Research Interests

Decentralized Receding Horizon Control of Large Scale Dynamically Decoupled Systems


The main concept of Receding Horizon Control (RHC) is to use the model of the system in order to predict its future evolution. Based on this prediction, at each time step a certain performance index is optimized under operating constraints with respect to a sequence of future input moves. The first of such optimal moves is the control action applied to the system. At the next time step, a new optimization is solved over a shifted prediction horizon.

The main idea behind our decentralized RHC framework is to break a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different subsystem and computes the local control inputs based only on its states and that of its neighbors. On each subsystem, the current state and the model of its neighbors are used to predict their possible trajectories and move accordingly. The information-exchange topology and interconnection constraints are described by a graph structure in the problem formulation.

The proposed framework provides several advantages:

  1. Can handle heterogenous subsystem dynamical models.
  2. Different objectives can be achieved by changing appropriate terms in the cost function (e.g. various maneuvering objectives in formation flying such as: formation keeping, formation joining and formation change).
  3. Individual subsystems use neighbor information to predict their behavior in order to fulfill interconnection constraints (such as collision avoidance) and act in a cooperative, rather than worst-case way (similarly to what we do while driving cars).
  4. Can handle constrained MIMO linear models as well as constrained MIMO piecewise linear models of subsystems.
  5. The problem is formulated and solved as small Mixed-Integer Linear Programs (MILPs) which can be translated into equivalent gain scheduled controllers for real-time implementation.
  6. Provides a systematic decentralized control design approach for large scale dynamically decoupled systems.


References:

Application Areas of Decentralized RHC


Distributed Control of Cross-Directional Paper Profile in Paper Machines

The papermaking process employs large arrays of actuators spread across a continuously moving web to control the cross-directional (CD) profiles of the paper properties as measured by a scanning gauge downstream from the actuators. A CD control system calculates actuator moves to maintain the measured CD profiles of paper properties on target. In a typical industrial CD control system controller computations are performed at the spatial resolution of the actuator profile. Such profiles have from 30 up to 300 elements, corresponding to the number of actuators. The measurement signals are obtained from the scanning sensor at a much higher spatial resolution with up to 2000 elements.

The weight control problem using a slice lip actuator array is considered. The weight per unit area of a sheet of paper, is an important factor in the quality of the finished product. Deviations in the paper sheet's weight from its target will affect many other properties. CD control of the weight of a paper sheet is accomplished by actuators at the headbox. The function of weight control actuators is to achieve an even distribution of the pulp fibers across the width of the wire belt, despite changing pulp properties.

We will consider the process which describes the spatial response of the weight properties as a function of the actuator profile. The dynamics of each actuator in the headbox is modeled as a first order system with deadtime. The deadtime models the transport delay equivalent to the time taken for the paper to travel from the actuators to the scanning sensor. Typically, the impulse response of individual actuators, also known as the cross-directional (CD) bump response is much narrower than the width of the paper sheet.

An important factor in CD control is the presence of actuator constraints, which represent maximum-minimum actuator positions and the presence of limits on relative positions between neighboring actuators. This latter restricts the bending of the slice lip (i.e. neighboring actuator positions cannot be too far from each other).

The control problem can be arranged in the form used in our decentralized RHC framework by considering independent actuator dynamics and an objective function which minimizes the error between the desired and actual paper weight profile. In summary, the paper machine application example can be described by the following features:
  1. Subsystems: Independently actuated elements along the slice lip profile in the paper headbox, where the inputs are the desired actuator movements and the outputs are the actual actuator positions.
  2. Subsystem Constraints: Bounds on actuator positions.
  3. Interaction Constraints: Bounded deviation between neighboring valve movements to prevent excessive bending and eventual breaking of the slice lip profile.
  4. Objective Function: Tracking of paper weight profiles in the presence of changing pulp properties. The paper weight measured by downstream sensors is a function of neighboring actuator positions.
  5. Graph: Depending on the bending restrictions for the slice lip, a time-invariant line graph or n-closest neighbor interconnection gives the underlying topology.

