Multiple-Timescale

Jillian Bennett defends Masters Thesis

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Jillian Bennett successfully defended her M.S. thesis on June 11th, 2025.  Jill has been with VSCL since her senior year in Spring 2023 and is highly engaged in control theory, and flight testing. The title of her thesis is: Nonlinear Adaptive Multiple Time Scale Stability Analysis For An Arbitrary Number Of Time Scales

 Multiple time scale systems are a set of subsystems that are dependent on each other yet have a large separation in the time which the dynamics progress. Systems of this sort are often simplified by dismissing the dependencies between vehicle states, however, the true dynamics get lost and are important to the stability of the system. Additionally, true systems have uncertain plant dynamics and disturbances that can cause instability. Therefore, a method of control must be used to account for uncertainties. Adaptive control has been shown to counteract these additional sources of motion. A combination of adaptive control and multiple time scale control for nonlinear systems is applicable to and necessary for the systems mentioned above and has been demonstrated in a method called [K]Control of Adaptive Multiple Time Scale Systems (KAMS), yet only accounts for two time scale systems. This work extends the theory and stability proof of KAMS to account for a system with any number of time scales. It also further analyzes the limitations to the time scale separation parameter size of a two and three time scale system.

Jill developed and conducted outstanding theory for nonlinear time scale systems, and the work will continue. Jill is doing a summer grad internship with Naval Research Laboratory to flight test the nonlinear multiple time scale control laws, and then she is staying with VSCL and continuing on to the Ph.D.  Very glad to have you for another degree Jill!

Jill’s research is supported by the Office of Naval Research on the project Novel Multiple Time Scale Adaptive Control for Uncertain Nonlinear Dynamical Systems. Jill’s is the 64th graduate degree completed that Dr. John Valasek has advised.

Dr. John Valasek Reaches Career Milestone

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In October Dr. John Valasek reached a career milestone by presenting at his 100th invited seminar/lecture/panelist.

Chronologically:

#1 “Fighter Agility Metrics, Research, and Test,” Lockheed Advanced Development Projects Division (Skunk Works), Burbank, CA, 13 July 1990.

#100 “Multiple-Time-Scale Nonlinear Output Feedback Control of Systems With Model Uncertainties,” Department of Aerospace Engineering, University of Maryland, College Park, MD, 9 October 2024.

Congratulations Dr. Valasek!

VSCL Awarded Research Contract for Novel Multiple Time Scale Adaptive Control for Uncertain Nonlinear Dynamical Systems by Office of Naval Research

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Dr. John Valasek and the Vehicle Systems & Control Laboratory has been awarded a multi-year (2023-2026) research grant by the Office of Naval Research (ONR) to investigate multiple time scale (MTS) adaptive control systems for naval applications such as unmanned air systems (UAS), high performance aircraft, and satellites. MTS systems are systems with some states that evolve quickly and some states that evolve slowly. These systems can have coupled fast and slow modes which occur simultaneously. MTS systems are particularly interesting from a controls perspective because the time scale separation in the plant can cause degraded performance or even instability under traditional control methods. Accounting for the time scales can remedy this problem. For example, a MTS control technique demonstrated significantly reduced rise times over traditional Nonlinear Dynamic Inversion (NDI). Similarly, traditional adaptive control has been demonstrated to have reduced performance on MTS systems. On the other hand, traditional control techniques that are specifically designed for MTS systems cannot account for systems with model uncertainties. Thus, a method of MTS control for uncertain systems is needed.

A novel methodology called [K]Control of Adaptive MTS Systems (KAMS) is developed which expands upon the class of dynamical systems to which MTS control and adaptive control can apply. While other techniques use elements of adaptive control and MTS control, other research stops short of fully and rigorously combining them. KAMS is a significant improvement over prior methods and provides insight into the physics of the system. It is capable of controlling systems with model uncertainty unlike traditional MTS control, and is robust to systems with unstable zeros unlike traditional adaptive control and feedback linearization.

In addition to investigating theoretical research questions for KAMS, hardware validation of the resulting theory will be performed with a flight testing evaluation campaign using a small unmanned air system (UAS), both fixed-wing and rotorcraft, operating in a challenging environment.

More details of the benefits of KAMS and the research objectives for this project can be found here: https://vscl.tamu.edu/research/novel-multiple-time-scale-adaptive-control-for-uncertain-nonlinear-dynamical-systems/

This project is part of VSCL’s ongoing work in the area of Autonomous, Nonlinear Control of Air, Space and Ground Systems

Valasek to give invited talk at the Systems and Control mini-symposia at the 2023 SIAM Conference on Control and Its Applications (CT23)

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Dr. John Valasek, Professor in the Department of Aerospace Engineering at Texas A&M University and Director of the Vehicle Systems & Control Laboratory, will give an invited talk titled “Multiple-Time-Scale Nonlinear Output Feedback Control of High Performance Aircraft, “ on 25 July 2023 for the Systems and Control mini-symposia at the SIAM Conference on Control and Its Applications (CT23), Philadelphia, PA, July 24-26, 2023.

