On LQG joint optimal scheduling and control under communication constraints

Abstract

In this paper, we consider a discrete-time stochastic system, where sensor measurements are sent over a network to the controller. The design objective is a non-classical multicriterion optimization problem for finite horizon, where the cost function consists of the linear quadratic cost reflecting the control performance and a communication cost penalizing information exchange between sensor and controller. It is shown that the joint optimization of scheduling and control can be separated into three subproblems: an optimal regulator problem, an estimation problem and an optimal scheduling problem. The obtained results are extended to TCP-like networks with random packet loss. In the proposed framework, we classify three classes of schedulers, a purely randomized, a deterministic and a state-dependent scheme, and compare their performance by a numerical example.

Structural characterization of optimal event-based controllers for linear stochastic systems

“…The obtained results extend the results of [12] to the case of noisy observations at the event-trigger. It is shown that the optimal event-triggered controller consists of an affine linear controller, where the gains can be obtained by standard methods.…”

Order reduction in optimal event-triggered control design for linear stochastic systems

“…In addition, the different information patterns [13] of event-trigger and controller prohibit a direct use of dynamic programming. However, it is shown in [7] that minimizing the cost function given by (3) for a finite horizon N can be divided into separate subproblems. Therein, the optimal control law is related to linear quadratic regulation and the event-triggering law can be posed in the framework of dynamic programming.…”

“…With the mild restriction to stationary policies, the reformulation techniques developed in [7] for finite horizon problems also apply for the average-cost problem.…”

“…Theorem 1 ( Structure of the optimal controller [7]): Let the event-trigger and controller be causal and stationary. Then, the optimal control law minimizing (3) is given by…”

“…The main contribution of this paper is twofold. Built on results in [7] for finite horizon, we first show that, under mild conditions, the calculation of the optimal event-triggered controller for the average-cost criterion can be separated into standard subproblems. Second, we show that the structure of the optimal event-trigger admits an approximative model-order reduction, where the reducedorder system has a dimension equal to the number of control inputs.…”