Optimizing Average Controllability of Networked Systems
In this paper, we consider the controllability of a networked system where each node in the network has higher order linear time-invariant (LTI) dynamics. We employ a quantitative measure for controllability based on average controllability. We relate this metric to the network topology and the dynamics of individual subsystems that constitute each node of the networked system. Using this, we show that, under certain assumptions, the average controllability increases with increased interactions across subsystems in the network. Next, we consider the problem of identifying an appropriate network topology when there are constraints on the number of links that exist in the network. This problem is formulated as a set function optimization problem. We show that for our problem, this set function is a monotone increasing supermodular function. Since maximization of such a function with cardinality constraints is a hard problem, we implement a greedy heuristic to obtain a sub-optimal solution.
Using personal environmental comfort systems to mitigate the impact of occupancy prediction errors on HVAC performance
Heating, Ventilation and Air Conditioning (HVAC) consumes a significant fraction of energy in commercial buildings. Hence, the use of optimization techniques to reduce HVAC energy consumption has been widely studied. Model predictive control (MPC) is one state of the art optimization technique for HVAC control which converts the control problem to a sequence of optimization problems, each over a finite time horizon. In a typical MPC, future system state is estimated from a model using predictions of model inputs, such as building occupancy and outside air temperature. Consequently, as prediction accuracy deteriorates, MPC performance–in terms of occupant comfort and building energy use–degrades. In this work, we use a custom-built building thermal simulator to systematically investigate the impact of occupancy prediction errors on occupant comfort and energy consumption. Our analysis shows that in our test building, as occupancy prediction error increases from 5 to 20% the performance of an MPC-based HVAC controller becomes worse than that of even a simple static schedule. However, when combined with a personal environmental control (PEC) system, HVAC controllers are considerably more robust to prediction errors. Thus, we quantify the effectiveness of PECs in mitigating the impact of forecast errors on MPC control for HVAC systems.
Scheduling for Stabilization over Capacity-Constrained Channels
We address the problem of stabilizing a set of discrete-time systems over a communication network. The network consists of capacity-constrained discrete-time Additive White Gaussian Noise (AWGN) channels. We consider the case when the number of channels is limited and propose a dynamic scheduling scheme that, at a given time, determines which subset of systems get access to the channel for feedback control. This problem is addressed by considering two separate problems - scheduling systems over noiseless channels and stabilizing a system over an AWGN channel. The scheduling problem is addressed in the switched system framework by making use of a min-type Lyapunov function. We provide a sufficient condition in the form of Linear Matrix Inequalities (LMIs) to schedule a subset of systems while achieving stability of all systems. We also explicitly determine the scheduling scheme. Next, we provide a novel LMI-based necessary and sufficient condition for stabilization of a discrete-time system over a discrete-time AWGN channel. Finally, we appropriately combine the two results to obtain an LMI-based sufficient condition for the join scheduling-stabilization problem.
D-stability under channel capacity constraints
We address the problem of stabilizing a system, with a certain desired dynamic performance, using control signal sent over a communication channel having a limited capacity. A desired dynamic performance of the closed-loop system is obtained by placing its poles in a specific region of the open left-half of the complex plane. Denoting such a region by D, this procedure is also called V-stabilization. We first analyze a single-input linear time-invariant (LTI) system with state-feedback control over a channel subjected to additive noise. Using tools from H2control theory, we pose the above stabilization problem as an optimization problem involving linear matrix inequalities (LMIs). Using this, we derive a sufficient condition for V-stabilization of the system subject to the channel capacity constraint. Further, we extend our analysis to a multi-input LTI system with state-feedback over a multi-input multi-output (MIMO) channel subjected to additive noise. The channel consists of multiple single-input single-output (SISO) subchannels connected in parallel. The total capacity of the MIMO channel is fixed, while the individual subchannel capacities can be freely allocated. We provide a necessary and sufficient condition for stabilization and a sufficient condition for V-stabilization of this system subject to the channel capacity constraints. We also propose a method to design the channel and an optimal controller.