CDC 2018 Workshop on

Parameter Convergence in Adaptive Control without Persistence of Excitation

Date, Time and Location: Sunday, December 16, 2018, 9:00 am – 1:00 pm, Splash 7-8, Fontainebleau Hotel, Miami Beach, FL, USA.

Organizers:

Ø Sayan Basu Roy, IIT Delhi, India.(email: sayanetce@gmail.com)

Ø Shubhendu Bhasin, IIT Delhi, India.(email: sbhasin@ee.iitd.ac.in)

Ø Rushikesh Kamalapurkar, Oklahoma State University, USA.(email:rushikesh.kamalapurkar@okstate.edu)

Objectives:

This workshop is aimed at providing a comprehensive understanding of recent adaptive control algorithms with a special focus on parameter convergence and transient performance improvement. Classical adaptive controllers typically guarantee closed-loop system stability and asymptotic convergence of tracking error, however, parameter convergence is only guaranteed if a stringent condition of persistence of excitation (PE) is satisfied by the regressor signal. Some recent contributions in adaptive control, like concurrent learning (CL), integral concurrent learning (ICL), Initial Excitation (IE)-based adaptive control, have shown that parameter convergence is possible without requiring the restrictive PE condition, rather milder conditions like a full-rank condition on past stored data along systems trajectory (in CL-based framework) or the condition of initial excitation (in IE-based framework) can suffice for parameter convergence, and thereby improve transient response by ensuring exponential stability. The workshop would cover crucial details of these recent developments for relaxing the PE condition for parameter convergence in adaptive control.

Broad Areas Covered:

Ø Stability/Convergence properties of Classical Adaptive Control

Ø Stability/Convergence properties of Composite Adaptive Control

Ø Persistence of Excitation (PE) condition and its practical limitations

Ø Recent Advances to relax the PE condition for parameter convergence

Ø Concurrent Learning (CL)-based Adaptive Control

Ø Integral Concurrent Learning (ICL)-based Adaptive Control

Ø Initial Excitation (IE)-based Adaptive Control

Expected Outcome:

The workshop aims to provide a comprehensive exposition to the issue of parameter convergence in adaptive control with an in-depth understanding of the underlying mathematical framework. The workshop attendees would be exposed to new classes of adaptive controllers which relax the PE condition for parameter convergence, and thereby guarantee exponential convergence of tracking and parameter estimation error to zero. As the design methodologies are mostly based on modifications in the adaptive estimation routine without hampering the classical Lyapunov-based component, these design algorithms would be widely applicable to a varied class of linear/nonlinear systems, which are already known to be stabilized by classical adaptive design methodologies.

Target Audience:

This workshop will be beneficial to a wide range of people from academia as well as industry (it is expected that the audience is having some preliminary understanding of classical adaptive control.), since the new techniques are on one hand analytically rigorous and on the other hand they have immediate practical significance in terms of transient performance and robustness enhancement of the adaptive controllers. For graduate students and researchers with an interest in adaptive control, this workshop would expose them to the recent advances in adaptive control with a focus on parameter convergence and transient performance improvement. This workshop also aims at attracting researchers interested in applications and practising engineers, who wish to know the implementation aspects of these new adaptive control techniques. Industries related to aircraft, spacecraft, robotics, process control etc., where adaptive control is popularly used, will especially benefit from the workshop, since they can learn how to suitably integrate these high performance adaptive control techniques with the existing adaptive control architecture.

List of Speakers:

Ø Sayan Basu Roy, IIT Delhi, India.

Ø Shubhendu Bhasin, IIT Delhi, India.

Ø Rushikesh Kamalapurkar, Oklahoma State University, USA.

Ø Girish Chowdhary, UIUC, USA.

Ø Warren Dixon, University of Florida, Gainesville, USA.

Tentative Title and Abstract of the Presentations:

Ø Adaptive Control and Parameter Convergence

by Sayan Basu Roy & Shubhendu Bhasin

Abstract: This talk would recapitulate the basic concepts of adaptive control in brief and comment on the stability/convergence properties of classical and composite adaptive controllers. The definition of persistence of excitation (PE) would be introduced with simple examples and its effect on parameter convergence would be discussed. The practical limitations of classical PE condition would be emphasised to motivate the need for recently developed adaptive controllers like concurrent learning (CL), integral concurrent learning (ICL) and initial excitation (IE)-based techniques, which ensure parameter convergence without requiring the restrictive PE condition.

Concurrent learning and beyond: Towards adaptive control with learning and guarantees

by Girish Chowdhary

Abstract: TBD

Related video:

Reference: Girish Chowdhary, Eric N. Johnson, Rajeev Chandramohan, M. Scott Kimbrell, and Anthony Calise. "Guidance and Control of Airplanes under Actuator Failures and Severe Structural Damage", Journal of Guidance, Control, and Dynamics, Vol. 36, No. 4 (2013), pp. 1093-1104.

Ø Integral Concurrent Learning and Finite Window Integrals

by Warren Dixon

Abstract: TBD

Ø Concurrent learning for simultaneous state and parameter estimation

by Rushikesh Kamalapurkar

Abstract: In this talk, concurrent learning techniques are described for a class of nonlinear systems where state measurements are unavailable. Excitation over a finite time-interval (as opposed to persistent excitation) is required for exponential convergence in the linear case and practical convergence in the nonlinear case for the state and the parameter estimates. Purging methods are developed to refresh the concurrent learning history stacks to capitalize on the improved state estimates. Applications of the developed method for model-based adaptive dynamic programming and model-based inverse reinforcement learning are also discussed.

Ø Initial Excitation based Adaptive Control and Two-tier Filter Architecture

by Sayan Basu Roy & Shubhendu Bhasin

Abstract: This talk would provide a comprehensive description of two-tier filter design based adaptive control mechanism, which ensures parameter convergence using a newly introduced concept of initial excitation (IE). It has been established in several research papers of the speakers that the IE condition is remarkably less stringent than the classical PE condition while being online-verifiable unlike PE. The talk would cover several aspects of the IE-based adaptive control including intuitive motivation, analytical proofs, algorithmic implementation and real world applications of the proposed set of adaptive controllers.