Stability and Performance Verification of Optimization-based Controllers
Milan Korda, Colin N. Jones

TL;DR
This paper introduces a sum-of-squares programming method to verify stability and performance of various optimization-based controllers for polynomial discrete-time systems, accommodating practical control scenarios.
Contribution
It develops a unified SOS-based framework to verify stability and performance of optimization-based controllers, including those with inexact models and soft constraints.
Findings
Applicable to a wide range of practical control problems.
Can verify stability and performance in stochastic and deterministic settings.
Handles controllers with fixed iteration solutions of first-order methods.
Abstract
This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the gain. The method applies to a wide range of practical control problems: For instance, a dynamical controller (e.g., a PID) plus input saturation, model predictive control with state estimation, inexact model and soft constraints, or a general optimization-based controller where the underlying problem is solved with a fixed number of iterations of a first-order method are all amenable to the proposed approach. The approach is based on the observation that the control input generated by…
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Taxonomy
TopicsAdvanced Control Systems Optimization · Control Systems and Identification · Advanced Optimization Algorithms Research
