Andrew G. Lamperski

Output feedback ℌ 2 model matching for decentralized systems with delays

This paper gives a new solution to the output feedback ℌ2 model matching problem for a large class of delayed information sharing patterns. Existing methods for similar problems typically reduce the decentralized problem to a centralized problem of higher state dimension. In contrast, this paper demonstrates that the decentralized model matching solution can be constructed from the original centralized solution via quadratic programming.

Lyapunov-Like Conditions for the Existence of Zeno Behavior in Hybrid and Lagrangian Hybrid Systems

Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a one- dimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form.

Dynamical Wall Following for a Wheeled Robot Using a Passive Tactile Sensor

Feedback from antennae - long, flexible tactile sensors - enables cockroaches and other arthropods to rapidly maneuver through poorly lit and cluttered environments. Inspired by their performance, we created a wall-following controller for a dynamic wheeled robot using tactile antenna feedback. We show this controller is stable for a wide range of control gains and robot system parameters. To test the controller, we constructed a two-link antenna that uses potentiometers and capacitive contact sensors. Experiments based on the prototype demonstrate that our controller robustly tracks unexpected corners ranging from -60° to +900.

Dynamic programming solutions for decentralized state-feedback LQG problems with communication delays

This paper presents explicit solutions for a class of decentralized LQG problems in which players communicate their states with delays. A method for decomposing the Bellman equation into a hierarchy of independent subproblems is introduced. Using this decomposition, all of the gains for the optimal controller are computed from the solution of a single algebraic Riccati equation.

Lyapunov Theory for Zeno Stability

Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood. The goal of this paper is to develop a stability theory for Zeno hybrid systems that parallels classical Lyapunov theory; that is, we present Lyapunov-like sufficient conditions for Zeno behavior obtained by mapping solutions of complex hybrid systems to solutions of simpler Zeno hybrid systems defined on the first quadrant of the plane. These conditions are applied to Lagrangian hybrid systems, which model mechanical systems undergoing impacts, yielding simple sufficient conditions for Zeno behavior. Finally, the results are applied to robotic bipedal walking.

Optimal decentralized state-feedback control with sparsity and delays

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition of the noise history, the control problem is split into independent subproblems that are solved using dynamic programming. The approach presented herein both unifies and generalizes many existing results.

On the structure of state-feedback LQG controllers for distributed systems with communication delays

This paper presents explicit solutions for a few distributed LQG problems in which players communicate their states with delays. The resulting control structure is reminiscent of a simple management hierarchy, in which a top level input is modified by newer, more localized information as it gets passed down the chain of command. It is hoped that the controller forms arising through optimization may lend insight into the control strategies of biological and social systems with communication delays.

Periodically Controlled Hybrid Systems

This paper introduces Periodically Controlled Hybrid Automata (PCHA) for describing a class of hybrid control systems. In a PCHA, control actions occur roughly periodically while internal and input actions may occur in the interim changing the discrete-state or the setpoint. Based on periodicity and subtangential conditions, a new sufficient condition for verifying invariance of PCHAs is presented. This technique is used in verifying safety of the planner-controller subsystem of an autonomous ground vehicle, and in deriving geometric properties of planner generated paths that can be followed safely by the controller under environmental uncertainties.

On the existence of Zeno behavior in hybrid systems with non-isolated Zeno equilibria

This paper presents proof-certificate based sufficient conditions for the existence of Zeno behavior in hybrid systems near non-isolated Zeno equilibria. To establish these conditions, we first prove sufficient conditions for Zeno behavior in a special class of hybrid systems termed first quadrant interval hybrid systems. The proof-certificate sufficient conditions are then obtained through a collection of functions that effectively ¿reduce¿ a general hybrid system to a first quadrant interval hybrid system. This paper concludes with an application of these ideas to Lagrangian hybrid systems, resulting in easily verifiable sufficient conditions for Zeno behavior.

Optimal state-feedback control under sparsity and delay constraints

This paper presents the solution to a general decentralized state-feedback problem, in which the plant and controller must satisfy the same combination of delay constraints and sparsity constraints. The control problem is decomposed into independent subproblems, which are solved by dynamic programming. In special cases with only sparsity or only delay constraints, the controller reduces to existing solutions.