Feedback Control Systems as Users of a Shared Network: Communication Sequences that Guarantee Stability

We investigate the stability of a collection of systems which are governed by linear dynamics and operate under limited communication. We view each system and its feedback controller as users on an idealized shared network which grants access only to a few system-controller pairs at any one time. A communication sequence, which plays the role of a network admission policy, specifies the amount of time available for each system to complete its feedback loop. Using Lyapunov theory, we give a sufficient condition for the existence of a stabilizing communication sequence and show how one can be constructed in a way that minimizes network usage. Our solution depends on the parameters of the underlying system(s) and on the number of controller-plant connections that can be maintained simultaneously. We include simulation results illustrating the main ideas.This paper will appear in IEEE Conference on Decision and Control, 2001

Biologically Inspired Algorithms for Optimal Control

In the past few years, efforts to codify the organizing principles behind biological systems have been capturing the attention of a growing number of researchers in the systems and control community. This endeavor becomes increasingly important as new technologies make it possible to engineer complex cooperating systems that are nevertheless faced with many of the challenges long-overcome by their natural counterparts. One area in particular where biology serves as an inspiring but still distant example, involves systems in which members of a species cooperate to form collectives whose abilities are beyond those of individuals. This paper looks to the process by which ants optimize their foraging trails as inspiration for an organizing principle by which groups of dynamical systems can solve a class of optimal control problems. We explore the use of a strategy termed `local pursuit', which allows members of the group to overcome their limitations with respect to sensing range and available information through the use of neighbor-to-neighbor interactions. Local pursuit enables the group to find an optimal solution by iteratively improving upon an initial feasible control. We show that our proposed strategy subsumes previous pursuit-based models for ant-trail optimization and applies to a large array of problems, including many of the classical situations in optimal control. The performance of our algorithm is illustrated in a series of numerical experiments. Ongoing work directions related to local pursuit are also discussed in this document

Optimal Control through Biologically-Inspired Pursuit

Inspired by the process by which ants gradually optimize their foraging trails, this paper investigates the cooperative solution of a class of free-final time, partially-constrained final state optimal control problems by a group of dynamic systems. A cooperative, pursuit-based algorithm is proposed for finding optimal solutions by iteratively optimizing an initial feasible control. The proposed algorithm requires only short-range, limited interactions between group members, and avoids the need for a "global map" of the environment on which the group evolves. The performance of the algorithm is illustrated in a series of numerical experiments

Local Pursuit as a Bio-Inspired Computational Optimal Control Tool

This paper explores the use of a bio-inspired control algorithm, termed ``local pursuit', as a numerical tool for computing optimal control-trajectory pairs in settings where analytical solutions are difficult to obtain. Inspired by the foraging activities of ant colonies, local pursuit has been the focus of recent work on cooperative optimization. It allows a group of agents to solve a broad class of optimal control problems (including fixed final time, partially-constrained final state problems) and affords certain benefits with respect to the amount of information (description of the environment, coordinate systems, etc.) required to solve the problem. Here, we present a numerical optimization method that combines local pursuit with the well-known technique of multiple shooting, and compare the computational efficiency and capabilities of the two approaches. The proposed method method can overcome some important limitations of multiple shooting by solving an optimal control problem ``in small pieces'. Specifically, the use of local pursuit increases the size of the problem that can be handled under a fixed set of computational resources. Furthermore, local pursuit can be effective in some situations where multiple shooting leads to an ill-conditioned nonlinear programming problem. The trade-off is an increase in computation time. We compare our pursuit-based method with direct multiple shooting using an example that involves optimal orbit transfer of a simple satellite

Biologically-Inspired Optimal Control via Intermittent Cooperation

We investigate the solution of a large class of fixed-final-state optimal control problems by a group of cooperating dynamical systems. We present a pursuit-based algorithm -- inspired by the foraging behavior of ants -- that requires each system-member of the group to solve a finite number of optimization problems as it follows other members of the group from a starting to a final state. Our algorithm, termed "sampled local pursuit", is iterative and leads the group to a locally optimal solution, starting from an initial feasible trajectory. The proposed algorithm is broad in its applicability and generalizes previous results; it requires only short-range sensing and limited interactions between group members, and avoids the need for a "global map" of the environment or manifold on which the group evolves. We include simulations that illustrate the performance of our algorithm

Stabilization of Networked Control Systems under Feedback-based Communication

We study the stabilization of a networked control system (NCS) in which multiple sensors and actuators of a physical plant share a communication medium to exchange information with a remote controller. The plant's sensors and actuators are allowed only limited access to the controller at any one time, in a way that is decided on-line using a feedback-based communication policy. Our NCS model departs from those in previous formulations in that the controller and plant handle communication disruptions by ``ignoring'' (in a sense that will be made precise) sensors and actuators that are not actively communicating. We present an algorithm that provides a complete and straightforward method for simultaneously determining stabilizing gains and communication policies and avoids the computational complexity and limitations associated with some previously proposed models. We introduce three feedback-based scheduling policies that quadratically stabilize the closed-loop NCS while achieving various objectives related to the system's rate of convergence, the priorities of different sensors and actuators, and the avoidance of chattering

Bio-Inspired Cooperative Optimal Control with Partially-Constrained Final State

Inspired by the process by which ants gradually optimize their foraging trails, this report investigates the cooperative solution of a class of free-final time, partially-constrained final state optimal control problems by a group of dynamic systems. A class of cooperative, pursuit-based algorithms are proposed for finding optimal solutions by iteratively optimizing an initial feasible control. The proposed algorithms require only short-range, limited interactions between group members, avoid the need for a ``global map'' of the environment on which the group evolves, and solve an optimal control problem in ``small'' pieces, in a manner which will be made precise. The performance of the algorithms is illustrated in a series of simulations and laboratory experiments

Stabilization of Networked Control Systems: Designing Effective Communication Sequences

This paper discusses the stabilization of a networked control system (NCS) whose sensors and actuators exchange information with a remote controller over a shared communication medium. Access to that medium is governed by a pair of periodic communication sequences. Under the model utilized here, the controller and plant handle communication disruptions by ``ignoring' (in a sense to be made precise) sensors and actuators that are not actively communicating. It is shown that under mild conditions, there exist periodic communication sequences that preserve the reachability and observability of the plant, leading to a straightforward design of a stabilizing feedback controller

Language-based Feedback Control Using Monte Carlo Sensing *

Abstract-Landmark-based graphs are a useful and parsimonious tool for representing large scale environments. Relating landmarks by means of feedback-control algorithms encoded in a motion description language provides a level of abstraction that enables autonomous vehicles to navigate effectively by composing strings in the language to form complex strategies that would be difficult to design at the level of sensors and actuators. In such a setting, feedback control requires one to pay attention not only to sensor and actuator uncertainty, but also to the ambiguity introduced by the fact that many landmarks may look similar when using a modest set of observations. This work discusses the generation of language-based feedback control sequences for landmark-based navigation together with the problem of sensing landmarks sufficiently well to make feedback meaningful. The paper makes two contributions. First, we extend previous work to include the costs of sensing with varying degrees of accuracy. Second, we describe a Monte Carlo based approach to landmark sensing which relies on the use of particle filters. We include simulation results that illustrate our approach