Distributed and event-based state estimation and control

In this thesis, state estimation and control are considered for dynamic systems with multiple distributed control agents (each equipped with sensing, actuation, and computation) that share data with each other over a broadcast network in order to coordinate their actions. With the state estimation algorithms that are developed for this class of systems, each agent can estimate the full state of the networked system based on its own sensor measurements and the sporadically transmitted measurements of the other agents. In order to ensure an efficient use of the shared communication resource, each agent transmits its sensory data only when certain events indicate that new data is required to meet a certain estimation performance. A balancing cube serves as the test bed to demonstrate that these event-based estimation algorithms can be used for event-based control when combining them with standard state-feedback controllers. The experimental results show that the event-based control system significantly reduces average network traffic as compared to a system that uses periodic data transmission. The two main parts of this thesis are 1) the development of distributed and event-based state estimation methods, and 2) the design and construction of the Balancing Cube as a test bed for distributed estimation and control. The key feature of the algorithms for distributed and event-based estimation is that each agent in the network broadcasts its local sensor measurements to all other agents only if the data is required in order for the other agents to meet a certain estimation performance. To be able to make this decision, each agent implements a state estimator that is connected to the broadcast network (a common bus). Since the state estimate is computed based on data received over the bus only (the local sensor data is used only when also broadcast), the estimates are the same on all agents and represent the common information in the network. The estimator can hence be

[1]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[2]  Rong-Jong Wai,et al.  Adaptive stabilizing and tracking control for a nonlinear inverted-pendulum system via sliding-mode technique , 2006, IEEE Trans. Ind. Electron..

[3]  Daniela Rus,et al.  Modular Robot Systems , 2010, IEEE Robotics & Automation Magazine.

[4]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[5]  Dennis S. Bernstein,et al.  Stabilization of a 3D axially symmetric pendulum , 2008, Autom..

[6]  Dennis S. Bernstein,et al.  Asymptotic Smooth Stabilization of the Inverted 3-D Pendulum , 2009, IEEE Transactions on Automatic Control.

[7]  lawa Kanas,et al.  Metric Spaces , 2020, An Introduction to Functional Analysis.

[8]  J.P. Hespanha,et al.  A Constant Factor Approximation Algorithm for Event-Based Sampling , 2007, 2007 American Control Conference.

[9]  Raffaello D'Andrea,et al.  Numerical models and controller design parameters for the balancing cube , 2012 .

[10]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[11]  Karl-Erik Årzén,et al.  A simple event-based PID controller , 1999 .

[12]  Panganamala Ramana Kumar,et al.  Cyber–Physical Systems: A Perspective at the Centennial , 2012, Proceedings of the IEEE.

[13]  Raffaello D'Andrea,et al.  The Cubli: A cube that can jump up and balance , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Alexandre M. Bayen,et al.  Evaluation of traffic data obtained via GPS-enabled mobile phones: The Mobile Century field experiment , 2009 .

[15]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[16]  Sudhir R. Ghorpade,et al.  A Course in Multivariable Calculus and Analysis , 2009 .

[17]  Christian Stöcker,et al.  Event-based control with incomplete state measurement and guaranteed performance* , 2012 .

[18]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[19]  J.S. Baras,et al.  Multiple Sampling for Estimation on a Finite Horizon , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[20]  Cleve B. Moler,et al.  Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later , 1978, SIAM Rev..

[21]  G. E. Taylor,et al.  Computer Controlled Systems: Theory and Design , 1985 .

[22]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .

[23]  Mircea Lazar,et al.  On Event Based State Estimation , 2009, HSCC.

[24]  Karl Henrik Johansson,et al.  Estimation over heterogeneous sensor networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[25]  Raffaello D'Andrea,et al.  Reduced communication state estimation for control of an unstable networked control system , 2011, IEEE Conference on Decision and Control and European Control Conference.

[26]  J. Farrell,et al.  The global positioning system and inertial navigation , 1999 .

[27]  Sebastian Trimpe,et al.  A limiting property of the matrix exponential with application to multi-loop control , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[28]  Rolf Findeisen,et al.  Stabilizing nonlinear predictive control over non deterministic communication networks , 2008 .

[29]  Davide Brunelli,et al.  Wireless Sensor Networks , 2012, Lecture Notes in Computer Science.

[30]  Nandit Soparkar,et al.  Trading computation for bandwidth: reducing communication in distributed control systems using state estimators , 2002, IEEE Trans. Control. Syst. Technol..

