A Distributed Approach to Efficient Model Predictive Control of Building HVAC Systems

Model based predictive control (MPC) is increasingly being seen as an attractive approach in controlling building HVAC systems. One advantage of the MPC approach is the ability to integrate weather forecast, occupancy information and utility price variations in determining the optimal HVAC operation. However, application to largescale building HVAC systems is limited by the large number of controllable variables to be optimized at every time instance. This paper explores techniques to reduce the computational complexity arising in applying MPC to the control of large-scale buildings. We formulate the task of optimal control as a distributed optimization problem within the MPC framework. A distributed optimization approach alleviates computational costs by simultaneously solving reduced dimensional optimization problems at the subsystem level and integrating the resulting solutions to obtain a global control law. Additional computational efficiency can be achieved by utilizing the occupancy and utility price profiles to restrict the control laws to a piecewise constant function. Alternatively, under certain assumptions, the optimal control laws can be found analytically using a dynamic programming based approach without resorting to numerical optimization routines leading to massive computational savings. Initial results of simulations on case studies are presented to compare the proposed algorithms

Distributed Model Predictive Control for building HVAC systems: A Case Study

Model based predictive control (MPC) in building HVAC systems incorporate predictions of weather and occupancy to determine the optimal operating setpoints. However, application of MPC strategies to large buildings might not be real time feasible due to the large number of degrees of freedom in the underlying optimization problem. Decomposing the problem into several smaller sub-problems to be solved in parallel is one way to circumvent the high computational requirements. Such an approach, termed Distributed MPC, requires certain approximations about the underlying sub-problems to converge to a consistent solution thus leading to a trade off between computational load and optimality. In this paper, we present a simulation based evaluation for a Distributed MPC formulation for a case study based on a medium sized commercial building. Results indicate that distributed MPC can offer near optimal control at a fraction of the computational time that centralized optimization based MPC requires while maintaining occupant comfort. Comparison with a few other viable control algorithms will be performed and merits and drawbacks of each approach pointed out

A generating function approach to the input-to-state stability of discrete time switched linear systems

A switched linear system is a dynamical system consisting of a number of linear subsystems along with a switching rule that determines the switching among subsystems. Such systems exhibit rich dynamics despite their relatively simple structure. Stability analysis of switched linear systems has received a lot of attention in recent times. Current approaches to stability analysis include Lyapunov methods, Lie Algebraic methods and LMI methods. The present work focuses on characterizing the input-to-state stability of switched linear systems using a new concept of generating functions. To this end we propose a generalized notion of input-to-state ℓ 2-gains of discrete time controlled switched linear systems and proceed to develop the theory of generating functions. A generating function is an appropriately defined power series whose domain of convergence characterizes the generalized input-to-state ℓ2-gains of switched linear system. After suitable theoretical development we are able to study relevant properties of the generating functions and relate them to input-to-state stability of switched linear systems. Using dynamic programming, we also formulate an efficient numerical computation method that can be used to bound the input-to-state ℓ2-gains of switched linear systems

A probabilistic measure of air traffic complexity in 3-D airspace

In this paper, we propose a new method to evaluate air traffic complexity in 3-D airspace through a probabilistic measure of the airspace occupancy. The key novelty of the approach is that uncertainty in the future aircraft positions is explicitly accounted for when evaluating complexity. Analytic—though approximate—expressions of the complexity measure are derived. Prospective applications for the proposed complexity metric include the timely identification of those multi-aircraft conflict situations that would be difficult to solve because of limited maneuverability space, and the design of trajectories so as to avoid congested regions that would require many tactical maneuvers to pass them through. Numerical examples are provided to illustrate the approach. Copyright © 2010 John Wiley & Sons, Ltd