David G. Galati

A Dynamical State Space Representation and Performance Analysis of a Feedback-Controlled Rotary Left Ventricular Assist Device

The left ventricular assist device (LVAD) is a mechanical device that can assist an ailing heart in performing its functions. The latest generation of such devices is comprised of rotary pumps which are generally much smaller, lighter, and quieter than the conventional pulsatile pumps. The rotary pumps are controlled by varying the rotor (impeller) speed. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician to meet the patients blood needs. However, an important challenge facing the increased use of these LVADs is the desire to allow the patient to return home. The development of an appropriate feedback controller for the pump speed is therefore crucial to meet this challenge. In addition to being able to adapt to changes in the patients daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of excessive pumping (known as suction) which may cause collapse of the ventricle. In this paper we will discuss some theoretical and practical issues associated with the development of such a controller. As a first step, we present and validate a state-space mathematical model, based on a nonlinear equivalent circuit flow model, which represents the interaction of the pump with the left ventricle of the heart. The associated model is a six-dimensional vector of time varying nonlinear differential equations. The time variation occurs over four consecutive intervals representing the contraction, ejection, relaxation, and filling phases of the left ventricle. The pump in the model is represented by a nonlinear differential equation which relates the pump rotational speed and the pump flow to the pressure difference across the pump. Using this model, we discuss a feedback controller which adjusts the pump speed based on the slope of the minimum pump flow signal, which is one of the model state variables that can be measured. The objective of the controller is to increase the speed until the envelope of the minimum pump flow signal reaches an extreme point and maintain it afterwards. Simulation results using the model equipped with this feedback controller are presented for two different scenarios of patient activities. Performance of the controller when measurement noise is added to the pump flow signal is also investigated.

Automatic decomposition of time series into step, ramp, and impulse primitives

Time series data that can be modeled as linear combinations of weighted and shifted primitive functions such as ramps, steps and impulses are representative of many industrial, manufacturing, and business processes. Data of this type also are found in statistical process control, structural health monitoring, and other system diagnosis applications. Often, the existence of one or more of these primitive functions may be indicative of the occurrence of a specific process event, making their detection and interpretation of great interest. The human eye is an exceptional tool at this kind of pattern recognition. However, for processes that generate large amounts of data the human eye encounters difficulties related to speed and consistency necessitating an automated approach. In this paper, we consider the problem of decomposing a time series into its steps, ramps, and impulses constituents and expressing it as a linear combination of weighted and shifted versions of these primitives. We express the problem as a least squares error minimization coupled with a combinatorial search to arrive at an acceptable decomposition. We show that under certain conditions, such decomposition is possible and can be obtained efficiently using a sliding window approach. We illustrate the results with several examples.

Effectiveness of the Nash strategies in competitive multi-team target assignment problems

Game theoretic approaches, the Nash strategies in particular, have often been criticized as being ineffective in competitive multi-team target assignment problems when compared to random or greedy targeting strategies. In this paper, we attempt to show that this is not the case. Using an attrition model composed of two teams of non-homogeneous fighting units simultaneously targeting each other, we compare the outcomes of various combinations of four targeting strategies used on each side: (1) A random strategy where each unit selects targets randomly, (2) A unit greedy strategy where each unit chooses the target that it is best suited to attack (3) A team optimal strategy where the units coordinate their choice of targets so as to optimize the overall team performance without considering possible adversarial strategies, and (4) A Nash strategy which guarantees that the other teams performance will deteriorate if it does not also use a Nash strategy. We compare the results for all possible combinations of these targeting strategies and show that for each team the Nash strategy outperforms all other strategies no matter what is the strategy employed by the other side.

A fast algorithm for unit level team resource allocation in a game environment

This paper deals with the problem of allocating tasks to members of a non-homogeneous team of entities that is in conflict with another team of non-homogeneous entities. Each team is assumed to have a finite number of tasks that need to be assigned to its members. The task assignment within each team is done in such a way as to optimize an overall team objective function which depends not only on the task assignments in that team, but also on the task assignment in the adversarial team as well. In this sense, the task assignment in each team must take into account the task assignment in the other team. Because of the presence of an adversarial relationship between the two teams, this problem is best formulated and solved within the framework of game theory. The Nash strategy is an important solution concept for this type of problems. Task assignments that are formulated as Nash strategies yield an equilibrium in that no team has an incentive to unilaterally alter the assignments in an attempt to improve its position. An issue that arises when solving for the Nash strategies is the dimensionality of the search space, which quickly becomes overwhelming even with relatively small numbers of entities and tasks. In this paper we discuss an algorithm, called unit level team resource allocation (ULTRA), which overcomes this scalability issue. We also present simulation results to illustrate the performance of this algorithm when compared to an exhaustive search.