References:


Monitoring Network of Cameras

Monitoring and surveillance in public areas is nowadays accomplished by using a plethora of cameras. As an example, main international airports can be equipped with more than hundreds of cameras. Future monitored areas  will be outfitted with fixed wide-angle cameras and "Pan-Tilt-Zoom" (PTZ) cameras which can communicate within a distributed network. These two types of cameras can be used to achieve different goals such as identifying multiple targets or identifying details on a moving target (e.g. the faces of several walking persons or the numberplates on moving cars). Pan, tilt and zoom factors can be controlled by PTZ cameras in order to achieve the desired goals. The accuracy and precision of the captured detail will depend on properties such as size, position and speed of the moving objects. These properties are better tracked by the wide-angle cameras. The goal is to design control strategies for achieving "good" tracking of the details.

The controller receives information about size, position and speed of the objects from wide-angle cameras and information about the current tracking accuracy and quality of the zoomed images from PTZ cameras. Based on such information, pan, tilt and zoom factors will be commanded to achieve optimal multi-objective tracking. In such a scenario, PTZ cameras are independently actuated systems, which need to cooperate to achieve a certain goal. (A typical example is tracking a walking person through the rooms and floors of a building). The interaction constraints between cameras will ensure that the orientation and zooming factors of neighboring cameras do not create a blind spot allowing unmonitored intrusion into the environment. Details of this application are under development and not ready for disclosure, however the characteristics of the decentralized RHC framework are easily identified for this example as well:

  1. Subsystems: Independently actuated cameras where Pan, Tilt and Zooming factors are controlled.
  2. Subsystem Constraints: Physical PTZ ranges of cameras.
  3. Interaction Constraints: Relative orientation and zooming factors have to be constrained to avoid (or minimize the size of) blind spots in a given area.
  4. Objective Function: Tracking of multiple targets and details on a target.
  5. Graph: The graph connection will be depend on the physical position of cameras. Cameras in two adjacent rooms need to exchange information if the rooms can be accessed from each other. There will be no need for communication if the rooms are far away and on different floors.

References:
UAV formation flight

Interest in the formation control of Unmanned Air Vehicles (UAVs) has grown significantly over the last years. The main motivation is the wide range of military and civilian applications where UAV formations could provide a low cost and efficient alternative to existing technology. Among them, distributed sensing applications are envisioned to be the most appealing. Such applications include Synthetic Aperture Radar interferometry, surveillance, damage assessment, reconnaissance, chemical or biological agent monitoring.

Formation flight can be viewed as a large control problem which computes the control inputs to Unmanned Aerial Vehicles (UAVs) in order to fly challenging maneuvers while maintaining relative positions as well as safe distances between each UAV pair. Optimal control has been one of the more successful techniques to formulate and tackle such a problem. Centralized optimal or suboptimal approaches have been used in different studies. However, as the number of UAVs increases, the solution of big, centralized, non-convex optimization problems becomes prohibitive, even having the most advanced optimization solver, or using oversimplified linear vehicle dynamics.

The Organic Air Vehicle (OAV) is a scalable autonomous ducted-fan vehicle, which is currently used at the Honeywell Research Laboratory in Minneapolis. Its small size and vertical take-off and landing capability offers several potential tactical advantages in future UAV applications. This is especially true for platoon- and other lower-level Reconnaissance, Surveillance, and Target Acquisition. The vehicle translates and rotates by modulating thrust and prop wash along its axis via the deflection of specific sets of vanes. For instance, to translate in a forward direction, the vehicle tilts by an angle proportional to the desired speed of travel in the given direction. Tilt angles are similar to pitch and roll angles in the helicopter coordinate system notation. The body x-axis points forward in the duct inlet plane. This is also the direction in which a mounted camera would point. It lies along the hinge of vane sets that are used for rolling motion. The body y-axis points to the right in the duct inlet plane. It lies along the hinge axis of vane sets used to pitch the vehicle. The body z-axis points down along the propeller axis.

The OAV is a highly nonlinear, constrained multi-input, multi-output (MIMO) system. OAV formation flight is a complex task which is rendered tractable via a hierarchical decomposition of the problem. In such a decomposition, the lower level is made up of the OAV dynamics equipped with efficient guidance and control loops. At the higher level, the controlled OAV can be represented sufficiently well as a constrained MIMO linear system.

