Funnel-Inspired Closed-Form Control for Satisfaction of Spatiotemporal Constraints and Multi-Agent Coordination

QC 20260402

Abstract

Autonomous systems have become integral to industry and society, spanning applications from robotic platforms to autonomous vehicles and beyond. Most contemporary engineering systems exhibit complex nonlinear dynamics and are often subject to time-varying uncertainties, making high-fidelity modeling difficult. At the same time, these systems are increasingly required to execute complex tasks that extend beyond classical objectives such as set-point tracking and stabilization. In many real-world scenarios, they must satisfy spatiotemporal specifications, requirements that depend jointly on space and time. Such specifications can be formulated as time-varying constraints in control systems, and enforcing them is crucial for enhanced performance, guaranteed safety, and reliable, timely task execution. 

Funnel-based control methods provide closed-form feedback laws that enforce certain classes of time-varying constraints for uncertain nonlinear systems. The main focus of this thesis is to develop new robust closed-form control schemes, rooted in the core ideas of funnel-based control, to address broader classes of time-varying constraints that cannot be treated directly by conventional funnel-based methods. In addition, the thesis investigates distributed coordination of multi-agent systems under spatial constraints, as well as the application of funnel-based methods to multi-agent formation control under transient performance requirements.

The first part of the thesis is devoted to extending funnel-based control methods, particularly prescribed performance control (PPC), to address time-varying hard (safety) and soft (performance) funnel-type specifications. We then revisit the standard PPC design to highlight its limitations and to motivate the need for a new control framework. Building on the PPC design philosophy, we propose a novel robust closed-form control scheme that enforces generic time-varying set invariance for high-relative-degree, multi-input multi-output uncertain nonlinear systems, thereby accommodating classes of time-varying constraints beyond those handled by standard PPC. Finally, we extend the proposed design to treat potentially conflicting generalized time-varying hard and soft specifications, further broadening the applicability of the method.

In the second part of the thesis, we shift the focus to multi-agent coordination problems. First, we present a novel coordinate-free formation control scheme for directed leader–follower multi-agent systems that achieves almost-global convergence to a desired shape. Fully decentralized robust controllers are synthesized by leveraging the PPC framework to impose prescribed transient and steady-state performance on the agents’ formation errors, while ensuring robustness to system uncertainties. A key ingredient of the approach is the use of bipolar coordinates to obtain orthogonal (decoupled) formation-error coordinates for each follower. This not only promotes almost-global convergence to the desired shape but also enables a systematic and effective application of PPC. Finally, we introduce a distributed, task-based implicit formation determination and control problem in which each agent is subject to spatial constraints with respect to other agents and the environment. We reformulate the problem as a distributed optimization scheme and, based on this formulation, develop a control protocol for kinematic agents.

Link to DiVA