Funnel-Based Control for Coupled Spatiotemporal Specifications

Abstract: In the past decade, the integration of spatiotemporal constraints into control systems has emerged as a crucial necessity, driven by the demand for enhanced performance, guaranteed safety, and the execution of complex tasks. Spatiotemporal constraints involve criteria that are dependent on both space and time, which can be represented by time-varying constraints in nonlinear control systems. Funnel-based control methods provide computationally tractable and robust feedback control laws to enforce time-varying constraints in uncertain nonlinear systems. This thesis begins by exploring the application of funnel-based control designs to address performance specifications in coordinate-free formation control of multi-agent systems. Moreover, we develop new robust feedback control schemes dealing with coupled spatiotemporal constraints in uncertain nonlinear systems that cannot be directly addressed by conventional funnel-based control methods.In the first part of the thesis, we present a novel coordinate-free formation control scheme for directed leader-follower multi-agent systems, exhibiting almost global convergence to the desired shape. The synthesis of fully decentralized robust controllers for agents is achieved through the application of the Prescribed Performance Control (PPC) method. This method imposes spatiotemporal funnel constraints on each agent's formation errors, ensuring a predefined transient and steady-state performance while maintaining robustness to system uncertainties. The core idea in this work is the utilization of bipolar coordinates to achieve orthogonal (decoupled) formation errors for each follower agent. This approach not only ensures the global convergence to the desired shape but also facilitates the effective application of the PPC method.In the second part of the thesis, first, we introduce a novel approach that extends funnel-based control schemes to deal with a specific class of time-varying hard and soft constraints. In this work, we employ an online Constraint Consistent Funnel (CCF) planning scheme to tackle couplings between hard and soft constraints. By satisfying these CCF constraints, we ensure adherence to hard (safety) constraints, while soft (performance) constraints are met only when they do not conflict with the hard constraints. Subsequently, we directly employ the PPC design method to craft a robust, low-complexity control law, ensuring that the system's outputs consistently stay within the online planned CCF constraints. In subsequent work, we tackle the challenge of satisfying a generalized class of potentially coupled time-varying output constraints. We show that addressing multiple constraints effectively boils down to formulating a single consolidating constraint. Ensuring the fulfillment of this consolidating constraint guarantees both convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Building on the PPC design method, we introduce a novel, robust low-complexity feedback control framework to handle this issue in uncertain high-order MIMO nonlinear control systems. Additionally, we present a mechanism for online modification of the consolidating constraint to secure a least-violating solution when constraint infeasibilities occur for an unknown time interval.