Abstract:  The Geometric Singular Perturbation theory (Fenichel, 1979) is a powerful control law development tool for multiple-timescale systems because it provides physical insight into the evolution of the states in more than one timescale. The behaviour of the full-order system can be approximated by the slow subsystem, provided that the fast states can be stabilised on an equilibrium manifold. The fast subsystem describes how the fast states evolve from their initial conditions to their equilibrium trajectory or the manifold. This presentation develops two nonlinear, multiple-time-scale, output feedback tracking controllers for a class of nonlinear, nonstandard systems with slow and fast states, slow and fast actuators, and model uncertainties. The class of systems is motivated by aircraft with uncertain inertias, control derivatives, engine time-constant, and without direct measurement of angle-of-attack and sideslip angle. Each controller is synthesized using time-scale separation, lower-order reduced subsystems, and estimates of unknown parameters and unmeasured states. The update laws are so chosen that errors remain ultimately bounded for the full-order system.

The controllers are simulated on a nonlinear, six-degree-of-freedom, F-16A Fighting Falcon model performing a demanding combined maneuver. The slow state tracker accomplishes the maneuver with less control effort, while the simultaneous slow and fast state tracker does so with a smaller number of gains to tune.

Eves and Valasek Publish “Slow Timescale Adaptive Control for Multiple-Timescale Systems,” in Journal of Guidance, Control, and Dynamics

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Ph.D. student Kameron Eves and Dr. John Valasek of VSCL published the paper “Slow Timescale Adaptive Control for Multiple-Timescale Systems,” in Journal of Guidance, Control, and Dynamics.

Multiple-timescale systems are a noteworthy class of dynamical systems that can be modeled with singularly perturbed differential equations. Adaptive control has not been studied in the context of singularly perturbed plants. This paper introduces and evaluates three methods of adaptive control for multiple-timescale systems. Each method is a framework that is valid for a wide class of adaptive control methods. Full-Order Adaptive Control (FOAC) applies adaptive control to the system as a whole.  It is straightforward but can be sensitive to timescale effects.  Reduced-Order Adaptive Control (ROAC) applies adaptive control to either the fast or slow modes only. This simplifies synthesis but can also constrain the range of valid timescale separation. [K]Control of Adaptive Multiple-timescale Systems (KAMS) fuses two adaptive control signals using multiple-timescale techniques.  KAMS takes advantage of model reduction unlike FOAC, and allows for unstable fast dynamics unlike ROAC. Generalized formal definitions, stability criteria, and examples are developed and presented for each method.  Results presented in the paper for the control of a Boeing 747-100/200 on approach show that [K]Control of Adaptive Multiple-timescale Systems has a desirable blend of performance and robustness because each reduced-order model is stabilized separately.

This publication is part of VSCL’s ongoing work in the area of nonlinear multiple time-scale control.  The early access version of the article can be viewed at https://arc.aiaa.org/doi/full/10.2514/1.G007439

Kameron Eves Defends Ph.D. Dissertation on Wednesday, 1 March 2023

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Kameron Eves (B.S. Mechanical Engineering, BYU) successfully defended his Ph.D. dissertation titled “Multiple-Timescale Adaptive Control for Uncertain Nonlinear Dynamical Systems”. Kameron’s dissertation investigated combining nonlinear multiple time-scale controllers that VSCL has been researching for the last 15 years, with adaptive controllers which VSCL has been researching for more than 20 years.  Multiple-timescale control has been shown to have difficulty with uncertain systems and adaptive control has been shown to have difficulty with multiple-timescale systems.  His dissertation describes a novel control methodology called [K]Control of Adaptive Multiple-timescale Systems (KAMS).  KAMS seeks to address systems that simultaneously exhibit uncertain and multiple-timescale behaviors.  Unlike traditional multiple-timescale control literature, KAMS uses adaptive control to stabilize the subsystems.  The reference models and adapting parameters used in adaptive control significantly complicate the stability analysis.  KAMS is a flexible theory and framework and the stability proofs apply to a wide array of adaptive algorithms and multiple-timescale fusion techniques.  Additionally, formal and numerical validation of how KAMS can relax the minimum phase assumption for a multitude of common adaptive control methods.  KAMS is demonstrated and evaluated on examples consisting of stabilization and attitude control of a quadrotor Unmanned Air System; fuel-efficient orbital transfer maneuvers; and preventing inlet unstart on hypersonic aircraft.

A proposal on KAMS was submitted to DoD sponsors, and the Office of Naval Research (ONR) awarded a three-year research project to continue this work, and flight test it.  Conference and journal papers are being written on this work.

Kameron’s is the 57th graduate degree earned by a VSCL graduate student.   Kameron graduated from the Mechanical Engineering Department at BYU in 2019, with minors in mathematics and business.  At BYU, Kameron worked in the Multiple Agent Intelligent Coordination and Control (MAGICC) laboratory.  He will be starting work as an Assistant Professor at Utah Tech University in June.