Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

Abstract

Summary This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.

Robust Tube-based Model Predictive Control for Time-constrained Robot Navigation

“…Tube-based approaches for affine in the control continuous-time nonlinear systems with constant matrices multiplying the control input vectors have been proposed in [14], which we aim to extend here in order to cover a larger class of nonlinear systems. Preliminary results in tube-based NMPC for nonlinear non-affine systems that state and input space have the same dimension can be found in our earlier work [15]. In the current paper, these results are extended to underactuated systems, which arise in robotic applications with Lagrangian kinematics/dynamics models and their controller design constitutes a challenging task.…”

“…Intuitively, the sets E, V and U are tightened accordingly, in order to guarantee that while the nominal states e, v and the nominal control input u are calculated, the corresponding real states e, v and real control input u satisfy the state and input constraints E, V and U, respectively. This constitutes a standard constraints set modification technique adopted in tube-based NMPC frameworks (for more details see [14], [15]). Define the terminal set by:…”

A Tube-based MPC Scheme for Interaction Control of Underwater Vehicle Manipulator Systems

“…Due to the fact that it is required to design a feedback control law that guarantees the minimization of the term F(t) − F des 2 , as t → ∞, under state and input constraints given by (9), we utilize a Nonlinear Model Predictive Control (NMPC) framework [8]- [10]. Furthermore, since the UVMS is under the presence of disturbances/uncertainties d ∈ D, we provide a robust analysis, the so-called tube-based robust NMPC approach [4], [11]. In particular, first, the error states and the corresponding transformed constraints sets are defined in Section IV-A.…”

Robust Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles

“…Due to the fact that only the state of the nominal system is used while the FHOCP (31a)-(31d) is solved, the on-line optimization does not depend on the disturbances. Thus, the feasibility proof follows same arguments as in [31], [35], [36] and is omitted here. Regarding the convergence analysis, due to the fact that the set P is an RPI set, it holds that:…”