graph curvature. An architecture that promotes, in some sense, security is the negative curvature of the graph, which is shown to hold in several physical and logical graphs and in the well know "scale free" model.

Distributed Bayesian hypothesis testing in sensor networks

Abstract: We consider the scenario of N distributed noisy sensors observing a single event. The sensors are distributed and can only exchange messages through a network. The sensor network is modelled by means of a graph, which captures the connectivity of different sensor nodes in the network. The task is to arrive at a consensus about the event after exchanging such messages. The focus of this paper is twofold: a) characterize conditions for reaching a consensus; b) derive conditions for when the consensus converges to the centralized MAP estimate. The novelty of the paper lies in applying belief propagation as a message passing strategy to solve a distributed hypothesis testing problem for a pre-specified network connectivity. We show that the message evolution can be re-formulated as the evolution of a linear dynamical system, which is primarily characterized by network connectivity. This leads to a fundamental understanding of as to which network topologies naturally lend themselves to consensus building and conflict avoidance.

Robust control synthesis with general frequency domain specifications: static gain feedback case

Abstract: This paper considers a robust control synthesis problem for uncertain linear systems to meet design specifications given in terms of multiple frequency domain inequalities in (semi)finite ranges. We restrict our attention to static gain feedback controllers. We develop a new multiplier method that allows for reduction of synthesis conditions to linear matrix inequality problems. We study conditions under which the reduction is exact (nonconservative) in the single-objective nominal setting. Although the multiplier method is conservative in the general setting of multi-objective robust control, numerical design examples demonstrate the utility of the method for the state feedback case.

Control of a ground vehicle using quadratic programming based control allocation techniques

Abstract: This paper examines the use of control allocation techniques for the control of multiple inputs to a ground vehicle to track a desired yaw rate trajectory while minimizing vehicle sideslip. The proposed controller uses quadratic programming accompanied by linear quadratic regulator gains designed around a linear vehicle model to arrive at a combination of vehicle commands. Several failure scenarios are examined and the results for two different quadratic programming approaches are presented along with a discussion of the advantages each method has to offer.

A study on decentralized receding horizon control for decoupled systems

Abstract: We consider a set of decoupled dynamical systems and an optimal control problem where cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a connected graph where each system is a node, and cost and constraints of the optimization problem associated to each node are only function of its state and the states of its neighbors. For such scenario, we propose a framework for designing decentralized receding horizon control (RHC) control schemes. In these decentralized schemes, a centralized RHC controller is broken into distinct RHC controllers of smaller sizes. Each RHC controller is associated to a different node and computes the local control inputs based only on the states of the node and of its neighbors. The proposed decentralized control schemes are formulated in a rigorous mathematical framework. Moreover, we highlight the main issues involved in guaranteeing stability and constraint fulfillment for such schemes and the degree of conservativeness that the decentralized approach introduces.

Decentralized cooperative search by networked UAVs in an uncertain environment

Abstract: This paper addresses the problem of cooperative search in a given environment by a team of unmanned aerial vehicles (UAVs). We present a decentralized control model for cooperative search and develop a real-time approach for online cooperation among vehicles, which is based on treating the possible paths of other vehicles as "soft obstacles" to be avoided. Using the approach of "rivaling force" between vehicles to enhance cooperation, each UAV takes into account the possible actions of other UAVs such that the overall information about the environment is increased. The simulation results illustrate the effectiveness of the proposed strategy.

Model predictive dynamic control allocation with actuator dynamics

Abstract: A model predictive, dynamic control allocation algorithm is developed in this paper for the inner loop of a re-entry vehicle guidance and control system. The purpose of the control allocation portion of the guidance and control architecture is to distribute control power among redundant control effectors to meet the desired control objectives under a set of constraints. Most existing algorithms neglect the actuator dynamics or deal with the actuator dynamics separately, thereby assuming a static relationship between actuator outputs (in our case, control surface deflections) and plant inputs (i.e., moments about the three body axis). We propose a dynamic control allocation scheme based on model-based predictive control (MPC) that directly takes into account actuators with noneligible dynamics and hard constraints. Model-based predictive control schemes compute the control inputs by optimizing an open-loop control objective over a future time interval at each control step. In our setup, the model-predictive control allocation problem is posed as a sequential quadratic programming problem with dynamic constraints, which can be cast into a linear complementary problem (LCP) and therefore solved by linear programming approaches in a finite number of iterations. The time-varying affine internal model used in the MPC design enhances the ability of the control loop to deal with unmodeled system nonlinearities. The approach can be easily extended to encompass a variety of linear actuator dynamics without the need to redesign the overall scheme. Results are based on the model of an experimental reusable launch vehicle, and compared with that of existing static control allocation schemes.

Lateral adaptive control for vehicle lane keeping

Abstract: We deal with the vehicle lateral control problem. More precisely, we solve this problem by properly applying the self-tuning regulator proposed in [Marino, R and Tomei, P (1995)] to the concerned vehicle lateral model. The interest of this solution is that only the lateral displacement at a look-ahead distance is used as the measure for the controller. From a practical point of view, this measure can be obtained through a vision system. Also, all the parameters are considered unknown, where it is only assumed that they belong to a known compact set. The controller is also robust to variations on curvature and lateral wind. Simulations illustrate the efficacy of the controller.

On robust stability of linear neutral systems with nonlinear parameter perturbations

Abstract: The robust stability of uncertain linear neutral systems with time-varying discrete and neutral delays is investigated. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Both delay-dependent and delay-derivative-dependent stability criteria are proposed and are formulated in the form of linear matrix inequalities (LMIs). The results in this paper contain some existing results as their special cases. A numerical example is also given to indicate significant improvements over some existing results.

Decentralized control of a large platoon of vehicles using non-identical controllers

Abstract: This paper studies the decentralized control of a platoon of identical vehicles when each control agent is assumed to only have knowledge of the distance between itself and its immediate forward neighbor. In particular, it is desired to solve the decentralized robust servomechanism problem (RSP), so that the vehicles' separation distances are regulated to specified set points, independent of the lead vehicle's velocity and such that the system is string stable. It is shown that for a large class of identical decentralized controllers, namely those decentralized controllers which solve the RSP and which have stable stabilizing compensators, e.g. a 3-term controller, that it is impossible to solve the above problem. This gives motivation to consider nonidentical decentralized controllers for the platoon vehicle problem, and it is shown in this case that it is possible to solve the above problem. A number of examples are included, including examples which have a large number of vehicles in a platoon, i.e. N=2000.