There has recently been significant interest in feedback stabilization problems over communication channels, including several with bit rate limited feedback. Motivated by considering one source of such bit rate limits, we study the problem of stabilization over a signal-to-noise ratio (SNR) constrained channel. We discuss both continuous and discrete time cases, and show that for either state feedback, or for output feedback delay-free, minimum phase plants, there are limitations on the ability to stabilize an unstable plant over an SNR constrained channel. These limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity bit rate over the same channel.

Author's Reply to Comments on Feedback Stabilization Over Signal-to-Noise Ratio Constrained Channels

Global buildings account for about 30% of the total energy consumption and carbon emission, raising severe energy and environmental concerns. Therefore, it is significant and urgent to develop novel smart building energy management (SBEM) technologies for the advance of energy efficient and green buildings. However, it is a nontrivial task due to the following challenges. First, it is generally difficult to develop an explicit building thermal dynamics model that is both accurate and efficient enough for building control. Second, there are many uncertain system parameters (e.g., renewable generation output, outdoor temperature, and the number of occupants). Third, there are many spatially and temporally coupled operational constraints. Fourth, building energy optimization problems can not be solved in real time by traditional methods when they have extremely large solution spaces. Fifthly, traditional building energy management methods have respective applicable premises, which means that they have low versatility when confronted with varying building environments. With the rapid development of Internet of Things technology and computation capability, artificial intelligence technology find its significant competence in control and optimization. As a general artificial intelligence technology, deep reinforcement learning (DRL) is promising to address the above challenges. Notably, the recent years have seen the surge of DRL for SBEM. However, there lacks a systematic overview of different DRL methods for SBEM. To fill the gap, this article provides a comprehensive review of DRL for SBEM from the perspective of system scale. In particular, we identify the existing unresolved issues and point out possible future research directions.

A Review of Deep Reinforcement Learning for Smart Building Energy Management

Personal comfort systems: A review on comfort, energy, and economics

Occupancy-based HVAC control systems in buildings: A state-of-the-art review

SUMMARY

This paper is concerned with the robust H ∞  filter design for a class of uncertain singular time-delayed Markovian jump systems, whose transition rate matrix has elementwise bounded uncertainties. By the LMI approach, a novel bounded real lemma is proposed such that the singular Markovian jump system is robustly exponentially mean-square admissible with a prescribed H ∞  performance index. Based on this, a sufficient condition for the existence of a robust H ∞  filter is developed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Robust H ∞ filtering for singular time-delayed systems with uncertain Markovian switching probabilities

Most modern HVAC systems in office buildings are unable to meet diverse comfort requirements of the occupants and are not energy efficient. We propose to mitigate both issues by using personal comf...

On the interaction between personal comfort systems and centralized HVAC systems in office buildings

We consider a classical control problem: the infinite horizon singular LQ problem, i.e., some inputs are unpenalized in the quadratic performance index. In this case, it is known that the slow dynamics is constrained to be in a proper subspace of the state-space, with the optimal input for the slow dynamics implementable by feedback. In this technical note we show that both the fast dynamics and the slow dynamics can be implemented by a feedback controller. Moreover, we show that the feedback controller cannot be a static feedback controller but can be PD, i.e., proportional+differentiate exactly once, in the state. We show that the closed loop system is a singular descriptor state space system and we also characterize the conditions on the system/performance index for existence of inadmissible initial conditions, i.e., initial conditions that cause impulsive solutions. There are no inadmissible initial conditions in the controlled system if and only if in the strictly proper transfer matrix from the unpenalized inputs to the penalized states, there exists at least one maximal minor of relative degree equal to the number of unpenalized inputs. In addition to the above, we prove solvability of the infinite horizon singular LQ problem under milder assumptions than in the literature.

/pdf/singular-lq-control-optimal-pd-controller-and-inadmissible-26odbgsdih.pdf

Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

We consider a classical control problem: the infinite horizon singular LQ problem, i.e., some inputs are unpenalized in the quadratic performance index. In this case, it is known that the slow dynamics is con- strained to be in a proper subspace of the state-space, with the optimal input for the slow dynamics implementable by feedback. In this technical note we show that both the fast dynamics and the slow dynamics can be implemented by a feedback controller. Moreover, we show that the feed- back controller cannot be a static feedback controller but can be PD, i.e., , in the state. We show that the closed loop system is as ingular descriptor state space system and we also characterize the conditions on the system/performance index for existence of inadmissible initial conditions, i.e., initial conditions that cause impulsive solutions. There are no inadmissible initial conditions in the con- trolled system if and only if in the strictly proper transfer matrix from the unpenalized inputs to the penalized states, there exists at least one maximal minor of relative degree equal to the number of unpenalized inputs. In ad- dition to the above, we prove solvability of the infinite horizon singular LQ problem under milder assumptions than in the literature.

Technical Notes and Correspondence Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

Intelligent control of heating, ventilation, and air conditioning (HVAC) systems in commercial buildings have been extensively studied in the literature. Although prior work has shown the benefits of using Model Predictive Control (MPC), existing work falls short either by relying on linear HVAC models or using MPC assuming control actions at a single (hourly) time scale, although more frequent control is feasible for some HVAC elements. Our main contribution is the use of a bi-linear thermal model and the careful modeling of the multiple time-scales inherent in the operation of an HVAC system, which permits the design of a multiple time-scale MPC control. We find that employing a multiple time-scale MPC results in significantly better comfort in comparison to a single time-scale MPC, typically without an increase in power consumption. Moreover, there exist cases where there is a significant reduction in power consumption (40%) for the two time-scale MPC in comparison to the single time-scale, with no decrease in comfort.

Multiple time-scale model predictive control for thermal comfort in buildings

We study Hamiltonian systems, namely, systems comprising of trajectories which are `stationary' with respect to a quadratic performance index: they play a central role in many optimal control problems. A typical assumption in the literature is that of `regularity': the resulting first-order dynamical system is a regular state space system and not a singular descriptor system. In this paper we show that the first order representation of a Hamiltonian is a singular descriptor system if and only if the interconnection of a related MIMO system G(s) with its dual (i.e. its adjoint) is ill-posed. We address the possibility of existence of inadmissible initial conditions, i.e. initial conditions that give rise to impulsive solutions. We characterize conditions on G(s) under which the corresponding singular Hamiltonian system has inadmissible initial conditions. Under suitable simplifying assumptions, which amount to studying an extreme case of ill-posedness, our main result states that there exist no inadmissible initial conditions if and only if the skew-symmetric part of the first moment about s = ∞ of the transfer matrix G(s) is nonsingular; a condition we show that is opposite to that for G(s) to be an all-pass filter. As a corollary, ill-posed interconnection of a square MIMO system with odd number of inputs (in particular, SISO systems) with its adjoint always contains in inadmissible initial conditions.

/pdf/stationary-trajectories-singular-hamiltonian-systems-and-ill-dyg49ead4g.pdf

Rachel Kalpana Kalaimani

Papers

On the interaction between personal comfort systems and centralized HVAC systems in office buildings

Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

Technical Notes and Correspondence Singular LQ Control, Optimal PD Controller and Inadmissible Initial Conditions

Multiple time-scale model predictive control for thermal comfort in buildings

Stationary trajectories, singular Hamiltonian systems and ill-posed interconnection