Data-driven distributed MPC of dynamically coupled linear systems

In this paper, we present a data-driven distributed model predictive control (MPC) scheme to stabilise the origin of dynamically coupled discrete-time linear systems subject to decoupled input constraints. The local optimisation problems solved by the subsystems rely on a distributed adaptation of the Fundamental Lemma by Willems et al., allowing to parametrise system trajectories using only measured input-output data without explicit model knowledge. For the local predictions, the subsystems rely on communicated assumed trajectories of neighbours. Each subsystem guarantees a small deviation from these trajectories via a consistency constraint. We provide a theoretical analysis of the resulting non-iterative distributed MPC scheme, including proofs of recursive feasibility and (practical) stability. Finally, the approach is successfully applied to a numerical example

An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem

In this paper, an off-policy reinforcement learning algorithm is designed to solve the continuous-time LQR problem using only input-state data measured from the system. Different from other algorithms in the literature, we propose the use of a specific persistently exciting input as the exploration signal during the data collection step. We then show that, using this persistently excited data, the solution of the matrix equation in our algorithm is guaranteed to exist and to be unique at every iteration. Convergence of the algorithm to the optimal control input is also proven. Moreover, we formulate the policy evaluation step as the solution of a Sylvester-transpose equation, which increases the efficiency of its solution. Finally, a method to determine a stabilizing policy to initialize the algorithm using only measured data is proposed.Comment: 7 page

On an integral variant of incremental input/output-to-state stability and its use as a notion of nonlinear detectability

We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system satisfies a certain continuity assumption involving the Osgood condition. We show that the proposed i-iIOSS notion is a necessary condition for the existence of a robustly globally asymptotically stable observer mapping in a time-discounted ``$L^2$-to-$L^\infty$'' sense. In combination, our results provide a general framework for a Lyapunov-based robust stability analysis of observers for continuous-time systems, which in particular is crucial for the use of optimization-based state estimators (such as moving horizon estimation).Comment: replaced with accepted versio