[31]  Dominique Bonvin,et al.  Global stabilization of an inverted pendulum-Control strategy and experimental verification , 2009, Autom..

[32]  J. Wen,et al.  Nonlinear Model Predictive Control for the Swing-Up of a Rotary Inverted Pendulum , 2004 .

[33]  T. Başar,et al.  Optimal Estimation with Limited Measurements , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[34]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[35]  Mark W. Spong,et al.  Underactuated mechanical systems , 1998 .

[36]  Bruno Sinopoli,et al.  Kalman filtering with intermittent observations , 2004, IEEE Transactions on Automatic Control.

[37]  S. Trimpe,et al.  The Balancing Cube: A Dynamic Sculpture As Test Bed for Distributed Estimation and Control , 2012, IEEE Control Systems.

[38]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[39]  J. E. Luntz,et al.  A distributed control system for flexible materials handling , 1997 .

[40]  Peter Neumann,et al.  Communication in industrial automation—What is going on? , 2004 .

[41]  Raffaello D'Andrea,et al.  An Experimental Demonstration of a Distributed and Event-Based State Estimation Algorithm , 2011 .

[42]  Ian F. Akyildiz,et al.  Wireless sensor networks: a survey , 2002, Comput. Networks.

[43]  A. Goldsmith,et al.  Wireless network design for distributed control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[44]  W. P. M. H. Heemels,et al.  On integration of event-based estimation and robust MPC in a feedback loop , 2010, HSCC '10.

[45]  Chee-Yee Chong,et al.  Sensor networks: evolution, opportunities, and challenges , 2003, Proc. IEEE.

[46]  Jan Lunze,et al.  Stability and performance of switching Kalman filters , 2002 .

[47]  Michael D. Lemmon,et al.  Weakly coupled event triggered output feedback control in wireless networked control systems , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[48]  Raffaello D'Andrea,et al.  Coordinating Hundreds of Cooperative, Autonomous Vehicles in Warehouses , 2007, AI Mag..

[49]  J.M. Fowler,et al.  A formation flight experiment , 2003, IEEE Control Systems.

[50]  Karl Henrik Johansson,et al.  Distributed Event-Triggered Estimation in Networked Systems , 2012, ADHS.

[51]  D. Bernstein,et al.  Dynamics and control of a 3D pendulum , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[52]  Kaustubh Pathak,et al.  Velocity and position control of a wheeled inverted pendulum by partial feedback linearization , 2005, IEEE Transactions on Robotics.

[53]  Raffaello D'Andrea,et al.  The Distributed Flight Array , 2010, 2010 IEEE International Conference on Robotics and Automation.

[54]  John Appelgren.  Robotic Adventure Across the Pacific: 313 Days, 17,486 Nautical km, One Cyclone, Millions of Data Points , 2013, IEEE Robotics & Automation Magazine.

[55]  Bart De Schutter,et al.  Online least-squares policy iteration for reinforcement learning control , 2010, Proceedings of the 2010 American Control Conference.

[56]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[57]  N. Harris McClamroch,et al.  Asymptotic Stabilization of the Inverted Equilibrium Manifold of the 3-D Pendulum Using Non-Smooth Feedback , 2009, IEEE Transactions on Automatic Control.

[58]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[59]  A. Nazli Gündes,et al.  Low order decentralized stabilizing controller design for a mobile inverted pendulum robot , 2009, 2009 American Control Conference.

[60]  J.P. Hespanha,et al.  Estimation under uncontrolled and controlled communications in Networked Control Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[61]  Karl Henrik Johansson,et al.  Actuator saturation and anti-windup compensation in event-triggered control , 2012, Discrete Event Dynamic Systems.

[62]  S. Elaydi.  An introduction to difference equations , 1995 .

[63]  Tai C Yang,et al.  Networked control system: a brief survey , 2006 .

[64]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[65]  Brett Ninness,et al.  Nonlinear model predictive control of an inverted pendulum , 2009, 2009 American Control Conference.

[66]  Sandra Hirche,et al.  Structural characterization of optimal event-based controllers for linear stochastic systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[67]  Sergei Lupashin,et al.  A platform for aerial robotics research and demonstration: The Flying Machine Arena , 2014 .

[68]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[69]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[70]  Thierry Floquet,et al.  Second‐order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum , 2008 .

[71]  Olfa Kanoun,et al.  Sensor technology advances and future trends , 2004, IEEE Transactions on Instrumentation and Measurement.