A Dynamical State Space Representation and Performance Analysis of a Feedback Controlled Rotary Left Ventricular Assist Device

The Left Ventricular Assist Device (LVAD) is a mechanical device that can assist an ailing natural heart in performing its functions. The latest generation of such devices is a rotary-type pump which is generally much smaller, lighter, and quieter than the conventional pulsatile-type pump. The rotary-type pumps are controlled by varying the rotor (impeller) speed. If the patient is in a health care facility, the pump speed can be adjusted manually by a trained clinician. However, an important challenge facing the increased use of these LVADs, is the desire to allow the patient to return home. The development of an appropriate patient adaptive feedback speed controller for the pump is therefore crucial to meet this challenge. In addition to being able to adapt to changes in the patient’s daily activities by automatically regulating the pump speed, the controller must also be able to prevent the occurrence of suction. In this paper we will discuss the theoretical and practical issues associated with the development of such a controller. As a flrst step, we will present a state-space mathematical model, based on a nonlinear equivalent circuit flow model, which represents the interaction of the pump with the left ventricle of the heart. The associated state space model is a 5-dimensional vector of time varying nonlinear difierential equations. The time variation occurs over 4 consecutive intervals representing the contraction, ejection, relaxation, and fllling phases of the left ventricle. The pump in the model is represented by a nonlinear equation which relates the pump rotational speed and the pump flow to the pressure difierence across the pump. Using this model, we will discuss a gradient based feedback controller which increases the pump speed to meet the patient requirements up to the point where suction may occur. At that point the controller will maintain a constant pump speed keeping the gradient of the minimum pump flow at zero. Simulation results using the model equipped with the feedback controller are presented for two cases representing two levels of patient activities. Performance of the controller for noisy measurements of pump blood flow is also investigated. Our results show that such a feedback controller performs very well and is fairly robust against measurements noise.© 2005 ASME

A game theoretic approach to team dynamics and tactics in mixed initiative control of automa-teams

The planning and operational hierarchy in future combat systems that involve unmanned aerial vehicles will very likely consist of three levels: a team composition and tasking (TCT) level, a team dynamics and tactics (TDT) level, and a cooperative path planning (CPP) level. In this paper, we discuss a game theoretic approach for the target assignment problem at the TDT level. This problem considers the issue of assigning tasks to individual UAVs which could involve attacking one or more fighting units on the other side. The approach considered in this paper involves estimating the reaction of the other side for every possible UAV target assignment that could be made and calculating the resulting Nash equilibrium solution. We discuss an algorithm for determining the Nash solution which overcomes issues related to scalability and is capable of handling target assignments with a large number of non-homogeneous units on each side. In this paper, we discuss both the open-loop and feedback implementations off this algorithm and present simulation results that can be used to assess their performance. Our simulation results show that the availability of sensor information on target damage, as the battle progresses, will allow the feedback implementation at the TDT level to optimally allocate the available UAV resources by avoiding the assignment of tasks that have already been satisfactorily accomplished, either fully or partially. We also introduce the concept of distance discount factor (DDF) to address the fact that targeting close but less significant targets could be more rewarding than targeting far but more significant units. We discuss and compare the results of the feedback implementation with and without DDF.

Team dynamics and tactics in strategies for Human-Automaton Resource Entity Deployment

Strategies for Human-Automaton Resource Entity Deployment (SHARED), is a software tool that addresses the challenge of hierarchical decision-making and control for battle planning and management in future combat systems. Its operational and planning hierarchy consists of three levels: Team Composition and Tasking (TCT), Team Dynamics and Tactics (TDT), and Cooperative Path Planning (CPP). In this paper, we discuss a game theoretic approach for the target assignment problem in the TDT. This problem deals with the issue of assigning tasks to units on one side which involves one or more units on the other side. A typical task would be to attack a unit or group of units on the other side. The algorithm used in this paper overcomes issues related to scalability and can handle target assignments with a large number of non-homogeneous units on each side. In the SHARED system, where target assignments need to be performed at successive steps during the battle, the algorithm can be implemented in both open-loop and feedback forms. In this paper, we discuss these two implementations and present simulation results that can be used to assess their performance. Our simulation results show that, the availability of feedback sensor information on target damage, as the battle progresses, will allow the TDT level to optimally allocate the available resources by avoiding the assignment of tasks that have already been satisfactorily accomplished, either fully or partially.

Near-Nash targeting strategies for heterogeneous teams of autonomous combat vehicles

Military strategists are currently seeking methodologies to control large numbers of autonomous assets. Automated planners based upon the Nash equilibrium concept in non-zero sum games are one option. Because such planners inherently consider possible adversarial actions, assets are able to adapt to, and to some extent predict, potential enemy actions. However, these planners must function properly both in cases in which a pure Nash strategy does not exist and in scenarios possessing multiple Nash equilibria. Another issue that needs to be overcome is the scalability of the Nash equilibrium. That is, as the dimensionality of the problem increases, the Nash strategies become unfeasible to compute using traditional methodologies. In this paper we introduce the concept of near-Nash strategies as a mechanism to overcome these difficulties. We then illustrate this concept by deriving the near-Nash strategies and using these strategies as the basis for an intelligent battle plan for heterogeneous teams of autonomous combat air vehicles in the Multi-Team Dynamic Weapon Target Assignment model.

Near-Nash Strategies in Competitive Multi-Team Target Assignment

While the Nash equilibrium represents an important strategy concept for non-cooperative scenarios such as military combat, it is often difficult to justify its use in scenarios in which its computation is unfeasible or its existence cannot be guaranteed. To justify the use of Nash-like strategies in such applications, we extend the concept of a Nash equilibrium to encompass a definition of near-Nash strategies. We then employ this definition in an efficient algorithm designed to calculate target assignment strategies in the Multi-Team Dynamic Weapon Target Assignment problem. Using this approach we demonstrate that our concept of near-Nash strategies generates results similar to those produced using the exact Nash strategies.Copyright