Showing papers presented at "American Control Conference in 2005"

A survey of consensus problems in multi-agent coordination

Abstract: As a distributed solution to multi-agent coordination, consensus or agreement problems have been studied extensively in the literature. This paper provides a survey of consensus problems in multi-agent cooperative control with the goal of promoting research in this area. Theoretical results regarding consensus seeking under both time-invariant and dynamically changing information exchange topologies are summarized. Applications of consensus protocols to multiagent coordination are investigated. Future research directions and open problems are also proposed.

A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems

Abstract: We present an iterative linear-quadratic-Gaussian method for locally-optimal feedback control of nonlinear stochastic systems subject to control constraints. Previously, similar methods have been restricted to deterministic unconstrained problems with quadratic costs. The new method constructs an affine feedback control law, obtained by minimizing a novel quadratic approximation to the optimal cost-to-go function. Global convergence is guaranteed through a Levenberg-Marquardt method; convergence in the vicinity of a local minimum is quadratic. Performance is illustrated on a limited-torque inverted pendulum problem, as well as a complex biomechanical control problem involving a stochastic model of the human arm, with 10 state dimensions and 6 muscle actuators. A Matlab implementation of the new algorithm is availabe at www.cogsci.ucsd.edu//spl sim/todorov.

Ultrafast consensus in small-world networks

Abstract: In this paper, we demonstrate a phase transition phenomenon in algebraic connectivity of small-world networks. Algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix and a measure of speed of solving consensus problems in networks. We demonstrate that it is possible to dramatically increase the algebraic connectivity of a regular complex network by 1000 times or more without adding new links or nodes to the network. This implies that a consensus problem can be solved incredibly fast on certain small-world networks giving rise to a network design algorithm for ultra fast information networks. Our study relies on a procedure called "random rewiring" due to Watts & Strogatz (Nature, 1998). Extensive numerical results are provided to support our claims and conjectures. We prove that the mean of the bulk Laplacian spectrum of a complex network remains invariant under random rewiring. The same property only asymptotically holds for scale-free networks. A relationship between increasing the algebraic connectivity of complex networks and robustness to link and node failures is also shown. This is an alternative approach to the use of percolation theory for analysis of network robustness. We also show some connections between our conjectures and certain open problems in the theory of random matrices.

Forest fire monitoring with multiple small UAVs

Abstract: Frequent updates concerning the progress of a forest fire are essential for effective and safe fire fighting. Since a forest fire is typically inaccessible by ground vehicles due to mountainous terrain, small unmanned air vehicles (UAVs) are emerging as a promising means of monitoring large forest fires. We present an effective UAV path planning algorithm utilizing infrared images that are collected on-board in real-time. To demonstrate the effectiveness of our path planning algorithm in realistic scenarios, we simulated the propagation of a forest fire with the EMBYR model. A new cooperative control mission concept is introduced where multiple low-altitude, short-endurance (LASE) UAVs are used for fire monitoring. By employing multiple UAVs, the effectiveness of the mission in terms of information update rate can be improved dramatically.

A new method for stabilization of networked control systems with random delays

Abstract: We consider the stabilization problem for a kind of networked control systems in discrete-time domain with random delays. The sensor-to-controller and controller-to-sensor delays are modeled as two Markov chains, and the resulting closed-loop systems are jump linear systems with two modes. The necessary and sufficient conditions on the existence of the stabilizing controllers are established. It is shown that the state-feedback gains are different with different modes. An iterative linear matrix inequality (LMI) approach is employed to calculate the state-feedback gains.

Multi-agent Kalman consensus with relative uncertainty

Abstract: In this paper, we propose discrete-time and continuous-time consensus update schemes motivated by the discrete-time and continuous-time Kalman filters. With certainty information encoded into each agent, the proposed consensus schemes explicitly account for relative confidence/reliability of information states from each agent in the team. We show mild sufficient conditions under which consensus can be achieved using the proposed consensus schemes in the presence of switching interaction topologies.

A tutorial on sum of squares techniques for systems analysis

Abstract: This tutorial is about new system analysis techniques that were developed in the past few years based on the sum of squares decomposition. We present stability and robust stability analysis tools for different classes of systems: systems described by nonlinear ordinary differential equations or differential algebraic equations, hybrid systems with nonlinear subsystems and/or nonlinear switching surfaces, and time-delay systems described by nonlinear functional differential equations. We also discuss how different analysis questions such as model validation and safety verification can be answered for uncertain nonlinear and hybrid systems.