[72]  A. Stubbs,et al.  Multivehicle systems control over networks: a hovercraft testbed for networked and decentralized control , 2006, IEEE Control Systems.

[73]  R.M. Murray,et al.  MVWT-II: the second generation Caltech Multi-Vehicle Wireless Testbed , 2004, Proceedings of the 2004 American Control Conference.

[74]  S. Campbell,et al.  Singular Perturbation of Autonomous Linear Systems , 1979 .

[75]  Karl Henrik Johansson,et al.  An experimental study on the fuel reduction potential of heavy duty vehicle platooning , 2010, 13th International IEEE Conference on Intelligent Transportation Systems.

[76]  Sebastian Trimpe,et al.  Event-based state estimation with variance-based triggering , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[77]  Michael D. Lemmon,et al.  Event-Triggered Feedback in Control, Estimation, and Optimization , 2010 .

[78]  S. Campbell.  Singular perturbation of autonomous linear systems, II , 1978 .

[79]  Seul Jung,et al.  Control Experiment of a Wheel-Driven Mobile Inverted Pendulum Using Neural Network , 2008, IEEE Transactions on Control Systems Technology.

[80]  Iven M. Y. Mareels,et al.  Decentralized control design of interconnected chains of integrators: A case study , 2008, Autom..

[81]  Vijay Kumar,et al.  Experimental Testbed for Large Multirobot Teams , 2008, IEEE Robotics Autom. Mag..

[82]  Martin Hilbert,et al.  The World’s Technological Capacity to Store, Communicate, and Compute Information , 2011, Science.

[83]  P. Horacek.  Laboratory Experiments for Control Theory Courses: A Survey , 2000 .

[84]  S. Trimpe,et al.  Event-Based State Estimation with Switching Static-Gain Observers ⋆ , 2012 .

[85]  John,et al.  Strapdown Inertial Navigation Technology - 2nd Edition , 2005 .

[86]  Jan Lunze.  Ein Beispiel für den Entwurf schaltender Beobachter (An Example for the Design of Switching Observers) , 2000 .

[87]  Y. Tipsuwan,et al.  Control methodologies in networked control systems , 2003 .

[88]  Christian Stöcker,et al.  Stability analysis of interconnected event-based control loops , 2012, ADHS.

[89]  John J. Craig,et al.  Introduction to robotics - mechanics and control (2. ed.) , 1989 .

[90]  D. Luenberger.  An introduction to observers , 1971 .

[91]  Sandra Hirche,et al.  On the Optimality of Certainty Equivalence for Event-Triggered Control Systems , 2013, IEEE Transactions on Automatic Control.

[92]  Daniel Lehmann,et al.  Event-based output-feedback control , 2011, 2011 19th Mediterranean Conference on Control & Automation (MED).

[93]  S. Bittanti,et al.  The difference periodic Ricati equation for the periodic prediction problem , 1988 .

[94]  Raffaello D'Andrea,et al.  Optimization-based iterative learning control for trajectory tracking , 2009, 2009 European Control Conference (ECC).

[95]  J.P. Hespanha,et al.  Optimal communication logics in networked control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[96]  Rong-Jong Wai,et al.  Design of Cascade Adaptive Fuzzy Sliding-Mode Control for Nonlinear Two-Axis Inverted-Pendulum Servomechanism , 2008, IEEE Transactions on Fuzzy Systems.

[97]  M. Lemmon,et al.  Event-triggered state estimation in vector linear processes , 2010, Proceedings of the 2010 American Control Conference.

[98]  Katsuhisa Furuta,et al.  Swinging up a pendulum by energy control , 1996, Autom..

[99]  Sebastian Trimpe,et al.  Accelerometer-based tilt estimation of a rigid body with only rotational degrees of freedom , 2010, 2010 IEEE International Conference on Robotics and Automation.

[100]  Russ Tedrake,et al.  Simulation-based LQR-trees with input and state constraints , 2010, 2010 IEEE International Conference on Robotics and Automation.

[101]  Jan Lunze,et al.  A state-feedback approach to event-based control , 2010, Autom..

[102]  N. McClamroch,et al.  Mathematical Models for the Triaxial Attitude Control Testbed , 2003 .

[103]  George W. Irwin,et al.  Wireless networked control systems with QoS-based sampling , 2007 .

[104]  Junmin Li,et al.  Decentralized Output-Feedback Neural Control for Systems With Unknown Interconnections , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[105]  Bohn Stafleu van Loghum,et al.  Online … , 2002, LOG IN.