Optimization approaches for controller and schedule codesign in networked control

We consider the offline optimization of a sequence for communication scheduling in networked control systems. Given a continuous-time Linear Quadratic Regulator (LQR) problem we design a sampled-data periodic controller based on the continuous time LQR controller that takes into account the limited communication medium and inter-sampling behavior. To allow for a Riccati equation approach, singularities in the weighting matrices and time-variance are accounted for using a lifting approach. Optimal scheduling can be obtained by solving a complex combinatorial optimization problem. Two stochastic algorithms will be proposed to find a (sub)optimal sequence and the associated optimal controller which is the result of a discrete algebraic Riccati equation for the given optimal sequence

Controllability, Observability in Networked Control

We reconsider and advance the analysis of structural properties (controllability and observability) of a class of linear Networked Control Systems (NCSs). We model the NCS as a periodic system with limited communication where the non updated signals can either be held constant (the zero-order-hold case) or reset to zero. Periodicity is dealt using the lifting technique. We prove that a communication sequence that avoids particularly defined pathological sampling rates and updates each actuator signal only once is sufficient to preserve controllability (and observability for the dual problem of sensor scheduling). These sequences can be shorter than previously established and we set a tight lower bound to them

Solvability of the Inverse Optimal Control problem based on the minimum principle

In this paper, the solvability of the Inverse Optimal Control (IOC) problem based on two existing minimum principal methods, is analysed. The aim of this work is to answer the question regarding what kinds of trajectories, that is depending on the initial conditions of the closed-loop system and system dynamics, of the original optimal control problem, will result in the recovery of the true weights of the reward function for both the soft and the hard-constrained methods [1], [2]. Analytical conditions are provided which allow to verify if a trajectory is sufficiently conditioned, that is, holds sufficient information to recover the true weights of an optimal control problem. It was found that the open-loop system of the original optimal problem has a stronger influence on the solvability of the Inverse Optimal Control problem for the hard-constrained method as compared to the soft-constrained method. These analytical results were validated via simulation.Comment: 8 pages, submitted to IEEE Transactions on Automatic Contro

Distributed optimisation and control of graph Laplacian eigenvalues for robust consensus via an adaptive multi-layer strategy

Functions of eigenvalues of the graph Laplacian matrix L, especially the extremal non-trivial eigenvalues, the algebraic connectivity2and the spectral radiusn, have been shown to be important in determining the performance in a host of consensus and synchronisation applications. In this paper, we focus on formulating an entirely distributed control law for the control of edge weights in an undirected graph to solve a constrained optimisation problem involving these extremal eigenvalues.As an objective for the distributed control law, edge weights must be found that minimise the spectral radius of the graph Laplacian, thereby maximising the robustness of the network to time delays under a simple linear consensus protocol. To constrain the problem, we use both local weight constraints that weights must be non-negative, and a global connectivity constraint, maintaining a designated minimum algebraic connectivity. This ensures that the network remains sufficiently well connected.The distributed control law is formulated as a multilayer strategy, using three layers of successive distributed estimation. Adequate timescale separation between the layers is of paramount importance for the proper functioning of the system, and we derive conditions under which the distributed system converges as we would expect for the centralised control or optimisation system to converge