Stability criteria for linear discrete-time systems with interval-like time-varying delay

Abstract: This paper is concerned with the stability problem for a class of uncertain linear discrete-time systems with time-varying delay. The delay is of an interval-like type, which means that both lower and upper bounds for the time-varying delay are available. The uncertainty under consideration is norm-bounded uncertainty. Based on Lyapunov-Krasovskii functional approach, delay-dependent stability criteria are obtained using a sum inequality which is first introduced and plays an important role in deriving stability conditions. The criteria are formulated in the form of linear matrix inequalities (LMIs). A numerical example is given to show the effectiveness of the proposed criteria.

A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems

Abstract: In this paper, a novel systematic design method, namely homogeneous domination approach, is developed for the global output feedback stabilization of nonlinear systems. The nonlinearities of the systems considered in this paper are neither linearly growing nor Lipschitz in immeasurable states, which make the most of existing methods inapplicable to solve the problem. By utilizing the homogeneous domination approach, a global output feedback stabilizer is explicitly constructed in two steps: i) we first design for the nominal linear system a unique homogeneous output feedback controller whose construction is genuinely nonlinear, rather than linear as used in the literature; ii) then we scale the homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally asymptotically stable. The homogeneous domination approach not only enables us to completely remove the linear growth condition, which has been the common assumption for global output feedback stabilization, but also provides us a new perspective to deal with the output feedback control problem for nonlinear systems.

Mixed-integer programming for control

Abstract: The article describes how mixed-integer programming (MIP) can be employed for feedback control. MIP can be used to find optimal trajectories subject to integer constraints, which can encode discrete decisions or nonconvexity, for example. This optimization can be performed online within model predictive control (MPC) to implement a feedback control law. The article discusses how to model systems using MIP, the implementation as a MPC, and techniques for fast solutions of the optimizations to make them suitable for real-time use.

Satellite attitude control by quaternion-based backstepping

Abstract: In this paper a result on attitude control of a microsatellite by integrator backstepping based on quaternion feedback is presented, and the controller is shown to make the closed loop equilibrium points asymptotic stable in the sense of Lyapunov. This is a part of a study of possible control methods for the spacecraft European Student Earth Orbiter (ESEO), a spacecraft included in the Student Space Exploration and Technology Initiative (SSETI) project initiated by ESA. The spacecraft is actuated by four reaction control thrusters and one reaction wheel, and simulation results based on data from the satellite are presented.

The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty

Abstract: In this paper the concept of maximal admissable set (MAS), introduced by Gilbert et al. (1991) for linear time-invariant systems, is extended to linear systems with polytopic uncertainty under linear state feedback. It is shown that by constructing a tree of state predictions using the vertices of the uncertainty polytope and by imposing state and input constraints on these predictions, a polyhedral robust invariant set can be constructed. The resulting set is proven to be the maximal admissable set. The number of constraints defining the invariant set is shown to be finite if the closed loop system is quadratically stable (i.e. has a quadratic Lyapunov function). An algorithm is also proposed that efficiently computes the polyhedral set without exhaustively exploring the entire prediction tree. This is achieved through the formulation of a more general invariance condition than that proposed in Gilbert et al. (1991) and by the removal of redundant constraints in intermediate steps. The efficiency and correctness of the algorithm is demonstrated by means of a numerical example.

Challenges and opportunities in automotive transmission control

Abstract: Automotive transmission is a key element in the powertrain that connects the power source to the wheels of a vehicle. To improve fuel economy, reduce emission and enhance driving performance, many new technologies have been introduced in the transmission area in recent years. This paper first reviews different types of automotive transmissions and explains their unique control characteristics. We then address the challenges facing automotive transmission control from three aspects: calibration, shift scheduling, and sensing, actuation and electronics. Along the way, research opportunities to further improve system performance are discussed.

Information consensus of asynchronous discrete-time multi-agent systems

Abstract: This paper studies the consensus problem of multi-agent systems in an asynchronous framework. Under certain assumptions, the consensus protocol leads to stable behaviors even if the updating instants and sets of the agents are asynchronously determined. The model of asynchronous multi-agent systems encompasses those synchronous ones with various communication patterns, i.e., issues of directional, delayed, or failed communication can be addressed in the same framework. The asynchronous results in this paper thus shed new light on the synchronous results reported in the literature. In particular, synchronous protocols under dynamically changing interaction topologies can be seen as a special case of the asynchronous protocol where all communication delays are zero.

An integrated approach to bearing fault diagnostics and prognostics

Abstract: This paper presents an integrated fault diagnostic and prognostic approach for bearing health monitoring and condition-based maintenance The proposed scheme consists of three main components including principal component analysis (PCA), hidden Markov model (HMM), and an adaptive stochastic fault prediction model The principal signal features extracted by PCA are utilized by HMM to generate a component health/degradation index, which is the input to an adaptive prognostics component for on-line remaining useful life prediction The effectiveness of the scheme is shown by simulation studies using experimental vibration data obtained from a bearing health monitoring testbed

On the point-to-point and traveling salesperson problems for Dubins' vehicle

Abstract: In this paper we study the length of optimal paths for Dubins' vehicle, i.e., a vehicle constrained to move forward along paths of bounded curvature. First, we obtain an upper bound on the optimal length in the point-to-point problem. Next, we consider the corresponding traveling salesperson problem (TSP). We provide an algorithm with worst-case performance within a constant factor approximation of the optimum. We also establish an asymptotic bound on the worst-case length of the Dubins' TSP.

