Value of Information in Feedback Control: Global Optimality

The rate-regulation tradeoff, defined between two objective functions, one penalizing the packet rate and one the regulation cost, can express the fundamental performance bound of networked control systems. However, the characterization of the set of globally optimal solutions in this tradeoff for multi-dimensional Gauss–Markov processes has been an open problem. In the present article, we characterize a policy profile that belongs to this set without imposing any restrictions on the information structure or the policy structure. We prove that such a policy profile consists of a symmetric threshold triggering policy based on the value of information and a certainty-equivalent control policy based on a non-Gaussian linear estimator. These policies are deterministic and can be designed separately. Besides, we provide a global optimality analysis for the value of information VoIk, a semantic metric that emerges from the rate-regulation tradeoff as the difference between the benefit and the cost of a data packet. We prove that it is globally optimal that a data packet containing sensory information at time k be transmitted to the controller only if VoIk becomes nonnegative. These results have important implications in the areas of communication and control

Value of Information in Feedback Control: Quantification

Although transmission of a data packet containing sensory information in a networked control system improves the quality of regulation, it has indeed a price from the communication perspective. It is, therefore, rational that such a data packet be transmitted only if it is valuable in the sense of a cost-benefit analysis. Yet, the fact is that little is known so far about this valuation of information and its connection with traditional event-triggered communication. In the present article, we study this intrinsic property of networked control systems by formulating a rate-regulation trade-off between the packet rate and the regulation cost with an event trigger and a controller as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this trade-off. In particular, we characterize an equilibrium in the rate-regulation trade-off, and quantify the value of information VoIk there as the variation in a so-called value function with respect to a piece of sensory information that can be communicated to the controller at each time k. We prove that, for a multi-dimensional Gauss--Markov process, VoIk is a symmetric function of the discrepancy between the state estimates at the event trigger and the controller, and that a data packet containing sensory information at time k should be transmitted to the controller only if VoIk is nonnegative. Moreover, we discuss that VoIk can be computed with arbitrary accuracy, and that it can be approximated by a closed-form quadratic function with a performance guarantee

Modelling, Monitoring, Control and Optimization for Complex Industrial Processes

This reprint includes 22 research papers and an editorial, collected from the Special Issue "Modelling, Monitoring, Control and Optimization for Complex Industrial Processes", highlighting recent research advances and emerging research directions in complex industrial processes. This reprint aims to promote the research field and benefit the readers from both academic communities and industrial sectors

Tradeoffs in stochastic event-triggered control

This paper studies the optimal output-feedback control of a linear time-invariant system where a stochastic event-based scheduler triggers the communication between the sensor and the controller. The primary goal of the use of this type of scheduling strategy is to provide significant reductions in the usage of the sensor-to-controller communication and, in turn, improve energy expenditure in the network. In this paper, we aim to design an admissible control policy, which is a function of the observed output, to minimize a quadratic cost function while employing a stochastic event-triggered scheduler that preserves the Gaussian property of the plant state and the estimation error. For the infinite horizon case, we present analytical expressions that quantify the tradeoff between the communication cost and control performance of such event-triggered control systems. This tradeoff is confirmed quantitatively via numerical examples. Besides, numerical simulations justify that the event-triggered control provides better quadratic control performance than the (traditional) periodic time-triggered control at the same average sampling rate.</p