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Trajectory planning plays a crucial role in autonomous driving and navigation by enabling robots to generate safe paths while minimizing travel costs and avoiding collisions. This paper addresses the issue of predicting dynamic obstacles for safe trajectory planning when prior information is unavailable and detection range is limited. We propose a learning framework using Gaussian Processes (GP) for motion prediction and uncertainty estimation, further enhanced by Recurrent Neural Networks (RNN) for more accurate predictions. In addition, we develop a receding horizon planning method, formulated as a stochastic optimization problem, to ensure safe, collision-free paths with confidence probabilities. Together, these contributions provide a robust framework for adaptive and safe trajectory generation in dynamic environments. Simulations were performed to demonstrate the effectiveness of the proposed strategy, where our approach (combining GP and RNN) outperformed a baseline method that utilized only GP. 

This paper presents a communication-efficient framework for distributed optimization using the Alternating Direction Method of Multipliers (ADMM). Building on prior work integrating Gaussian process regression and uniform quantization, we propose novel quantization strategies that adapt both mid-value, window length, and resolution at each iteration. We introduce joint and individual mechanisms for making communication decisions and assigning quantization bits based on agent-specific uncertainties. To address performance degradation near convergence, where variance stagnates, we incorporate a hybrid approach that switches to a quantization refinement method when prediction improvements plateau. This hybrid scheme maintains algorithmic convergence while significantly reducing communication overhead. Extensive simulations on a distributed quadratic cost-sharing problem demonstrate that the proposed methods notably decrease the number of transmitted bits while preserving solution accuracy. Among all tested approaches, the hybrid method offers the most robust and consistent trade-off between accuracy and communication efficiency across a wide range of parameter settings. 

Heating, ventilation, and air conditioning (HVAC) systems account for a significant portion of energy consumption in developed countries. Accurately identifying their dynamics is crucial for developing effective controllers. However, it is challenging due to the system’s nonlinearities and variations across building types. Data-driven approaches have shown great promise in modeling the dynamics of HVAC systems, replacing traditional ordinary differential equations. However, relying solely on data can lead to poor generalization, particularly when the training data is limited or when unknown disturbances, such as weather conditions and occupant behavior, are present. Physics-informed machine learning (PIML) techniques have been developed for integrating physical principles into machine learning methods to improve the accuracy and data efficiency of modeling of dynamical systems. This paper investigates PIML techniques that incorporate three different physical properties: monotonicity, boundedness, and system structure. These models are benchmarked against physics-agnostic machine learning (PAML) approaches and the gray-box modeling technique to further highlight the performance of PIML models in terms of accuracy, robustness, and data efficiency for modeling HVAC systems from real data. Experimental data collected from a real-world HVAC system are used for systematically studying and analyzing thirteen gray-box, PAML, and PIML modeling techniques in different scenarios. Our results demonstrate that PIML models outperform PAML models in predicting the temperature dynamics of HVAC systems, especially when the training data is limited, unreliable, or noisy, with accurate and robust performance. Furthermore, we identify which physical properties are the most beneficial for enhancing machine learning performance for HVAC system identification. 

This paper investigates the problem of informative path planning for a mobile robotic sensor network in spatially temporally distributed mapping. The robots are able to gather noisy measurements from an area of interest during their movements to build a Gaussian process (GP) model of a spatio-temporal field. The model is then utilized to predict the spatio-temporal phenomenon at different points of interest. To spatially and temporally navigate the group of robots so that they can optimally acquire maximal information gains while their connectivity is preserved, we propose a novel multi-step prediction informative path planning optimization strategy employing our newly defined local cost functions. By using the dual decomposition method, it is feasible and practical to effectively solve the optimization problem in a distributed manner. The proposed method was validated through synthetic experiments utilizing real-world data sets. 

The deep operator network (DeepONet) architecture is a promising approach for learning functional operators, that can represent dynamical systems described by ordinary or partial differential equations. However, it has two major limitations, namely its failures to account for initial conditions and to guarantee the temporal causality – a fundamental property of dynamical systems. This paper proposes a novel causal deep operator network (Causal-DeepONet) architecture for incorporating both the initial condition and the temporal causality into data-driven learning of dynamical systems, overcoming the limitations of the original DeepONet approach. This is achieved by adding an independent root network for the initial condition and independent branch networks conditioned, or switched on/off, by time-shifted step functions or sigmoid functions for expressing the temporal causality. The proposed architecture was evaluated and compared with two baseline deep neural network methods and the original DeepONet method on learning the thermal dynamics of a room in a building using real data. It was shown to not only achieve the best overall prediction accuracy but also enhance substantially the accuracy consistency in multistep predictions, which is crucial for predictive control.