Efe C. Balta

Aren Karapetyan, Anastasios Tsiamis, Efe C. Balta et al.

The setting of an agent making decisions under uncertainty and under dynamic constraints is common for the fields of optimal control, reinforcement learning, and recently also for online learning. In the online learning setting, the quality of an agent's decision is often quantified by the concept of regret, comparing the performance of the chosen decisions to the best possible ones in hindsight. While regret is a useful performance measure, when dynamical systems are concerned, it is important to also assess the stability of the closed-loop system for a chosen policy. In this work, we show that for linear state feedback policies and linear systems subject to adversarial disturbances, linear regret implies asymptotic stability in both time-varying and time-invariant settings. Conversely, we also show that bounded input bounded state stability and summability of the state transition matrices imply linear regret.

Efe C. Balta, Andrea Iannelli, Roy S. Smith et al.

In Iterative Learning Control (ILC), a sequence of feedforward control actions is generated at each iteration on the basis of partial model knowledge and past measurements with the goal of steering the system toward a desired reference trajectory. This is framed here as an online learning task, where the decision-maker takes sequential decisions by solving a sequence of optimization problems having only partial knowledge of the cost functions. Having established this connection, the performance of an online gradient-descent based scheme using inexact gradient information is analyzed in the setting of dynamic and static regret, standard measures in online learning. Fundamental limitations of the scheme and its integration with adaptation mechanisms are further investigated, followed by numerical simulations on a benchmark ILC problem.

Riccardo Zuliani, Efe C. Balta, John Lygeros

Model-based policy optimization often struggles with inaccurate system dynamics models, leading to suboptimal closed-loop performance. This challenge is especially evident in Model Predictive Control (MPC) policies, which rely on the model for real-time trajectory planning and optimization. We introduce a novel policy optimization framework for MPC-based policies combining differentiable optimization with zeroth-order optimization. Our method combines model-based and model-free gradient estimation approaches, achieving faster transient performance compared to fully data-driven approaches while maintaining convergence guarantees, even under model uncertainty. We demonstrate the effectiveness of the proposed approach on a nonlinear control task involving a 12-dimensional quadcopter model.

Anastasios Vlachos, Anastasios Tsiamis, Aren Karapetyan et al.

In this paper, we consider the problem of predicting unknown targets from data. We propose Online Residual Learning (ORL), a method that combines online adaptation with offline-trained predictions. At a lower level, we employ multiple offline predictions generated before or at the beginning of the prediction horizon. We augment every offline prediction by learning their respective residual error concerning the true target state online, using the recursive least squares algorithm. At a higher level, we treat the augmented lower-level predictors as experts, adopting the Prediction with Expert Advice framework. We utilize an adaptive softmax weighting scheme to form an aggregate prediction and provide guarantees for ORL in terms of regret. We employ ORL to boost performance in the setting of online pedestrian trajectory prediction. Based on data from the Stanford Drone Dataset, we show that ORL can demonstrate best-of-both-worlds performance.

Riccardo Zuliani, Efe C. Balta, John Lygeros

Model-based policy optimization is a well-established framework for designing reliable and high-performance controllers across a wide range of control applications. Recently, this approach has been extended to model predictive control policies, where explicit dynamical models are embedded within the control law. However, the performance of the resulting controllers, and the convergence of the associated optimization algorithms, critically depends on the accuracy of the models. In this paper, we demonstrate that combining gradient-based policy optimization with recursive system identification ensures convergence to an optimal controller design and showcase our finding in several control examples.

Anastasios Tsiamis, Aren Karapetyan, Yueshan Li et al.

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement PLOT on a real quadrotor and provide open-source software, thus, showcasing one of the first successful applications of online control methods on real hardware.

Muhammad Zakwan, Vaibhav Gupta, Alireza Karimi et al.

This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.

Panagiotis D. Grontas, Antonio Terpin, Efe C. Balta et al.

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX with effective tuning heuristics.

Veronica Centorrino, Rawan Hoteit, Efe C. Balta et al.

This paper studies equality-constrained minimization problems through the lens of feedback control. We introduce a unified control-theoretic framework by showing that a PID feedback law acting on the dual variable induces the PID saddle-point flow (PID-SPF), a broad class of saddle-point dynamics associated with the augmented Lagrangian. This framework recovers several classical primal-dual flows as special cases. We prove that the equilibria of the proposed flow coincide with the stationary points of the original problem. Our analysis reveals how the feedback gains affect the optimization: integral action enforces constraint satisfaction, proportional action introduces the augmented Lagrangian structure, and derivative action modifies the geometry of the primal dynamics by inducing a state-dependent Riemannian metric. Moreover, for convex problems with affine constraints, we establish global exponential convergence by leveraging contraction theory for all admissible PID gains, providing in the process explicit bounds on the convergence rate. Finally, we validate our theoretical results on numerical examples including an application to bilevel optimization.

Christopher König, Raamadaas Krishnadas, Efe C. Balta et al.

Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However, Bayesian optimization methods are computationally expensive and therefore difficult to use in real-time critical scenarios. In this work, we propose a real-time purely data-driven, model-free approach for adaptive control, by online tuning low-level controller parameters. We base our algorithm on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization, for handling performance and stability criteria. We introduce multiple computational and algorithmic modifications for computational efficiency and parallelization of optimization steps. We further evaluate the algorithm's performance on a real precision-motion system utilized in semiconductor industry applications by modifying the payload and reference stepsize and comparing it to an interpolated constrained optimization-based baseline approach.

Francesco Micheli, Efe C. Balta, Anastasios Tsiamis et al.

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of uncontrollable contextual variables. We consider the setting where the context distribution is uncertain but known to lie within an ambiguity set defined as a ball in the Wasserstein distance. We propose a novel algorithm for Wasserstein Distributionally Robust Bayesian Optimization that can handle continuous context distributions while maintaining computational tractability. Our theoretical analysis combines recent results in self-normalized concentration in Hilbert spaces and finite-sample bounds for distributionally robust optimization to establish sublinear regret bounds that match state-of-the-art results. Through extensive comparisons with existing approaches on both synthetic and real-world problems, we demonstrate the simplicity, effectiveness, and practical applicability of our proposed method.

Mohamed Abdalmoaty, Efe C. Balta, John Lygeros et al.

It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based methods, is sensitive to the assumptions on the data distribution and is usually based on relatively complex sequential Monte Carlo algorithms. We develop a simple recursive online estimation algorithm based on an output-error predictor, for the identification of continuous-time stochastic parametric Wiener models through stochastic approximation. The method is applicable to generic model parameterizations and, as demonstrated in the numerical simulation examples, it is robust with respect to the assumptions on the spectrum of the disturbance process.