Dissipative Deep Neural Dynamical Systems

In this paper, we provide sufficient conditions for dissipativity and local asymptotic stability of discrete-time dynamical systems parametrized by deep neural networks. We leverage the representation of neural networks as pointwise affine maps, thus exposing their local linear operators and making them accessible to classical system analytic and design methods. This allows us to "crack open the black box" of the neural dynamical system's behavior by evaluating their dissipativity, and estimating their stationary points and state-space partitioning. We relate the norms of these local linear operators to the energy stored in the dissipative system with supply rates represented by their aggregate bias terms. Empirically, we analyze the variance in dynamical behavior and eigenvalue spectra of these local linear operators with varying weight factorizations, activation functions, bias terms, and depths.Comment: Under review at IEEE Open Journal of Control System

Robust Differentiable Predictive Control with Safety Guarantees: A Predictive Safety Filter Approach

In this paper, we propose a novel predictive safety filter that is robust to bounded perturbations and is combined with a learning-based control called differentiable predictive control (DPC). The proposed method provides rigorous guarantees of safety in the presence of bounded perturbations and implements DPC so long as the DPC control satisfies the system constraints. The approach also incorporates two forms of event-triggering to reduce online computation. The approach is comprised of a robust predictive safety filter that extends upon existing work to reject disturbances for discrete-time, time-varying nonlinear systems with time-varying constraints. The safety filter is based on novel concepts of robust, discrete-time barrier functions and can be used to filter any control law. Here we use the safety filter in conjunction with DPC as a promising policy optimization method. The approach is demonstrated on a single-integrator, two-tank system, and building example.Comment: Submitted to Automatic

Experimental Demonstration of Model Predictive Control in a Medium-Sized Commercial Building

This paper presents the implementation and experimental demonstration results of a practically effective and computationally efficient model predictive control (MPC) algorithm used to optimize the energy use of the heating, ventilation, and air-conditioning (HVAC) system in a multi-zone medium-sized commercial building. Advanced building control technologies are key enablers for intelligent operations of future buildings, however, adopting these technologies are quite difficult in practice mainly due to the cost-sensitive nature of the building industry. This paper presents the results of implementing optimization-based control algorithm and demonstrates the effectiveness of its energy-saving feature and improved thermal comfort along with lessons-learned. The performance of the implemented MPC algorithm was estimated relative to baseline days (heuristic-based control) with similar outdoor air temperature patterns during the cooling and shoulder seasons (September to November, 2013), and it was concluded that MPC reduced the total electrical energy consumption by more than 20% on average while improving thermal comfort in terms of temperature and maintaining similar zone CO2 levels