Anuradha M. Annaswamy

Benjamin M. Jenkins, Anuradha M. Annaswamy, Eugene Lavretsky et al.

The convergence properties of adaptive systems in terms of excitation conditions on the regressor vector are well known. With persistent excitation of the regressor vector in model reference adaptive control the state error and the adaptation error are globally exponentially stable, or equivalently, exponentially stable in the large. When the excitation condition however is imposed on the reference input or the reference model state it is often incorrectly concluded that the persistent excitation in those signals also implies exponential stability in the large. The definition of persistent excitation is revisited so as to address some possible confusion in the adaptive control literature. It is then shown that persistent excitation of the reference model only implies local persistent excitation (weak persistent excitation). Weak persistent excitation of the regressor is still sufficient for uniform asymptotic stability in the large, but not exponential stability in the large. We show that there exists an infinite region in the state-space of adaptive systems where the state rate is bounded. This infinite region with finite rate of convergence is shown to exist not only in classic open-loop reference model adaptive systems, but also in a new class of closed-loop reference model adaptive systems.

Rabab Haider, Anuradha M. Annaswamy

Mixed integer problems are ubiquitous in decision making, from discrete device settings and design parameters, unit production, and on/off or yes/no decision in switches, routing, and social networks. Despite their prevalence, classical optimization approaches for combinatorial optimization remain prohibitively slow for fast and accurate decision making in dynamic and safety-critical environments with hard constraints. To address this gap, we propose SiPhyR (pronounced: cipher), a physics-informed machine learning framework for end-to-end learning to optimize for combinatorial problems. SiPhyR employs a novel physics-informed rounding approach to tackle the challenge of combinatorial optimization within a differentiable framework that has certified satisfiability of safety-critical constraints. We demonstrate the effectiveness of SiPhyR on an emerging paradigm for clean energy systems: dynamic reconfiguration, where the topology of the electric grid and power flow are optimized so as to maintain a safe and reliable power grid in the presence of intermittent renewable generation. Offline training of the unsupervised framework on representative load and generation data makes dynamic decision making via the online application of Grid-SiPhyR computationally feasible.

Venkatesh Venkataramanan, Sridevi Kaza, Anuradha M. Annaswamy

With increasing penetration of Distributed Energy Resources (DERs) in grid edge including renewable generation, flexible loads, and storage, accurate prediction of distributed generation and consumption at the consumer level becomes important. However, DER prediction based on the transmission of customer level data, either repeatedly or in large amounts, is not feasible due to privacy concerns. In this paper, a distributed machine learning approach, Federated Learning, is proposed to carry out DER forecasting using a network of IoT nodes, each of which transmits a model of the consumption and generation patterns without revealing consumer data. We consider a simulation study which includes 1000 DERs, and show that our method leads to an accurate prediction of preserve consumer privacy, while still leading to an accurate forecast. We also evaluate grid-specific performance metrics such as load swings and load curtailment and show that our FL algorithm leads to satisfactory performance. Simulations are also performed on the Pecan street dataset to demonstrate the validity of the proposed approach on real data.

Yingnan Cui, Joseph E. Gaudio, Anuradha M. Annaswamy

We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in the presence of time-varying unknown parameters, the parameter estimation error converges uniformly to a compact set under conditions of persistent excitation, with the size of the compact set proportional to the time-variation of unknown parameters. Leveraging a projection operator, the second algorithm is shown to result in boundedness guarantees when the plant has constant unknown parameters. Simulations show better convergence results compared to recursive least squares (RLS) and comparable results to RLS with forgetting factor.

Arnab Sarker, Peter Fisher, Joseph E. Gaudio et al.

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no unmodeled dynamics, the proposed approach can ensure a $\tilde{O}(\sqrt{T})$ regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

Joseph E. Gaudio, Travis E. Gibson, Anuradha M. Annaswamy et al.

Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent methods unstable or weakens their convergence guarantees. Inspired by methods employed in adaptive control, this paper proposes new algorithms for the case when time-varying features are present, and demonstrates provable performance guarantees. In particular, we develop a unified variational perspective within a continuous time algorithm. This variational perspective includes higher order learning concepts and normalization, both of which stem from adaptive control, and allows stability to be established for dynamical machine learning problems where time-varying features are present. These higher order algorithms are also examined for provably correct learning in adaptive control and identification. Simulations are provided to verify the theoretical results.