Control & Stability

Feedback and stability

This thread supplies the dynamical perspective for the entire program. A continually adapting learner changes the environment, data distribution, and evaluation conditions it will encounter next. Its updates therefore form a closed-loop dynamical system rather than a sequence of independent optimization problems. My long-term interest is in translating ideas from system identification and stability analysis into guarantees for adaptive models and agent systems.

A feedback block diagram: an objective enters a summing junction, the learner updates its parameters, its policy acts on the environment, which determines the data it sees next, and an evaluator turns outcomes into feedback that returns to the junction. Below, two trajectories of repeated adaptation in parameter space: a stable spiral that settles, and an unstable one that oscillates and drifts. The loop changes its own data, evaluator, environment, and target; the guarantees wanted are stability, identification, convergence, and a robustness margin. — Scroll sideways to see the full diagram.

Key Questions

What is the appropriate notion of stability for a learner whose updates change its future data and evaluation conditions?
How can such a system be identified when the learner's interventions alter the environment?
When do locally improving updates produce globally stable behavior rather than drift, oscillation, or collapse?

Selected Publications

Extending The Concept of Analog Butterworth Filter For Fractional Domain

Signal Processing 2014

Designs fractional-order Butterworth filters in the complex w-plane, including under-, hyper-, and ultra-damped poles, and demonstrates the formulation in simulations and a frequency-domain design example.
Simulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors

Math. Comp. Simulation 2014

Uses real-coded genetic-algorithm optimization to tune PID controllers for four Lorenz-family multi-wing chaotic systems, with robustness checked across initial conditions.
Stability Analysis Of Delayed System Using Bode's Integral

ICCCI 2013

Tunes PID controllers for delayed plants using Bode's integral and a Padé approximation of the delay, then compares the approach with genetic-algorithm tuning in MATLAB simulations.
Identification of nonlinear systems from the knowledge around different operating conditions: a feed-forward multilayer Artificial Neural Net (ANN) based approach

PDGC 2012

Identifies nonlinear systems from outputs near several linearized operating points using feed-forward multilayer neural networks, evaluated on nuclear-reactor monitoring and AC-servo control.
Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems

ICCCNT 2012

Applies real-coded genetic-algorithm optimization to tune PID control of Lorenz-like multi-wing chaotic attractors and compares the resulting state trajectories.
Optimized Quality Factor of Fractional Order Analog Filters with Band-Pass and Band-Stop Characteristics

ICCCNT 2012

Studies fractional-order band-pass and band-stop filters, whose characteristics are unavailable to conventional integer-order filters below second order, and optimizes their quality factor.
Least square and instrumental variable system identification of AC servo position control system with fractional Gaussian noise

ICEAS 2011

Compares least-squares and instrumental-variable estimators for identifying an AC-servo position-control system under white and fractional Gaussian measurement noise.