Randy A. Freeman

Robust Nonlinear Control Design

The apparatus comprises a desiccant chamber, operatively disposed between a gas compressor and a receiver, through which a gas to be dried therein is conducted, and valving for depressurizing the chamber and venting the same to atmosphere, when the receiver is fully charged. A pressure-sensing element automatically operates the valving. The apparatus has means insuring a valved return to a receiver-charging condition or operational mode automatically following apparatus shut down. The method sets forth the steps of chamber-drying the gas, monitoring the chamber-charged condition, shunting gas away from the receiver thereafter, and depressurizing and venting of the chamber.

Inverse Optimality in Robust Stabilization

The concept of a robust control Lyapunov function ({\Bf rclf}) is introduced, and it is shown that the existence of an {\Bf rclf} for a control-affine system is equivalent to robust stabilizability via continuous state feedback. This extends Artsteins theorem on nonlinear stabilizability to systems with disturbances. It is then shown that every {\Bf rclf} satisfies the steady-state Hamilton--Jacobi--Isaacs (HJI) equation associated with a meaningful game and that every member of a class of pointwise min-norm control laws is optimal for such a game. These control laws have desirable properties of optimality and can be computed directly from the {\Bf rclf} without solving the HJI equation for the upper value function.

Stability and Convergence Properties of Dynamic Average Consensus Estimators

We analyze two different estimation algorithms for dynamic average consensus in sensing and communication networks, a proportional algorithm and a proportional-integral algorithm. We investigate the stability properties of these estimators under changing inputs and network topologies as well as their convergence properties under constant or slowly-varying inputs. In doing so, we discover that the more complex proportional-integral algorithm has performance benefits over the simpler proportional algorithm

Multi-Agent Coordination by Decentralized Estimation and Control

We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to the problem of controlling the moment statistics describing the location and shape of a swarm. We derive conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology.

Brief paper: Decentralized estimation and control of graph connectivity for mobile sensor networks

The ability of a robot team to reconfigure itself is useful in many applications: for metamorphic robots to change shape, for swarm motion towards a goal, for biological systems to avoid predators, or for mobile buoys to clean up oil spills. In many situations, auxiliary constraints, such as connectivity between team members and limits on the maximum hop-count, must be satisfied during reconfiguration. In this paper, we show that both the estimation and control of the graph connectivity can be accomplished in a decentralized manner. We describe a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimator, we further propose a decentralized gradient controller for each agent to maintain global connectivity during motion.

Decentralized Environmental Modeling by Mobile Sensor Networks

Cooperating mobile sensors can be used to model environmental functions such as the temperature or salinity of a region of ocean. In this paper, we adopt an optimal filtering approach to fusing local sensor data into a global model of the environment. Our approach is based on the use of proportional-integral (PI) average consensus estimators, whereby information from each mobile sensor diffuses through the communication network. As a result, this approach is scalable and fully decentralized, and allows changing network topologies and anonymous agents to be added and subtracted at any time. We also derive control laws for mobile sensors to move to maximize their sensory information relative to current uncertainties in the model. The approach is demonstrated by simulations including modeling ocean temperature.

Design of “softer” robust nonlinear control laws

Abstract We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily ‘hard’ control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design ‘softer’ control laws which exhibit the high-gain properties to a much lesser extent. We show that the ‘soft’ designs eliminate the chattering exhibited by the ‘hard’ designs and achieve the same or better performance with less control effort.

Guaranteed stability of haptic systems with nonlinear virtual environments

Design of haptic systems that guarantee stable interaction is a challenging task. Virtual environments are typically highly nonlinear-resulting in a nonpassive discrete-time model. This paper will investigate how nonlinear mass/spring/damper virtual environments can be designed to guarantee the absence of oscillations and other chaotic behavior in the signal presented to the human operator. In particular, delayed and nondelayed implementation of the mass/spring/damper virtual environment is considered, revealing a nonintuitive result with regard to the allowable local stiffness.

Distributed estimation and control of swarm formation statistics

We describe distributed estimation algorithms that allow robots in a communication network to maintain estimates of summary statistics describing the shape of the swarm. We show that these estimators, combined with motion controllers implemented on each robot, result in the swarm formation statistics being driven to desired values in the presence of a changing network topology and the addition and deletion of robots

Control Lyapunov functions: new ideas from an old source

A control design method for nonlinear systems based on control Lyapunov functions and inverse optimality is analyzed. This method is shown to recover the LQ optimal control when applied to linear systems. More generally, it is shown to recover the optimal control whenever the level sets of the control Lyapunov function match those of the optimal value function. The method can be readily applied to feedback linearizable systems, and the resulting inverse optimal control law is generally much different from the linearizing control law. Examples in two dimensions are given to illustrate both the strengths and the weaknesses of the method.