First order reset elements and the Clegg integrator revisited

Abstract: We revisit a class of reset control systems containing first order reset elements (FORE) and Clegg integrators and propose a new class of models for these systems. The proposed model generalizes the models available in the literature and we illustrate, using the Clegg integrator, that it is more appropriate for describing the behavior of reset systems. Then, we state computable sufficient conditions for L/sub 2/ stability of the new class of models. Our results are based on LMIs and they exploit quadratic and piecewise quadratic Lyapunov functions. Finally, a result on stabilization of linear minimum phase systems with relative degree one using high gain FOREs is stated. We present two examples to illustrate our results. In particular, we show that for some systems a FORE can achieve lower L/sub 2/ gain than the underlying linear controller without resets.

Optimal trajectory generation in ocean flows

Abstract: In this paper it is shown that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater gliders in a dynamic ocean environment. This opens the opportunity for optimal path planning of autonomous underwater vehicles by studying the global flow geometry via dynamical systems methods. Optimal glider paths were computed for a 2-dimensionaI kinematic model of an end-point glider problem. Numerical solutions to the optimal control problem were obtained using Nonlinear Trajectory Generation (NTG) software. The resulting solution is compared to corresponding results on LCS obtained using the Direct Lyapunov Exponent method. The velocity data used for these computations was obtained from measurements taken in August, 2000, by HF-Radar stations located around Monterey Bay, CA, USA.

Dynamic inversion for nonaffine-in-control systems via time-scale separation: part I

Abstract: This paper presents a new method for approximate dynamic inversion for nonaffine-in-control systems via time-scale separation. The control signal is sought as a solution of "fast" dynamics and is shown to asymptotically stabilize the original nonaffine system. Sufficient conditions are formulated, which are consistent with the assumptions of Tikhonov's theorem in singular perturbations theory. Several examples illustrate the theoretical results.

Cooperative hybrid control of robotic sensors for perimeter detection and tracking

Abstract: In this paper, we present a decentralized coordination algorithm that allows a robotic swarm to locate and track a dynamic perimeter. A cooperative communication scheme is used by the team to rapidly detect a perimeter. Collision-free cycling behavior emerges by composing simple reactive control laws. The decentralized framework could potentially allow the algorithm to scale to many robots. Extensive simulation results and experiments verify the validity and scalability of the proposed cooperative control scheme.

Control allocation for yaw stabilization in automotive vehicles using multiparametric nonlinear programming

Abstract: We investigate the use of a nonlinear control allocation scheme for automotive vehicles. Such a scheme is useful in e.g. yaw or roll stabilization of the vehicle. The control allocation allows a modularization of the control task, such that a higher level control system specifies a desired moment to work on the vehicle, while the control allocation distributes this moment among the individual wheels by commanding appropriate wheel slips. The control allocation problem is defined as a nonlinear optimization problem, to which an explicit piecewise linear approximate solution function is computed off-line. Such a solution function can computationally efficiently be implemented in real time with at most a few hundred arithmetic operations per sample. Yaw stabilization of the vehicle yaw dynamics is used as an example of use of the control allocation. Simulations show that the controller stabilizes the vehicle in an extreme manoeuvre where the vehicle yaw dynamics otherwise becomes unstable.

Reducing motion artifact in wearable bio-sensors using MEMS accelerometers for active noise cancellation

Abstract: This paper presents an active noise cancellation method using a MEMS accelerometer that recovers wearable sensor signals corrupted by body motion. The method is developed for a finger ring photoplethysmograph (PPG) sensor, the signal of which is susceptive to the hand motion of the wearer. A MEMS accelerometer (ACC) imbedded in the PPG sensor detects the hand acceleration, and is used for recovering the corrupted PPG signal, based upon two different methods of modeling the process of signal corruption. The correlation between the acceleration and the distorted PPG signal is analyzed, and a low-order FIR model relating the signal distortion to the hand acceleration is obtained. The model parameters are identified in real time with a recursive least square method. Experiments show that the active noise cancellation method can recover ring PPG sensor signals corrupted with 2G of acceleration in the longitudinal direction of the digital artery.