Nonlinear control of the inner loop (i.e. attitude and rate loops and the position and velocity loops) are accomplished via nonlinear dynamic inversion and robust multivariable control to
achieve a desired dynamics. Essentially, the nonlinearities of the various loops are cancelled (to a certain degree) by inversion and a desired dynamics is imposed on the resulting system so that the behavior resembles a set of integrators. However, this is only true when the inversion is perfect. Since perfect inversion rarely occurs in reality, the response of these state variables tend to be more similar to a first or second order transfer function rather than a pure integrator.

Assuming that near-perfect dynamic inversion takes place most of the time, the dynamics from the commanded position and heading to the outputs (which may be selected as actual positions and heading) is that of a multivariable linear system. The non-perfect dynamic inversion will introduce coupling terms between the N, E, h desired positions and their actual positions. In OAV formation flight, at the higher level we model OAVs with a constrained linear MIMO system of second order for each axis. The inputs to the system dynamics are accelerations along the N, E, h-axes, and the states are velocities and positions along the N, E, h-axes.

Future scenarios will implement hundreds of OAVs flying in formation. OAV formation flight falls in the class of problems considered in our decentralized RHC framework using the high-level dynamics of the each OAV. The cost function will depend on the formation's mission and will include terms that minimize relative distances and/or velocities between neighboring vehicles. The coupling constraints arise from collision avoidance. The interaction graph is full (each vehicle has to avoid all the other vehicles) but it is often approximated with a time-varying graph based on a "closest spatial neighbors" model. In summary, the formation flight application example is identified by the following characteristics:

  1. Subsystems: Independently actuated, decoupled vehicle dynamics with acceleration, velocity or position command inputs along the N, E, h-axes. The states of each vehicle represent velocities and positions along the N, E, h-axes.
  2. Subsystem Constraints: Bounds on speed and acceleration of the vehicles.
  3. Interaction Constraints: Collision avoidance constraints between vehicles.
  4. Objective Function: Minimization of relative distance and absolute position errors in order to achieve a desired formation and arrive at a specified target, respectively.
  5. Graph: Time-varying graph based on a "closest spatial neighbors" model.


Sample references:


Real-Time Receding Horizon Control


The Software-Enabled Control (SEC) program sponsored by the Defense Advanced Research Projects Agency (DARPA) of the United States represents the first large-scale, targeted effort toward integration of advances in computing and control of autonomous, uninhabited air vehicles (UAVs). The SEC vision was to enable advanced control systems that exploit information to significantly increase the performance and reliability of these vehicles. As part of the SEC program, the University of Minnesota (UMN) / University of California, Berkeley (UCB) team developed a unified design framework to synthesize and simulate individual vehicle management systems.

On-line control customization for Uninhabited Air Vehicles (UAVs) was the focus of our efforts during the five year program. Advances in on-line control customization have enabled a dramatic increase in military effectiveness by increasing the level of autonomy in UAVs, probability of mission success and survivability, expanding the range of UAV missions while reducing air vehicle fatigue and life cycle costs.  The benefits to the military include use of extremely aggressive maneuvering of UAVs to achieve mission directives, accommodation of goal changes in real-time, life-extending control, a reduced need for hardware redundancy while allowing more complex control strategies without increased software production and verification costs. A key component of our research was the integration of our algorithms into the Open Control Platform (OCP) software infrastructure.

During the five year program advances were made in the areas of modeling, receding horizon control (RHC), linear parameter-varying (LPV) control, fault detection, reconfiguration, anytime control algorithms and real-time control interfaces and algorithms. An application programming interface (API) was developed to support implementation of receding horizon control (RHC) schemes within the Open Control Platform (OCP) real-time software environment. A prototype implementation of the RHC API for a quadratic programming based generic RHC scheme was developed for flight testing on the DARPA SEC fixed-wing final demonstration testbed. The API framework relies on a real-time software infrastructure and provides a high-level interface to control engineers, which simplifies the embedded control design and implementation process significantly. The RHC API was successfully flight tested on a full-scale aircraft in the DARPA-sponsored Software Enabled Control program final demonstration experiment.


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Aerospace and Automotive Applications


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System Identification


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Last updated:   October 8, 2006