Pushkin Kachroo

Feedback control theory for dynamic traffic assignment

Modelling and Problem Formulation.- Dynamic Traffic Routing Problem in Distributed Parameter Setting.- Fuzzy Feedback Control for Dynamic Traffic Routing.- Feedback Linearization for Dynamic Traffic Routing.- Sliding Mode Control for Dynamic Traffic Routing.- Network Level problem: System Optimal.- Network Level Problem: User Equilibrium.

Vehicle merging control design for an automated highway system

The merging process in an automated highway system (AHS) is divided into a speed adjustment stage and a lane merging stage. Three important parameters, namely acceptability, availability and pursuability, are analyzed to characterize the AHS lane gap features for the ideal, smooth and safe merging of the ramp vehicles. Three control guidance laws, namely linear, optimal and parabolic speed profiles, are developed to describe the desired behaviors of the merging vehicle based on the merging quality and safety. The desired states of the merging vehicle are generated through the outer loop by specified control guidance law. The tracking errors compared with desired states are eliminated by the proper design of controllers in the inner loop. Both longitudinal and lateral controllers are designed using sliding mode control theory that can handle the nonlinear and model uncertainties of the vehicle dynamics. The simulation results show encouraging results.

Solution to the user equilibrium dynamic traffic routing problem using feedback linearization

In this paper, the Dynamic Traffic Routing problem is defined as the real-time point diversion of traffic during non-recurrent congestion. This dynamic traffic routing problem is then formulated as a feedback control problem that determines the time-dependent split parameters at the diversion point for routing the incoming traffic flow onto the alternate routes in order to achieve a user-equilibrium traffic pattern. Feedback linearization technique is used to solve this specific user-equilibrium formulation of the Dynamic Traffic Routing problem. The control input is the traffic split factor at the diversion point. By transforming the dynamics of the system into canonical form, a control law is obtained which cancels the nonlinearities of the system. Simulation results show that the performance of this controller on a test network is quite promising.

System dynamics and feedback control problem formulations for real time dynamic traffic routing

This paper formulates the Dynamic Traffic Routing (DTR) problem as a real-time feedback control problem. Three different forms of the formulation are presented: 1.(1) distributed parameter system form derived from the conservation law; 2.(2) space discretized continuous lumped parameter form; 3.(3) space and time discretized lumped parameter form. These formulations can be considered as the starting points for development of feedback control laws for the different control problems stated in this paper. This paper presents the feedback control problems, and does not discuss in detail the methodology of solution techniques which could be used to solve these problems. However, for the sake of completeness a brief treatment of the three forms are included in this paper to show possible ways to design the controllers.

Robust feedback control of a single server queueing system

Abstract. This paper extends previous work of Ball et al. [BDKY] to control of a model of a simple queueing server. There are n queues of customers to be served by a single server who can service only one queue at a time. Each queue is subject to an unknown arrival rate, called a “disturbance” in accord with standard usage from H∞ theory. An H∞-type performance criterion is formulated. The resulting control problem has several novel features distinguishing it from the standard smooth case already studied in the control literature: the presence of constraining dynamics on the boundary of the state space to ensure the physical property that queue lengths remain nonnegative, and jump discontinuities in any nonconstant state-feedback law caused by the finiteness of the admissible control set (choice of queue to be served). We arrive at the solution to the appropriate Hamilton–Jacobi equation via an analogue of the stable invariant manifold for the associated Hamiltonian flow (as was done by van der Schaft for the smooth case) and relate this solution to the (lower) value of a restricted differential game, similar to that formulated by Soravia for problems without constraining dynamics. An additional example is included which shows that the projection dynamics used to maintain nonnegativity of the state variables must be handled carefully in more general models involving interactions among the different queues. Primary motivation comes from the application to traffic signal control. Other application areas, such as manufacturing systems and computer networks, are mentioned.

Stochastic learning feedback hybrid automata for dynamic power management in embedded systems

Dynamic power management (DPM) refers to the strategies employed at system level to reduce energy expenditure (i.e. to prolong battery life) in embedded systems. The trade-off involved in DPM techniques is between the reductions of energy consumption and latency suffered by the tasks. Such trade-offs need to be decided at runtime, making DPM an on-line problem. We formulate DPM as a hybrid automaton control problem and integrate stochastic control. The control strategy is learnt dynamically using stochastic learning hybrid automata (SLHA) with feedback learning algorithms. Simulation-based experiments show the expediency of the feedback systems in stationary environments. Further experiments reveal that SLHA attains better trade-offs than several former predictive algorithms under certain trace data.

Feedback Control of Crowd Evacuation in One Dimension

This paper studies crowd models in one dimension. The focus of this paper is on the design of nonlinear feedback controllers for these models. Two different models are studied where dynamics are represented by a single partial differential equation (PDE) in one case and a system of hyperbolic PDEs in another, and control models are proposed for both. These include advective, diffusive, and advective-diffusive controls. The models representing evacuation dynamics are based on the laws of conservation of mass and momentum and are described by nonlinear hyperbolic PDEs. As such, the system is distributed in nature. We address the design of feedback control for these models in a distributed setting where the problem of control and stability is formulated directly in the framework of PDEs. The control goal is to design feedback controllers to control the movement of people during evacuation and avoid jams and shocks.

Feedback Control Design and Stability Analysis of One Dimensional Evacuation System

This paper presents design of nonlinear feedback controllers for two different models representing evacuation dynamics in one dimension. The models presented here are based on the laws of conservation of mass and momentum. The first model is the classical one equation model for a traffic flow based on conservation of mass with a prescribed relationship between density and velocity. The other model is a two equation model in which the velocity is independent of the density. This model is based on conservation of mass and momentum. The equations of motion in both cases are described by nonlinear partial differential equations. We address the feedback control problem for both models. The objective is to synthesize a nonlinear distributed feedback controller that guarantees stability of a closed loop system. The problem of control and stability is formulated directly in the framework of partial differential equations. Sufficient conditions for Lyapunov stability for distributed control are derived

FUZZY FEEDBACK CONTROL FOR REAL-TIME DYNAMIC TRAFFIC ROUTING: USER EQUILIBRIUM MODEL FORMULATIONS AND CONTROLLER DESIGN

The formulation of a system dynamics model for the dynamic traffic routing (DTR) problem is addressed, specifically for the application of real-time feedback control. Also addressed is the design of fuzzy feedback control laws for this problem. Fuzzy feedback control is suitable for solving the DTR problem, which is nonlinear and time varying and contains uncertainties. To illustrate the applicability of fuzzy logic in the design of feedback control for DTR, a simple software simulation was conducted that provided encouraging results.

Control of rotary cranes using fuzzy logic

Rotary cranes (tower cranes) are common industrial structures that are used in building construction, factories, and harbors. These cranes are usually operated manually. With the size of these cranes becoming larger and the motion expected to be faster, the process of controlling them has become difficult without using automatic control methods. In general, the movement of cranes has no prescribed path. Cranes have to be run under different operating conditions, which makes closed-loop control attractive.