Travel time prediction using the GPS test vehicle and Kalman filtering techniques

Abstract: A sudden traffic surge immediately after special events (e.g., conventions, concerts) can create substantial traffic congestion in the area where the events are held. It is desired that the special events related traffic performance can be measured so that the traffic flow can be improved via some existing methods such as a temporary traffic signal timing adjustment. This paper focuses on the study of the arterial travel time prediction using the Kalman filtering and estimation technique, and a graduation ceremony is chosen as our case study. The Global Positioning System (GPS) test vehicle technique is used to collect after events travel time data. Based on the real-time data collected, a discrete-time Kalman filter is then applied to predict travel time exiting the area under study. An assessment of the performance and its effectiveness at the test site are investigated. The approaches to further improve the accuracy of the prediction error are also discussed.

Optimal control with unreliable communication: the TCP case

Abstract: The paper considers the linear quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We consider the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common transfer control protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon our previous results on estimation with unreliable communication, the paper shows the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.

Consensus algorithms are input-to-state stable

Abstract: In many cooperative control problems, a shared knowledge of information provides the basis for cooperation. When this information is different for each agent, a state of noncooperation can result. Consensus algorithms ensure that after some time the agents would agree on the information critical for coordination, called the coordination variable. In this paper we show that if the coordination algorithm is input-to-state stable where the input is considered to be the discrepancy between the coordination variable known to each vehicle, then cooperation is guaranteed when a consensus scheme is used to synchronize information. A coordinated timing example is shown in simulation to illustrate the notions of stability when a coordination algorithm is augmented with a consensus strategy.

State and configuration feedback for almost global tracking of simple mechanical systems on a general class of Lie groups

Abstract: We present a general intrinsic tracking controller design for fully-actuated simple mechanical systems, when the configuration space is one of a general class of Lie groups. We show that if a suitable error function can he found, then a general smooth and hounded reference trajectory may be tracked asymptotically from almost every initial condition, with locally exponential convergence. Such functions may be shown to exist on any compact Lie group, or on any product of a compact Lie group and R/sup n/. In the case of compact Lie groups, we show that the full-state feedback law composed with an exponentially convergent velocity estimator, also converges globally for almost every initial tracking error. We explicitly compute these controllers on SO(3), and simulate their performance for the axisymmetric top problem.

Cascaded control concept of a robot with two degrees of freedom driven by four artificial pneumatic muscle actuators

Abstract: Pneumatic muscles are interesting in their use as actuators in robotics, since they have a high power/weight ratio, a high-tension force and a long durability. This paper presents a two-axis planar articulated robot, which is driven by four pneumatic muscles. Every actuator is supplied by one electronic servo valve in 3/3-way function. Part of this work is the derivation of the model description, which describes a high nonlinear dynamic behavior of the robot. Main focus is the physical model for the pneumatic muscle and a detailed model description for the servo valves. The aim is to control the tool center point (TCP) of the manipulator, which bases here on a fast subsidiary torque regulator of the drive system compensating the nonlinear effects. As the robot represents a MIMO system, a second control objective is defined, which corresponds here to the average pressure of each muscle-pair. An optimisation-strategy is presented to meet the maximum stiffness of the controlled drive system. As the torque controller assures a fast linear input/output behavior, a standardized controller is implemented which bases here on the Computed Torque Method to track the TCP. Measurement results show the efficiency of the presented cascaded control concept.

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

Abstract: This work considers the problem of stabilization of nonlinear systems subject to state and control constraints. We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time for which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.

Motion planning with wireless network constraints

Abstract: This work discusses feasibility aspects of motion planning for groups of agents connected by a range-constrained wireless network. Specifically, we address the difficulties encountered when trajectories are required to preserve the connectedness of the network. The analysis utilizes a quantity called the connectivity robustness of the network, which can be calculated in a distributed fashion, and thus is applicable to distributed motion planning problems arising in control of vehicle networks. Further, these results show that network constraints posed as connectivity robustness constraints have minimal impact on reachability, provided that an appropriate topology control algorithm is implemented. This contrasts with more naive approaches to connectivity maintenance, which can significantly reduce the reachable set.

Real-time implementation of model predictive control

Abstract: A real-time implementation of model predictive control (MPC) is presented in this paper. MPC, also known as receding horizon control and moving horizon control, is widely accepted as the controller of choice for multivariable systems that have inequality constraints on system states, inputs and outputs. For processes with slow dynamics and low sampling rates, MPC is typically implemented on a dedicated computer. For systems with fast dynamics such as those in MEMS, a hardware embedded MPC would be an appropriate controller implementation since the size and the application precludes the use of a dedicated computer. Recent manufacturing advances have opened the path for the fabrication of micromechanical devices and electronic subsystems under the same manufacturing and packaging process, thereby opening the path for the use of advanced control algorithms towards systems-on-chip applications.